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A. van Keulen
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Incorporating geometric nonlinearity into topology optimization arises two main challenges: (1) high computational costs of solving the nonlinear governing equations, and (2) convergence difficulties in the analysis due to “low-density areas" compressed by neighboring stiffer regions. These challenges are addressed in this thesis, which then, focuses on applying topology optimization of geometrically nonlinear structures to design compliant mechanisms tracing user-definedmotion paths.
First of all, Chapter 2 addresses the challenge of high computational cost by introducing reduced-order models (ROMs). The proposed method targets ROM bases consisting of a small set of base vectors, while maintaining accuracy. To this end, several fully automated techniques are developed and integrated for updating and maintaining the ROM basis, with path derivatives incorporated to better capture the behavior of highly flexible structures. In parallel, approximate sensitivity analysis methods are introduced to simplify computations and improve the efficiency of the optimization process. The effectiveness of the ROMs is demonstrated by numerical examples, which showsubstantial reductions in computational effort.
However, the efficiency of the proposed ROMs can deteriorate when faced with the second challenge, i.e., convergence difficulties arise fromthe compression of low-density regions. Such compression typically leads to “inside-out" elements in 2D structures or spurious local buckling in shells and plates. The former, i.e., “inside-out" elements, often causes computational divergence, while the latter, i.e., spurious local buckling, though not always divergent, can significantly increase the number of iterations required for convergence. These spurious instability modes are inevitably incorporated into the proposed ROM basis, which can render ROM analyses even less efficient than full-order ones. To mitigate this problem, two strategies are investigated in Chapter 3: (1) removing spurious instability modes from the ROM basis, and (2) eliminating them directly from the underlying physics. The latter approach is also applicable to standard FOM analyses. Their effectiveness is demonstrated through shell model examples, which provide detailed insights into the benefits and limitations of each approach.
To move beyond algorithmic developments, Chapters 4 and 5 apply geometrically nonlinear topology optimization to the practical design of path-generation compliant mechanisms. A main challenge in this context is ensuring material connectivity among the input, output, and support fixtures within the design domain. This challenge is addressed in Chapter 4 using a simple yet effective formulation that combines compliance and volume constraints. Here, compliance upper bounds are specified according to engineering requirements, while volume constraints are enforced through a proposed three-phase scheme. Building on this foundation, Chapter 5 applies the formulation to design path-generation mechanisms capable of tracing long-distance motion paths. In particular, shells and plates are explored because their compactness and flexible nature make them especially effective for achieving such motions. Finally, experiments on 3D printed prototypes validate the effectiveness of the proposed formulations in producing functional designs. ...
First of all, Chapter 2 addresses the challenge of high computational cost by introducing reduced-order models (ROMs). The proposed method targets ROM bases consisting of a small set of base vectors, while maintaining accuracy. To this end, several fully automated techniques are developed and integrated for updating and maintaining the ROM basis, with path derivatives incorporated to better capture the behavior of highly flexible structures. In parallel, approximate sensitivity analysis methods are introduced to simplify computations and improve the efficiency of the optimization process. The effectiveness of the ROMs is demonstrated by numerical examples, which showsubstantial reductions in computational effort.
However, the efficiency of the proposed ROMs can deteriorate when faced with the second challenge, i.e., convergence difficulties arise fromthe compression of low-density regions. Such compression typically leads to “inside-out" elements in 2D structures or spurious local buckling in shells and plates. The former, i.e., “inside-out" elements, often causes computational divergence, while the latter, i.e., spurious local buckling, though not always divergent, can significantly increase the number of iterations required for convergence. These spurious instability modes are inevitably incorporated into the proposed ROM basis, which can render ROM analyses even less efficient than full-order ones. To mitigate this problem, two strategies are investigated in Chapter 3: (1) removing spurious instability modes from the ROM basis, and (2) eliminating them directly from the underlying physics. The latter approach is also applicable to standard FOM analyses. Their effectiveness is demonstrated through shell model examples, which provide detailed insights into the benefits and limitations of each approach.
To move beyond algorithmic developments, Chapters 4 and 5 apply geometrically nonlinear topology optimization to the practical design of path-generation compliant mechanisms. A main challenge in this context is ensuring material connectivity among the input, output, and support fixtures within the design domain. This challenge is addressed in Chapter 4 using a simple yet effective formulation that combines compliance and volume constraints. Here, compliance upper bounds are specified according to engineering requirements, while volume constraints are enforced through a proposed three-phase scheme. Building on this foundation, Chapter 5 applies the formulation to design path-generation mechanisms capable of tracing long-distance motion paths. In particular, shells and plates are explored because their compactness and flexible nature make them especially effective for achieving such motions. Finally, experiments on 3D printed prototypes validate the effectiveness of the proposed formulations in producing functional designs. ...
Incorporating geometric nonlinearity into topology optimization arises two main challenges: (1) high computational costs of solving the nonlinear governing equations, and (2) convergence difficulties in the analysis due to “low-density areas" compressed by neighboring stiffer regions. These challenges are addressed in this thesis, which then, focuses on applying topology optimization of geometrically nonlinear structures to design compliant mechanisms tracing user-definedmotion paths.
First of all, Chapter 2 addresses the challenge of high computational cost by introducing reduced-order models (ROMs). The proposed method targets ROM bases consisting of a small set of base vectors, while maintaining accuracy. To this end, several fully automated techniques are developed and integrated for updating and maintaining the ROM basis, with path derivatives incorporated to better capture the behavior of highly flexible structures. In parallel, approximate sensitivity analysis methods are introduced to simplify computations and improve the efficiency of the optimization process. The effectiveness of the ROMs is demonstrated by numerical examples, which showsubstantial reductions in computational effort.
However, the efficiency of the proposed ROMs can deteriorate when faced with the second challenge, i.e., convergence difficulties arise fromthe compression of low-density regions. Such compression typically leads to “inside-out" elements in 2D structures or spurious local buckling in shells and plates. The former, i.e., “inside-out" elements, often causes computational divergence, while the latter, i.e., spurious local buckling, though not always divergent, can significantly increase the number of iterations required for convergence. These spurious instability modes are inevitably incorporated into the proposed ROM basis, which can render ROM analyses even less efficient than full-order ones. To mitigate this problem, two strategies are investigated in Chapter 3: (1) removing spurious instability modes from the ROM basis, and (2) eliminating them directly from the underlying physics. The latter approach is also applicable to standard FOM analyses. Their effectiveness is demonstrated through shell model examples, which provide detailed insights into the benefits and limitations of each approach.
To move beyond algorithmic developments, Chapters 4 and 5 apply geometrically nonlinear topology optimization to the practical design of path-generation compliant mechanisms. A main challenge in this context is ensuring material connectivity among the input, output, and support fixtures within the design domain. This challenge is addressed in Chapter 4 using a simple yet effective formulation that combines compliance and volume constraints. Here, compliance upper bounds are specified according to engineering requirements, while volume constraints are enforced through a proposed three-phase scheme. Building on this foundation, Chapter 5 applies the formulation to design path-generation mechanisms capable of tracing long-distance motion paths. In particular, shells and plates are explored because their compactness and flexible nature make them especially effective for achieving such motions. Finally, experiments on 3D printed prototypes validate the effectiveness of the proposed formulations in producing functional designs.
First of all, Chapter 2 addresses the challenge of high computational cost by introducing reduced-order models (ROMs). The proposed method targets ROM bases consisting of a small set of base vectors, while maintaining accuracy. To this end, several fully automated techniques are developed and integrated for updating and maintaining the ROM basis, with path derivatives incorporated to better capture the behavior of highly flexible structures. In parallel, approximate sensitivity analysis methods are introduced to simplify computations and improve the efficiency of the optimization process. The effectiveness of the ROMs is demonstrated by numerical examples, which showsubstantial reductions in computational effort.
However, the efficiency of the proposed ROMs can deteriorate when faced with the second challenge, i.e., convergence difficulties arise fromthe compression of low-density regions. Such compression typically leads to “inside-out" elements in 2D structures or spurious local buckling in shells and plates. The former, i.e., “inside-out" elements, often causes computational divergence, while the latter, i.e., spurious local buckling, though not always divergent, can significantly increase the number of iterations required for convergence. These spurious instability modes are inevitably incorporated into the proposed ROM basis, which can render ROM analyses even less efficient than full-order ones. To mitigate this problem, two strategies are investigated in Chapter 3: (1) removing spurious instability modes from the ROM basis, and (2) eliminating them directly from the underlying physics. The latter approach is also applicable to standard FOM analyses. Their effectiveness is demonstrated through shell model examples, which provide detailed insights into the benefits and limitations of each approach.
To move beyond algorithmic developments, Chapters 4 and 5 apply geometrically nonlinear topology optimization to the practical design of path-generation compliant mechanisms. A main challenge in this context is ensuring material connectivity among the input, output, and support fixtures within the design domain. This challenge is addressed in Chapter 4 using a simple yet effective formulation that combines compliance and volume constraints. Here, compliance upper bounds are specified according to engineering requirements, while volume constraints are enforced through a proposed three-phase scheme. Building on this foundation, Chapter 5 applies the formulation to design path-generation mechanisms capable of tracing long-distance motion paths. In particular, shells and plates are explored because their compactness and flexible nature make them especially effective for achieving such motions. Finally, experiments on 3D printed prototypes validate the effectiveness of the proposed formulations in producing functional designs.
Laser Powder Bed Fusion (LPBF) has emerged as an influential metal additive manufacturing technology capable of producing geometrically complex, high-performance components. However, the process is governed by extremely high thermal gradients, rapid solidification, and repeated thermal cycles, all of which strongly influence microstructure formation, defect generation, and final part quality. Accurate part-scale thermal simulation is therefore essential for predicting process outcomes and guiding process-parameter optimization. This thesis advances the semi-analytical thermal modeling framework for LPBF, addressing limitations in existing semi-analytical methods and demonstrating its applicability to melt-pool prediction, overheating mitigation, and microstructural evolution analysis.
Conventional Finite Element Method (FEM)–based part-scale models face a fundamental challenge due to the multiscale nature of LPBF. The small laser spot size and associated steep temperature gradients require a fine Finite Element (FE) mesh near the heat source, while the large build volume demands computationally efficient discretization. Adaptive remeshing strategies alleviate part of this difficulty but incur high computational cost because the mesh must be updated frequently as the laser traverses the geometry. Semi-analytical methods provide an alternative by employing closed-form thermal solutions for moving point or line heat sources in a semi-infinite medium, thereby capturing the steep temperature gradients analytically without requiring local mesh refinement. However, the state-of-the-art semi-analytical formulations were limited to simple geometries with straight boundaries.
This thesis first extends the semi-analytical method by introducing a generalized image-source formulation capable of handling curved boundaries. Image sources offset the boundary heat flux induced by the regular heat sources, thereby enforcing appropriate boundary conditions, while decoupling the mesh size from the characteristic length scale dictated by laser spot size. Image source positions and power modulation factors are derived using local boundary curvature, supported by NURBS representations of arbitrary geometries, enabling the use of image sources for complex shapes. Numerical examples confirm that the modulated image-source approach dramatically reduces boundary heat-flux error and enables accurate temperature prediction with significantly coarser meshes. This advancement marks an important step in extending semi-analytical approaches to realistic part geometries.
The second methodological development replaces the FEM-based complementary field computation with isogeometric analysis (IGA) in a semi-analytical thermal modeling framework. IGA employs NURBS basis functions that exactly represent geometry, allowing the simulation of realistic parts with complex geometries. In addition, with the exact geometric representation and higher-order continuity of NURBS basis functions, the numerical complementary field can be resolved with significantly fewer degrees of freedom. Comparative studies show that the IGA-based formulation reduces computational cost by an order of magnitude while maintaining accuracy, making it highly attractive for large-scale LPBF simulations.
The semi-analytical thermal modeling framework is then applied to study overheating phenomena in LPBF of magnesium alloy. Using a triangular prism part geometry, the study reveals how geometric constraints—particularly decreasing scan vector length toward the tip of a triangular layer—lead to reduced cooling time, rapid heat accumulation, and significant increases in melt-pool depth. However, extremely short vectors experience insufficient heating duration, causing a sudden drop in melt-pool depth. Two mitigation strategies are proposed: extending zero-power ghost vectors and adjusting laser power based on vector length. Both numerical predictions and experimental results validate their effectiveness in homogenizing melt-pool depth and reducing porosity.
Finally, the semi-analytical thermal model is employed to investigate phase transformations in Ti-6Al-4V during LPBF under varying volumetric energy densities. Higher energy densities promote greater decomposition of martensite due to reheating from subsequent layers, whereas layers built at the end of the process contain a higher percentage of martensite phase because rapid cooling favors martensite formation. The semi analytical model successfully captures the thermal transients required to drive these phase-transformation predictions. Besides, the effects of laser scanning strategies and the number of scanning lasers are also investigated, showing little influence on the overall phase fractions.
In summary, this thesis advances the semi-analytical modeling framework for LPBF and demonstrates its strong potential for predicting melt-pool behavior, mitigating defects, and understanding microstructural evolution.
...
Conventional Finite Element Method (FEM)–based part-scale models face a fundamental challenge due to the multiscale nature of LPBF. The small laser spot size and associated steep temperature gradients require a fine Finite Element (FE) mesh near the heat source, while the large build volume demands computationally efficient discretization. Adaptive remeshing strategies alleviate part of this difficulty but incur high computational cost because the mesh must be updated frequently as the laser traverses the geometry. Semi-analytical methods provide an alternative by employing closed-form thermal solutions for moving point or line heat sources in a semi-infinite medium, thereby capturing the steep temperature gradients analytically without requiring local mesh refinement. However, the state-of-the-art semi-analytical formulations were limited to simple geometries with straight boundaries.
This thesis first extends the semi-analytical method by introducing a generalized image-source formulation capable of handling curved boundaries. Image sources offset the boundary heat flux induced by the regular heat sources, thereby enforcing appropriate boundary conditions, while decoupling the mesh size from the characteristic length scale dictated by laser spot size. Image source positions and power modulation factors are derived using local boundary curvature, supported by NURBS representations of arbitrary geometries, enabling the use of image sources for complex shapes. Numerical examples confirm that the modulated image-source approach dramatically reduces boundary heat-flux error and enables accurate temperature prediction with significantly coarser meshes. This advancement marks an important step in extending semi-analytical approaches to realistic part geometries.
The second methodological development replaces the FEM-based complementary field computation with isogeometric analysis (IGA) in a semi-analytical thermal modeling framework. IGA employs NURBS basis functions that exactly represent geometry, allowing the simulation of realistic parts with complex geometries. In addition, with the exact geometric representation and higher-order continuity of NURBS basis functions, the numerical complementary field can be resolved with significantly fewer degrees of freedom. Comparative studies show that the IGA-based formulation reduces computational cost by an order of magnitude while maintaining accuracy, making it highly attractive for large-scale LPBF simulations.
The semi-analytical thermal modeling framework is then applied to study overheating phenomena in LPBF of magnesium alloy. Using a triangular prism part geometry, the study reveals how geometric constraints—particularly decreasing scan vector length toward the tip of a triangular layer—lead to reduced cooling time, rapid heat accumulation, and significant increases in melt-pool depth. However, extremely short vectors experience insufficient heating duration, causing a sudden drop in melt-pool depth. Two mitigation strategies are proposed: extending zero-power ghost vectors and adjusting laser power based on vector length. Both numerical predictions and experimental results validate their effectiveness in homogenizing melt-pool depth and reducing porosity.
Finally, the semi-analytical thermal model is employed to investigate phase transformations in Ti-6Al-4V during LPBF under varying volumetric energy densities. Higher energy densities promote greater decomposition of martensite due to reheating from subsequent layers, whereas layers built at the end of the process contain a higher percentage of martensite phase because rapid cooling favors martensite formation. The semi analytical model successfully captures the thermal transients required to drive these phase-transformation predictions. Besides, the effects of laser scanning strategies and the number of scanning lasers are also investigated, showing little influence on the overall phase fractions.
In summary, this thesis advances the semi-analytical modeling framework for LPBF and demonstrates its strong potential for predicting melt-pool behavior, mitigating defects, and understanding microstructural evolution.
...
Laser Powder Bed Fusion (LPBF) has emerged as an influential metal additive manufacturing technology capable of producing geometrically complex, high-performance components. However, the process is governed by extremely high thermal gradients, rapid solidification, and repeated thermal cycles, all of which strongly influence microstructure formation, defect generation, and final part quality. Accurate part-scale thermal simulation is therefore essential for predicting process outcomes and guiding process-parameter optimization. This thesis advances the semi-analytical thermal modeling framework for LPBF, addressing limitations in existing semi-analytical methods and demonstrating its applicability to melt-pool prediction, overheating mitigation, and microstructural evolution analysis.
Conventional Finite Element Method (FEM)–based part-scale models face a fundamental challenge due to the multiscale nature of LPBF. The small laser spot size and associated steep temperature gradients require a fine Finite Element (FE) mesh near the heat source, while the large build volume demands computationally efficient discretization. Adaptive remeshing strategies alleviate part of this difficulty but incur high computational cost because the mesh must be updated frequently as the laser traverses the geometry. Semi-analytical methods provide an alternative by employing closed-form thermal solutions for moving point or line heat sources in a semi-infinite medium, thereby capturing the steep temperature gradients analytically without requiring local mesh refinement. However, the state-of-the-art semi-analytical formulations were limited to simple geometries with straight boundaries.
This thesis first extends the semi-analytical method by introducing a generalized image-source formulation capable of handling curved boundaries. Image sources offset the boundary heat flux induced by the regular heat sources, thereby enforcing appropriate boundary conditions, while decoupling the mesh size from the characteristic length scale dictated by laser spot size. Image source positions and power modulation factors are derived using local boundary curvature, supported by NURBS representations of arbitrary geometries, enabling the use of image sources for complex shapes. Numerical examples confirm that the modulated image-source approach dramatically reduces boundary heat-flux error and enables accurate temperature prediction with significantly coarser meshes. This advancement marks an important step in extending semi-analytical approaches to realistic part geometries.
The second methodological development replaces the FEM-based complementary field computation with isogeometric analysis (IGA) in a semi-analytical thermal modeling framework. IGA employs NURBS basis functions that exactly represent geometry, allowing the simulation of realistic parts with complex geometries. In addition, with the exact geometric representation and higher-order continuity of NURBS basis functions, the numerical complementary field can be resolved with significantly fewer degrees of freedom. Comparative studies show that the IGA-based formulation reduces computational cost by an order of magnitude while maintaining accuracy, making it highly attractive for large-scale LPBF simulations.
The semi-analytical thermal modeling framework is then applied to study overheating phenomena in LPBF of magnesium alloy. Using a triangular prism part geometry, the study reveals how geometric constraints—particularly decreasing scan vector length toward the tip of a triangular layer—lead to reduced cooling time, rapid heat accumulation, and significant increases in melt-pool depth. However, extremely short vectors experience insufficient heating duration, causing a sudden drop in melt-pool depth. Two mitigation strategies are proposed: extending zero-power ghost vectors and adjusting laser power based on vector length. Both numerical predictions and experimental results validate their effectiveness in homogenizing melt-pool depth and reducing porosity.
Finally, the semi-analytical thermal model is employed to investigate phase transformations in Ti-6Al-4V during LPBF under varying volumetric energy densities. Higher energy densities promote greater decomposition of martensite due to reheating from subsequent layers, whereas layers built at the end of the process contain a higher percentage of martensite phase because rapid cooling favors martensite formation. The semi analytical model successfully captures the thermal transients required to drive these phase-transformation predictions. Besides, the effects of laser scanning strategies and the number of scanning lasers are also investigated, showing little influence on the overall phase fractions.
In summary, this thesis advances the semi-analytical modeling framework for LPBF and demonstrates its strong potential for predicting melt-pool behavior, mitigating defects, and understanding microstructural evolution.
Conventional Finite Element Method (FEM)–based part-scale models face a fundamental challenge due to the multiscale nature of LPBF. The small laser spot size and associated steep temperature gradients require a fine Finite Element (FE) mesh near the heat source, while the large build volume demands computationally efficient discretization. Adaptive remeshing strategies alleviate part of this difficulty but incur high computational cost because the mesh must be updated frequently as the laser traverses the geometry. Semi-analytical methods provide an alternative by employing closed-form thermal solutions for moving point or line heat sources in a semi-infinite medium, thereby capturing the steep temperature gradients analytically without requiring local mesh refinement. However, the state-of-the-art semi-analytical formulations were limited to simple geometries with straight boundaries.
This thesis first extends the semi-analytical method by introducing a generalized image-source formulation capable of handling curved boundaries. Image sources offset the boundary heat flux induced by the regular heat sources, thereby enforcing appropriate boundary conditions, while decoupling the mesh size from the characteristic length scale dictated by laser spot size. Image source positions and power modulation factors are derived using local boundary curvature, supported by NURBS representations of arbitrary geometries, enabling the use of image sources for complex shapes. Numerical examples confirm that the modulated image-source approach dramatically reduces boundary heat-flux error and enables accurate temperature prediction with significantly coarser meshes. This advancement marks an important step in extending semi-analytical approaches to realistic part geometries.
The second methodological development replaces the FEM-based complementary field computation with isogeometric analysis (IGA) in a semi-analytical thermal modeling framework. IGA employs NURBS basis functions that exactly represent geometry, allowing the simulation of realistic parts with complex geometries. In addition, with the exact geometric representation and higher-order continuity of NURBS basis functions, the numerical complementary field can be resolved with significantly fewer degrees of freedom. Comparative studies show that the IGA-based formulation reduces computational cost by an order of magnitude while maintaining accuracy, making it highly attractive for large-scale LPBF simulations.
The semi-analytical thermal modeling framework is then applied to study overheating phenomena in LPBF of magnesium alloy. Using a triangular prism part geometry, the study reveals how geometric constraints—particularly decreasing scan vector length toward the tip of a triangular layer—lead to reduced cooling time, rapid heat accumulation, and significant increases in melt-pool depth. However, extremely short vectors experience insufficient heating duration, causing a sudden drop in melt-pool depth. Two mitigation strategies are proposed: extending zero-power ghost vectors and adjusting laser power based on vector length. Both numerical predictions and experimental results validate their effectiveness in homogenizing melt-pool depth and reducing porosity.
Finally, the semi-analytical thermal model is employed to investigate phase transformations in Ti-6Al-4V during LPBF under varying volumetric energy densities. Higher energy densities promote greater decomposition of martensite due to reheating from subsequent layers, whereas layers built at the end of the process contain a higher percentage of martensite phase because rapid cooling favors martensite formation. The semi analytical model successfully captures the thermal transients required to drive these phase-transformation predictions. Besides, the effects of laser scanning strategies and the number of scanning lasers are also investigated, showing little influence on the overall phase fractions.
In summary, this thesis advances the semi-analytical modeling framework for LPBF and demonstrates its strong potential for predicting melt-pool behavior, mitigating defects, and understanding microstructural evolution.
Computational Optimization of Minimum Ionizing Timing Detector Components
Improving Timing Resolution through Numerical Design Optimization
The objective of particle detectors in high-energy physics research is to reveal the fundamental laws of nature. The Minimum Ionizing Particle Detector (MTD) has been designed to enhance the timing precision of theCMS (Compact Muon Solenoid) detector at CERN to 50 ps under the increased number of particle impacts after upgrading the Large Hadron Collider (LHC) to the High-Luminosity LHC. The Barrel Timing Layer (BTL) segment of the MTD uses silicon photodetectors (SiPMs), whose timing accuracy depends on their operating temperature and the number of photons they detect. This dissertation presents numerical methods to improve the timing precision of these SiPMs through the design of thermoelectrical coolers and scintillation crystals. On the one hand, thermoelectrical coolers (TECs) can lower the SiPMs temperature, reducing signal-to-noise ratio and recovering radiation-induced damage through controlled annealing procedures. We provide an analytical model to study the landscape of TEC topology optimization with a lower temperature objective, power constraints and two density design variables. This study leads to the recommendation of penalization coefficients for SIMP (solid isotropic material with penalization) in the form of kp = kσ > kα with kp the thermal conductivity, kσ the electrical conductivity and kα the Seebeck’s penalization coefficient to reduce the nonconvexity induced by the power constraint. These coefficients reduce nonconvexity from power constraints, allowing FEM topology optimization via SIMP to achieve lower material volumes and temperatures without volume constraints and filtering schemes. FEM optimization examples are provided, which incorporate electrical working points through a voltage gradient design variable and constant material properties. These examples reduce the temperature by up to 10 ◦C compared to the optimal electrical working point of the original designs. Finally, comparing these results with designs with non-linear, temperature-dependent properties shows that the use of constant material properties can lower computational costs and improve design performance. Although optimized designs achieve lower temperatures, TECs are fragile. The construction of the BTL highlights this fragility, prompting an extension of the design to address operational thermal and mechanical loads. This work introduces a FEM-based topology optimization for the coupled thermoelectromechanical problem using SIMP. This also includes the formulation with nonlinear material properties, and how to deal with the checkerboarding with the extended mechanical degree Celsiuss of freedom. The optimized designs reduce stress concentrations by half while enhancing cooling capabilities. On the other hand, we complement the lower signal-to-noise ratio obtained from using TECs, with an increased number of photon impacts enhancing the SiPM signal. The number of photons created or the scintillation light yield depends on the material composition of the scintillators. However, the photon arrival count at SiPMs is influenced by their reflective surfaces and volume. We provide a model of BTL within GEANT4, a ray-tracing particle-matter interaction software. This model incorporates the effect of the particle impact location and is used in conjunction with NSGAII (non-dominated sorting genetic algorithm) to optimize scintillator shapes to increase the photon detection count. The study uses multiple objective functions based on the stochastic nature of the arrival photons. From these results, the recommended objective function is the mean light collection per energy deposition and the ionizing particle track length, reducing statistical errors and accounting for energy deposition. The results provide relative gains to the original designs in the objective function between 15 and 38%. To overcome the computational limits of Monte Carlo methods, we follow up by translating the scintillation equations into a transient wave for FEM simulations, matching GEANT4 pulse shapes. Furthermore, we perform a shape optimization using a static frequency domain scintillation model replicating the variable influence within GEANT4. The optimal designs obtained with FEM are validated within GEANT4, obtaining gains of the order of 7.7%. These gains were achieved with less than 1% of the computational resources needed to perform the GEANT4 optimizations.
...
The objective of particle detectors in high-energy physics research is to reveal the fundamental laws of nature. The Minimum Ionizing Particle Detector (MTD) has been designed to enhance the timing precision of theCMS (Compact Muon Solenoid) detector at CERN to 50 ps under the increased number of particle impacts after upgrading the Large Hadron Collider (LHC) to the High-Luminosity LHC. The Barrel Timing Layer (BTL) segment of the MTD uses silicon photodetectors (SiPMs), whose timing accuracy depends on their operating temperature and the number of photons they detect. This dissertation presents numerical methods to improve the timing precision of these SiPMs through the design of thermoelectrical coolers and scintillation crystals. On the one hand, thermoelectrical coolers (TECs) can lower the SiPMs temperature, reducing signal-to-noise ratio and recovering radiation-induced damage through controlled annealing procedures. We provide an analytical model to study the landscape of TEC topology optimization with a lower temperature objective, power constraints and two density design variables. This study leads to the recommendation of penalization coefficients for SIMP (solid isotropic material with penalization) in the form of kp = kσ > kα with kp the thermal conductivity, kσ the electrical conductivity and kα the Seebeck’s penalization coefficient to reduce the nonconvexity induced by the power constraint. These coefficients reduce nonconvexity from power constraints, allowing FEM topology optimization via SIMP to achieve lower material volumes and temperatures without volume constraints and filtering schemes. FEM optimization examples are provided, which incorporate electrical working points through a voltage gradient design variable and constant material properties. These examples reduce the temperature by up to 10 ◦C compared to the optimal electrical working point of the original designs. Finally, comparing these results with designs with non-linear, temperature-dependent properties shows that the use of constant material properties can lower computational costs and improve design performance. Although optimized designs achieve lower temperatures, TECs are fragile. The construction of the BTL highlights this fragility, prompting an extension of the design to address operational thermal and mechanical loads. This work introduces a FEM-based topology optimization for the coupled thermoelectromechanical problem using SIMP. This also includes the formulation with nonlinear material properties, and how to deal with the checkerboarding with the extended mechanical degree Celsiuss of freedom. The optimized designs reduce stress concentrations by half while enhancing cooling capabilities. On the other hand, we complement the lower signal-to-noise ratio obtained from using TECs, with an increased number of photon impacts enhancing the SiPM signal. The number of photons created or the scintillation light yield depends on the material composition of the scintillators. However, the photon arrival count at SiPMs is influenced by their reflective surfaces and volume. We provide a model of BTL within GEANT4, a ray-tracing particle-matter interaction software. This model incorporates the effect of the particle impact location and is used in conjunction with NSGAII (non-dominated sorting genetic algorithm) to optimize scintillator shapes to increase the photon detection count. The study uses multiple objective functions based on the stochastic nature of the arrival photons. From these results, the recommended objective function is the mean light collection per energy deposition and the ionizing particle track length, reducing statistical errors and accounting for energy deposition. The results provide relative gains to the original designs in the objective function between 15 and 38%. To overcome the computational limits of Monte Carlo methods, we follow up by translating the scintillation equations into a transient wave for FEM simulations, matching GEANT4 pulse shapes. Furthermore, we perform a shape optimization using a static frequency domain scintillation model replicating the variable influence within GEANT4. The optimal designs obtained with FEM are validated within GEANT4, obtaining gains of the order of 7.7%. These gains were achieved with less than 1% of the computational resources needed to perform the GEANT4 optimizations.
This dissertation develops an optimization framework for multi-axis additive manufacturing, with a particular focus on wire arc additive manufacturing (WAAM). It introduces the novel space-time topology optimization approach that integrates structural design and fabrication sequence planning by defining material distribution across both spatial and temporal dimensions.
In this framework, a pseudo-density field defines the structural layout, while a pseudo-time field encode the fabrication sequence, offering detailed insights into the layer-by-layer manufacturing process. Two key advancements are developed in order to improve the manufacturability: First, a thermal regularization method is proposed to ensure a smooth and continuous pseudo-time field without local minima. Second, a layer geometry control scheme is implemented to improve the consistency of the layer dimensions.
The framework is further adopted to address challenges associated with residual stress and thermal-induced distortion in WAAM, employing the inherent strain method as a simplified process simulation model. In addition, the anisotropic nature of material properties in WAAM is considered, enabling the rational alignment of material deposition orientation to enhance performance.
Numerical results demonstrate the feasibility and effectiveness of the proposed optimization framework, inspiring the exploration of the innovative potential offered by multi-axis additive manufacturing. ...
In this framework, a pseudo-density field defines the structural layout, while a pseudo-time field encode the fabrication sequence, offering detailed insights into the layer-by-layer manufacturing process. Two key advancements are developed in order to improve the manufacturability: First, a thermal regularization method is proposed to ensure a smooth and continuous pseudo-time field without local minima. Second, a layer geometry control scheme is implemented to improve the consistency of the layer dimensions.
The framework is further adopted to address challenges associated with residual stress and thermal-induced distortion in WAAM, employing the inherent strain method as a simplified process simulation model. In addition, the anisotropic nature of material properties in WAAM is considered, enabling the rational alignment of material deposition orientation to enhance performance.
Numerical results demonstrate the feasibility and effectiveness of the proposed optimization framework, inspiring the exploration of the innovative potential offered by multi-axis additive manufacturing. ...
This dissertation develops an optimization framework for multi-axis additive manufacturing, with a particular focus on wire arc additive manufacturing (WAAM). It introduces the novel space-time topology optimization approach that integrates structural design and fabrication sequence planning by defining material distribution across both spatial and temporal dimensions.
In this framework, a pseudo-density field defines the structural layout, while a pseudo-time field encode the fabrication sequence, offering detailed insights into the layer-by-layer manufacturing process. Two key advancements are developed in order to improve the manufacturability: First, a thermal regularization method is proposed to ensure a smooth and continuous pseudo-time field without local minima. Second, a layer geometry control scheme is implemented to improve the consistency of the layer dimensions.
The framework is further adopted to address challenges associated with residual stress and thermal-induced distortion in WAAM, employing the inherent strain method as a simplified process simulation model. In addition, the anisotropic nature of material properties in WAAM is considered, enabling the rational alignment of material deposition orientation to enhance performance.
Numerical results demonstrate the feasibility and effectiveness of the proposed optimization framework, inspiring the exploration of the innovative potential offered by multi-axis additive manufacturing.
In this framework, a pseudo-density field defines the structural layout, while a pseudo-time field encode the fabrication sequence, offering detailed insights into the layer-by-layer manufacturing process. Two key advancements are developed in order to improve the manufacturability: First, a thermal regularization method is proposed to ensure a smooth and continuous pseudo-time field without local minima. Second, a layer geometry control scheme is implemented to improve the consistency of the layer dimensions.
The framework is further adopted to address challenges associated with residual stress and thermal-induced distortion in WAAM, employing the inherent strain method as a simplified process simulation model. In addition, the anisotropic nature of material properties in WAAM is considered, enabling the rational alignment of material deposition orientation to enhance performance.
Numerical results demonstrate the feasibility and effectiveness of the proposed optimization framework, inspiring the exploration of the innovative potential offered by multi-axis additive manufacturing.
Acoustic waves due to their non-destructive and non-reactive nature, have been extensively used as information carriers in various applications including, medical imaging, material characterization, distance and velocity measurement, and flow rate measurement, among others. In an ultrasonic flowmeter (UF), the upstream and downstream travel times of ultrasound pulses across the fluid are measured, whose difference is directly related to the flow rate. However, during the measurement, a significant amount of the pulse’s energy leaks through the solid pipe (parasitic signal) and interferes with the fluid signal (working signal) known as crosstalk. Since crosstalk can lead to measurement errors and in extreme cases complete signal losses, we explore possibilities of phononic crystals (PnCs) to mitigate crosstalk from UFs.
PnCs are periodic structures possessing unusual dynamic characteristics due to the presence of band gaps (BGs)—frequency ranges where elastic and acoustic waves are attenuated. Because of BGs, they are explored in several applications, including vibration isolation, energy harvesting, acoustic wave steering, super/hyperlens, wave focusing, and cloaking. However, extending the PnCs to real applications such as the crosstalk reduction in UFs, is still very challenging since the application has multiple requirements and can be subjected to extreme environmental conditions. We design PnC waveguides to possess BGs in the UF’s operating frequencies, thereby acting as wave filters to alleviate crosstalk.... ...
PnCs are periodic structures possessing unusual dynamic characteristics due to the presence of band gaps (BGs)—frequency ranges where elastic and acoustic waves are attenuated. Because of BGs, they are explored in several applications, including vibration isolation, energy harvesting, acoustic wave steering, super/hyperlens, wave focusing, and cloaking. However, extending the PnCs to real applications such as the crosstalk reduction in UFs, is still very challenging since the application has multiple requirements and can be subjected to extreme environmental conditions. We design PnC waveguides to possess BGs in the UF’s operating frequencies, thereby acting as wave filters to alleviate crosstalk.... ...
Acoustic waves due to their non-destructive and non-reactive nature, have been extensively used as information carriers in various applications including, medical imaging, material characterization, distance and velocity measurement, and flow rate measurement, among others. In an ultrasonic flowmeter (UF), the upstream and downstream travel times of ultrasound pulses across the fluid are measured, whose difference is directly related to the flow rate. However, during the measurement, a significant amount of the pulse’s energy leaks through the solid pipe (parasitic signal) and interferes with the fluid signal (working signal) known as crosstalk. Since crosstalk can lead to measurement errors and in extreme cases complete signal losses, we explore possibilities of phononic crystals (PnCs) to mitigate crosstalk from UFs.
PnCs are periodic structures possessing unusual dynamic characteristics due to the presence of band gaps (BGs)—frequency ranges where elastic and acoustic waves are attenuated. Because of BGs, they are explored in several applications, including vibration isolation, energy harvesting, acoustic wave steering, super/hyperlens, wave focusing, and cloaking. However, extending the PnCs to real applications such as the crosstalk reduction in UFs, is still very challenging since the application has multiple requirements and can be subjected to extreme environmental conditions. We design PnC waveguides to possess BGs in the UF’s operating frequencies, thereby acting as wave filters to alleviate crosstalk....
PnCs are periodic structures possessing unusual dynamic characteristics due to the presence of band gaps (BGs)—frequency ranges where elastic and acoustic waves are attenuated. Because of BGs, they are explored in several applications, including vibration isolation, energy harvesting, acoustic wave steering, super/hyperlens, wave focusing, and cloaking. However, extending the PnCs to real applications such as the crosstalk reduction in UFs, is still very challenging since the application has multiple requirements and can be subjected to extreme environmental conditions. We design PnC waveguides to possess BGs in the UF’s operating frequencies, thereby acting as wave filters to alleviate crosstalk....
Phononic crystals can be designed to have bandgaps---ranges of frequencies whose propagation through the material is prevented. They are therefore attractive for vibration isolation applications in different industries, where unwanted vibrations reduce performance. Yet, important steps are still to be made for the integration of phononic crystals into engineering practice. For instance, methods for large scale production are still in development. Furthermore, it is essential that design methods are established to enable the design of phononic crystals that meet all of the, often conflicting, requirements for practical applications. This thesis focuses on the latter challenge by proposing a computational design method for phononic crystals based on the combination of an advanced finite element method and level set-based topology optimization.
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Phononic crystals can be designed to have bandgaps---ranges of frequencies whose propagation through the material is prevented. They are therefore attractive for vibration isolation applications in different industries, where unwanted vibrations reduce performance. Yet, important steps are still to be made for the integration of phononic crystals into engineering practice. For instance, methods for large scale production are still in development. Furthermore, it is essential that design methods are established to enable the design of phononic crystals that meet all of the, often conflicting, requirements for practical applications. This thesis focuses on the latter challenge by proposing a computational design method for phononic crystals based on the combination of an advanced finite element method and level set-based topology optimization.
Reducing greenhouse emissions can be achieved by better insulating buildings. However, wall thickness increases significantly if conventional insulation materials are used. Conventional vacuum insulation panels (VIPs) offer a solution to this problem. VIPs have potential, but can not compete with conventional insulation materials due to their high pricing. A new concept vacuum insulation panel is introduced by the start-up company IQ-Bizz. To what extent this concept panel is a feasible alternative to conventional VIPs is the main research question of this thesis. The concept panel consists of two honeycomb plates, an intermediate foil and an MF2 panel envelope. The panel's geometry is chosen such that heat transfer through the panel is minimal and failure of the panel does not occur. Finite element models, verified by analytical calculations, have been used for evaluating the concept panel's structural and thermal performance. A thermal performance (R-value) of 6.23 m^2K/W is evaluated for a one-centimetre thick square panel with sides of one metre. Conventional VIPs of equal size have an R-value of 2.5 m^2K/W. The global warming potential of the concept is roughly 9 kg compared to 15 kg for conventional VIPs. A conventional VIP's price of roughly 21 euros is compared to the material costs of the concept panel of 8 euros. All performance parameters of the concept panel are higher compared to conventional VIPs. However, the concept panel's thermal performance is expected to be lower, and its environmental impact and price higher. Further research is required for a better evaluation of these performance parameters. Nevertheless, this thesis shows that the vacuum insulation panel concept has promising potential.
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Reducing greenhouse emissions can be achieved by better insulating buildings. However, wall thickness increases significantly if conventional insulation materials are used. Conventional vacuum insulation panels (VIPs) offer a solution to this problem. VIPs have potential, but can not compete with conventional insulation materials due to their high pricing. A new concept vacuum insulation panel is introduced by the start-up company IQ-Bizz. To what extent this concept panel is a feasible alternative to conventional VIPs is the main research question of this thesis. The concept panel consists of two honeycomb plates, an intermediate foil and an MF2 panel envelope. The panel's geometry is chosen such that heat transfer through the panel is minimal and failure of the panel does not occur. Finite element models, verified by analytical calculations, have been used for evaluating the concept panel's structural and thermal performance. A thermal performance (R-value) of 6.23 m^2K/W is evaluated for a one-centimetre thick square panel with sides of one metre. Conventional VIPs of equal size have an R-value of 2.5 m^2K/W. The global warming potential of the concept is roughly 9 kg compared to 15 kg for conventional VIPs. A conventional VIP's price of roughly 21 euros is compared to the material costs of the concept panel of 8 euros. All performance parameters of the concept panel are higher compared to conventional VIPs. However, the concept panel's thermal performance is expected to be lower, and its environmental impact and price higher. Further research is required for a better evaluation of these performance parameters. Nevertheless, this thesis shows that the vacuum insulation panel concept has promising potential.
Shape and size optimization of a wind turbine transport structure
Structural optimization with a compliant ship foundation
Due to the growing quest for renewable energy, wind turbines grow in size. This means that higher demands are posed on the transporting structures, also called tower grillages, which brings its challenges for their design. The fact that the structures considered in this thesis are placed on a ship makes the design even more complicated. Therefore, a procedure is developed in this thesis that is able to optimize a tower grillage, while keeping the underlying ship intact. This tool is based on a combination of size and shape optimization.
The optimization is performed with the dual annealing algorithm. The objective is mass reduction, with the stress in the grillage, and stress and buckling in the ship as constraints. These constraints are taken into account by a penalty function. The design variables are the angles at which the radial supports attach and the thicknesses of the radial supports and the other elements of the grillage. The main question that is answered in this thesis is how this optimization procedure can help in the design of a tower grillage, where the underlying ship structure is implemented as a boundary condition.
First, a single layout is optimized with the ship modelled as a rigid boundary condition. Next, a model of a section of the ship is made and used as the boundary condition on the tower grillage. A comparison between these models showed that the main differences in stress between the two optimization results
are seen in the largest parts of the grillage: the sides, the flanges and the can. The maximum stress in the latter two elements is larger, which also results in larger thicknesses in the optimization with the ship. This affects the average mass in the ship, which is increased with 5.7% when compared to the grillage on the rigid constraint.
After that, a full grillage is optimized. A first attempt demonstrated that the stress in the ship could only be decreased a little with the initial settings of the optimization. That required a slightly different model, to make sure that the stress in the ship remains acceptable. With that model, a mass decrease
of 32 tons could be obtained, which is a decrease of 9.1 % compared to the original design by Vuyk Engineering.
From the different optimization steps became clear that the main factors influencing the optimal distribution of radial supports are the lengths of the supports, and the location of the outer brackets. The compliance of the ship changes the stresses in the grillage, and therefore the optimization result. The
stress in the ship can be reduced only to some extent, so the effect of a stress violation in the initial design is that a new bracket design needs to be made. The results show that the stress is governing for the current optimization, and buckling is not.
The conclusion is that the current procedure can help in the design by providing a global image of lighter layouts which avoid stress and buckling constraint violations in the ship. However, the limitation of the research is that the result is only a global image. It is therefore considered not worth the effort and
time to apply the current method in an engineering environment. It does however show the potential of this method, so future enhancements can make the procedure suitable for engineering. ...
The optimization is performed with the dual annealing algorithm. The objective is mass reduction, with the stress in the grillage, and stress and buckling in the ship as constraints. These constraints are taken into account by a penalty function. The design variables are the angles at which the radial supports attach and the thicknesses of the radial supports and the other elements of the grillage. The main question that is answered in this thesis is how this optimization procedure can help in the design of a tower grillage, where the underlying ship structure is implemented as a boundary condition.
First, a single layout is optimized with the ship modelled as a rigid boundary condition. Next, a model of a section of the ship is made and used as the boundary condition on the tower grillage. A comparison between these models showed that the main differences in stress between the two optimization results
are seen in the largest parts of the grillage: the sides, the flanges and the can. The maximum stress in the latter two elements is larger, which also results in larger thicknesses in the optimization with the ship. This affects the average mass in the ship, which is increased with 5.7% when compared to the grillage on the rigid constraint.
After that, a full grillage is optimized. A first attempt demonstrated that the stress in the ship could only be decreased a little with the initial settings of the optimization. That required a slightly different model, to make sure that the stress in the ship remains acceptable. With that model, a mass decrease
of 32 tons could be obtained, which is a decrease of 9.1 % compared to the original design by Vuyk Engineering.
From the different optimization steps became clear that the main factors influencing the optimal distribution of radial supports are the lengths of the supports, and the location of the outer brackets. The compliance of the ship changes the stresses in the grillage, and therefore the optimization result. The
stress in the ship can be reduced only to some extent, so the effect of a stress violation in the initial design is that a new bracket design needs to be made. The results show that the stress is governing for the current optimization, and buckling is not.
The conclusion is that the current procedure can help in the design by providing a global image of lighter layouts which avoid stress and buckling constraint violations in the ship. However, the limitation of the research is that the result is only a global image. It is therefore considered not worth the effort and
time to apply the current method in an engineering environment. It does however show the potential of this method, so future enhancements can make the procedure suitable for engineering. ...
Due to the growing quest for renewable energy, wind turbines grow in size. This means that higher demands are posed on the transporting structures, also called tower grillages, which brings its challenges for their design. The fact that the structures considered in this thesis are placed on a ship makes the design even more complicated. Therefore, a procedure is developed in this thesis that is able to optimize a tower grillage, while keeping the underlying ship intact. This tool is based on a combination of size and shape optimization.
The optimization is performed with the dual annealing algorithm. The objective is mass reduction, with the stress in the grillage, and stress and buckling in the ship as constraints. These constraints are taken into account by a penalty function. The design variables are the angles at which the radial supports attach and the thicknesses of the radial supports and the other elements of the grillage. The main question that is answered in this thesis is how this optimization procedure can help in the design of a tower grillage, where the underlying ship structure is implemented as a boundary condition.
First, a single layout is optimized with the ship modelled as a rigid boundary condition. Next, a model of a section of the ship is made and used as the boundary condition on the tower grillage. A comparison between these models showed that the main differences in stress between the two optimization results
are seen in the largest parts of the grillage: the sides, the flanges and the can. The maximum stress in the latter two elements is larger, which also results in larger thicknesses in the optimization with the ship. This affects the average mass in the ship, which is increased with 5.7% when compared to the grillage on the rigid constraint.
After that, a full grillage is optimized. A first attempt demonstrated that the stress in the ship could only be decreased a little with the initial settings of the optimization. That required a slightly different model, to make sure that the stress in the ship remains acceptable. With that model, a mass decrease
of 32 tons could be obtained, which is a decrease of 9.1 % compared to the original design by Vuyk Engineering.
From the different optimization steps became clear that the main factors influencing the optimal distribution of radial supports are the lengths of the supports, and the location of the outer brackets. The compliance of the ship changes the stresses in the grillage, and therefore the optimization result. The
stress in the ship can be reduced only to some extent, so the effect of a stress violation in the initial design is that a new bracket design needs to be made. The results show that the stress is governing for the current optimization, and buckling is not.
The conclusion is that the current procedure can help in the design by providing a global image of lighter layouts which avoid stress and buckling constraint violations in the ship. However, the limitation of the research is that the result is only a global image. It is therefore considered not worth the effort and
time to apply the current method in an engineering environment. It does however show the potential of this method, so future enhancements can make the procedure suitable for engineering.
The optimization is performed with the dual annealing algorithm. The objective is mass reduction, with the stress in the grillage, and stress and buckling in the ship as constraints. These constraints are taken into account by a penalty function. The design variables are the angles at which the radial supports attach and the thicknesses of the radial supports and the other elements of the grillage. The main question that is answered in this thesis is how this optimization procedure can help in the design of a tower grillage, where the underlying ship structure is implemented as a boundary condition.
First, a single layout is optimized with the ship modelled as a rigid boundary condition. Next, a model of a section of the ship is made and used as the boundary condition on the tower grillage. A comparison between these models showed that the main differences in stress between the two optimization results
are seen in the largest parts of the grillage: the sides, the flanges and the can. The maximum stress in the latter two elements is larger, which also results in larger thicknesses in the optimization with the ship. This affects the average mass in the ship, which is increased with 5.7% when compared to the grillage on the rigid constraint.
After that, a full grillage is optimized. A first attempt demonstrated that the stress in the ship could only be decreased a little with the initial settings of the optimization. That required a slightly different model, to make sure that the stress in the ship remains acceptable. With that model, a mass decrease
of 32 tons could be obtained, which is a decrease of 9.1 % compared to the original design by Vuyk Engineering.
From the different optimization steps became clear that the main factors influencing the optimal distribution of radial supports are the lengths of the supports, and the location of the outer brackets. The compliance of the ship changes the stresses in the grillage, and therefore the optimization result. The
stress in the ship can be reduced only to some extent, so the effect of a stress violation in the initial design is that a new bracket design needs to be made. The results show that the stress is governing for the current optimization, and buckling is not.
The conclusion is that the current procedure can help in the design by providing a global image of lighter layouts which avoid stress and buckling constraint violations in the ship. However, the limitation of the research is that the result is only a global image. It is therefore considered not worth the effort and
time to apply the current method in an engineering environment. It does however show the potential of this method, so future enhancements can make the procedure suitable for engineering.
Multi-stable beam-type metastructures exhibiting snap-through behavior have been extensively studied in recent years , as their stable states can be maintained without the need of external power supply. By arranging a series of beams exhibiting bi-stability, multi-stable metastructures can be constructed. However, current designs of multi-stable metastructures are limited in terms of structural kinematics and the associated functionalities are not fully explored. This thesis aims to present design strategies that can facilitate new kinematic behavior and functionalities for multi-stable metastructures (i.e., energy absorption and shape reconfiguration). Specifically, we investigate the additional rotational degrees of freedom by incorporating rotational compliance in both 2D and 3D designs. In doing so, multi-stable metastructures are capable of realizing both translational and rotational motion, facilitating their applicability in soft robotics and deployable structures. Moreover, the energy dissipation of multi-stable metastructures are studied, where we have proposed design strategies that can enhance the energy absorption without using more materials. In addition, it is demonstrated that multi-stable metastructures can also be designed to realize shape reconfiguration of a morphing surface, where the stability requirement and accessible configurations have been presented. Such multi-stable metastructures exhibiting translational and rotational degrees of freedoms hold great potential for developing reconfigurable structures and energy absorbers.
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Multi-stable beam-type metastructures exhibiting snap-through behavior have been extensively studied in recent years , as their stable states can be maintained without the need of external power supply. By arranging a series of beams exhibiting bi-stability, multi-stable metastructures can be constructed. However, current designs of multi-stable metastructures are limited in terms of structural kinematics and the associated functionalities are not fully explored. This thesis aims to present design strategies that can facilitate new kinematic behavior and functionalities for multi-stable metastructures (i.e., energy absorption and shape reconfiguration). Specifically, we investigate the additional rotational degrees of freedom by incorporating rotational compliance in both 2D and 3D designs. In doing so, multi-stable metastructures are capable of realizing both translational and rotational motion, facilitating their applicability in soft robotics and deployable structures. Moreover, the energy dissipation of multi-stable metastructures are studied, where we have proposed design strategies that can enhance the energy absorption without using more materials. In addition, it is demonstrated that multi-stable metastructures can also be designed to realize shape reconfiguration of a morphing surface, where the stability requirement and accessible configurations have been presented. Such multi-stable metastructures exhibiting translational and rotational degrees of freedoms hold great potential for developing reconfigurable structures and energy absorbers.
Topology optimization for dynamic and controlled systems
With application to motion system design
High-precision motion systems are crucial for many applications, such as in semiconductor equipment, microscopy, robotics, and medical devices. Next to high operating speeds, high accuracy and precision are required, which makes the design of these systems a challenging task. Dynamics, feedback control, and their interaction all play an important role in the design and its final performance. This thesis shows that topology optimization in combination with additive manufacturing offers new opportunities for the automated design of motion systems with unprecedented performance. The first challenge addressed is the manufacturability of the designs, for which a systematic optimization setup is presented allowing directly producible designs. This is verified by manufacturing and testing an optimized design. Furthermore, the computational time required for full-scale topology optimization is reduced significantly, by using reduced-order models and approximation of design sensitivities. Thirdly, effective optimization formulations are introduced that allow combined optimization of topology and controller for closed-loop performance, such as bandwidth, closed-loop stability, and disturbance rejection properties. Combining all these techniques, this thesis demonstrates that it is possible to perform integrated controller-structure topology optimization of motion systems of industry-relevant complexity.
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High-precision motion systems are crucial for many applications, such as in semiconductor equipment, microscopy, robotics, and medical devices. Next to high operating speeds, high accuracy and precision are required, which makes the design of these systems a challenging task. Dynamics, feedback control, and their interaction all play an important role in the design and its final performance. This thesis shows that topology optimization in combination with additive manufacturing offers new opportunities for the automated design of motion systems with unprecedented performance. The first challenge addressed is the manufacturability of the designs, for which a systematic optimization setup is presented allowing directly producible designs. This is verified by manufacturing and testing an optimized design. Furthermore, the computational time required for full-scale topology optimization is reduced significantly, by using reduced-order models and approximation of design sensitivities. Thirdly, effective optimization formulations are introduced that allow combined optimization of topology and controller for closed-loop performance, such as bandwidth, closed-loop stability, and disturbance rejection properties. Combining all these techniques, this thesis demonstrates that it is possible to perform integrated controller-structure topology optimization of motion systems of industry-relevant complexity.
In conventional aircrafts, lift control is achieved by using flap systems. It would be beneficial if flap systems could be replaced by a variable-camber morphing wing. It has been shown that variable-camber morphing wings can significantly improve the aerodynamic performance of the aircraft due to the smoothness of the surface, making it possible to fly more efficiently, reduce fuel consumption and reduce the impact on the environment. However, the design of such a variable-camber morphing wing is challenging due to the conflicting requirements of the structure. The wing should be flexible so it can morph, stiff so it can withstand aerodynamic pressures and light weight to reduce fuel consumption. The aim of this work is to provide a method for the density-based topology optimization of compliant morphing structures. The method includes a novel formulation for the objective function which compares the deformed shape of the structure with a desired deformed shape by using a dot product. This method is applied to obtain an optimized design of a compliant variable-camber morphing wing. The obtained design was converted to a prototype by 3D printing and an experiment was performed to assess if the deformed shapes of the prototype were similar to the ones predicted by the analysis in the topology optimization. The experiment showed that for small deformations the output shape matched the predicted output shape. For larger deflections, there was a slight difference. However, the obtained shapes were still quadratic-like and so it is expected that for larger deformations the designed trailing edge will still have superior aerodynamic performance than conventional flap systems.
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In conventional aircrafts, lift control is achieved by using flap systems. It would be beneficial if flap systems could be replaced by a variable-camber morphing wing. It has been shown that variable-camber morphing wings can significantly improve the aerodynamic performance of the aircraft due to the smoothness of the surface, making it possible to fly more efficiently, reduce fuel consumption and reduce the impact on the environment. However, the design of such a variable-camber morphing wing is challenging due to the conflicting requirements of the structure. The wing should be flexible so it can morph, stiff so it can withstand aerodynamic pressures and light weight to reduce fuel consumption. The aim of this work is to provide a method for the density-based topology optimization of compliant morphing structures. The method includes a novel formulation for the objective function which compares the deformed shape of the structure with a desired deformed shape by using a dot product. This method is applied to obtain an optimized design of a compliant variable-camber morphing wing. The obtained design was converted to a prototype by 3D printing and an experiment was performed to assess if the deformed shapes of the prototype were similar to the ones predicted by the analysis in the topology optimization. The experiment showed that for small deformations the output shape matched the predicted output shape. For larger deflections, there was a slight difference. However, the obtained shapes were still quadratic-like and so it is expected that for larger deformations the designed trailing edge will still have superior aerodynamic performance than conventional flap systems.
Magnets for High Energy Physics applications built to date are generally superconducting magnets, which operate at cryogenic temperatures. The reliability and safety of the applications are entirely dependent on good design which in turn rely heavily on predictable materials performance. Where at these low temperatures the fracture toughness is of importance to be known (alongside mechanical properties such yield and tensile strength). At CERN at the materials and engineering department (EN-MME-MA) a testing facility is being commissioned for the measurement of mechanical at cryogenic temperatures. A tensile test facility has been realised, yet no such set-up is available for fracture toughness measurement. The aim of this thesis was to develop a test set-up for the measurement of the fracture toughness in order to realise a universal cryogenic testing system, which can be used for both tensile tests and fracture toughness test at low temperatures. A design for a set-up is proposed for the measurement of the fracture toughness which can be employed within the current cryostat. The design of the tooling and cryostat have been extensively verified using numerical methods taking into account thermal effects (such as conduction and contraction) and the varying material properties at these low temperatures. A modified C(T) specimen is proposed for more robust and reliable set-up. For this modified specimen it is shown with numerical methods that the modification are expected to have a negligible impact on the fracture toughness measurements. Tests have been performed using the proposed design with four specimen fabricated from two different materials (SS316L and Ti6Al4V), at both room temperature and at 4 K (using liquid helium). The set-up is shown to provide sufficient data for the characterisation of the fracture toughness for both Linear Elastic Fracture Mechanics tests as well as Elastic Plastic Fracture mechanics tests.
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Magnets for High Energy Physics applications built to date are generally superconducting magnets, which operate at cryogenic temperatures. The reliability and safety of the applications are entirely dependent on good design which in turn rely heavily on predictable materials performance. Where at these low temperatures the fracture toughness is of importance to be known (alongside mechanical properties such yield and tensile strength). At CERN at the materials and engineering department (EN-MME-MA) a testing facility is being commissioned for the measurement of mechanical at cryogenic temperatures. A tensile test facility has been realised, yet no such set-up is available for fracture toughness measurement. The aim of this thesis was to develop a test set-up for the measurement of the fracture toughness in order to realise a universal cryogenic testing system, which can be used for both tensile tests and fracture toughness test at low temperatures. A design for a set-up is proposed for the measurement of the fracture toughness which can be employed within the current cryostat. The design of the tooling and cryostat have been extensively verified using numerical methods taking into account thermal effects (such as conduction and contraction) and the varying material properties at these low temperatures. A modified C(T) specimen is proposed for more robust and reliable set-up. For this modified specimen it is shown with numerical methods that the modification are expected to have a negligible impact on the fracture toughness measurements. Tests have been performed using the proposed design with four specimen fabricated from two different materials (SS316L and Ti6Al4V), at both room temperature and at 4 K (using liquid helium). The set-up is shown to provide sufficient data for the characterisation of the fracture toughness for both Linear Elastic Fracture Mechanics tests as well as Elastic Plastic Fracture mechanics tests.
Manipulating post-buckled compliant mechanisms
Buckling mode interaction as a novel method of stiffness compensation
Bistable vibration energy harvesters are an interesting alternative to their linear counterparts. They allow for large amplitude oscillations between their stable equilibria, from which much energy can be generated. However, the stable equilibria are separated by a potential energy barrier that has to be overcome. Therefore, we cannot guarantee these oscillations, and the performance advantage diminishes. As a solution to this, a novel method of stiffness compensation in compliant bistable mechanisms is explored to lower the potential barrier. This method makes use of interaction between the buckling modes. Whereas this phenomenon is most undesired in structures due to their increasing proneness to catastrophic failure, we cleverly use it to our advantage. During the deflection required for the large amplitude oscillations, a transition between these buckling modes occurs, causing the increase in potential energy. By bringing the corresponding buckling loads closer together, the transition is eased and the potential barrier is lowered. An analytical framework was set up as a fundamental test of this method. Using a discrete analytical model of a bistable buckled four-bar linkage with torsion springs, it was shown that the potential barrier can be flattened upon matching the first two critical buckling loads, resulting in static balancing. This was achieved by making two torsion springs three times stiffer with respect to the other two springs. To put theory into practice, three compliant mechanisms were designed using the ratio between the first two buckling loads. Their force-deflection characteristics were experimentally determined and it was shown that the stiffness may be tuned according to the ratio between the buckling loads. Furthermore, it was shown that in designs having the first two buckling loads equal to each other, near zero stiffness is achieved. Hence, this method is proven a successful addition to the arsenal of methods in stiffness compensation and static balancing of compliant mechanisms.
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Bistable vibration energy harvesters are an interesting alternative to their linear counterparts. They allow for large amplitude oscillations between their stable equilibria, from which much energy can be generated. However, the stable equilibria are separated by a potential energy barrier that has to be overcome. Therefore, we cannot guarantee these oscillations, and the performance advantage diminishes. As a solution to this, a novel method of stiffness compensation in compliant bistable mechanisms is explored to lower the potential barrier. This method makes use of interaction between the buckling modes. Whereas this phenomenon is most undesired in structures due to their increasing proneness to catastrophic failure, we cleverly use it to our advantage. During the deflection required for the large amplitude oscillations, a transition between these buckling modes occurs, causing the increase in potential energy. By bringing the corresponding buckling loads closer together, the transition is eased and the potential barrier is lowered. An analytical framework was set up as a fundamental test of this method. Using a discrete analytical model of a bistable buckled four-bar linkage with torsion springs, it was shown that the potential barrier can be flattened upon matching the first two critical buckling loads, resulting in static balancing. This was achieved by making two torsion springs three times stiffer with respect to the other two springs. To put theory into practice, three compliant mechanisms were designed using the ratio between the first two buckling loads. Their force-deflection characteristics were experimentally determined and it was shown that the stiffness may be tuned according to the ratio between the buckling loads. Furthermore, it was shown that in designs having the first two buckling loads equal to each other, near zero stiffness is achieved. Hence, this method is proven a successful addition to the arsenal of methods in stiffness compensation and static balancing of compliant mechanisms.
In this thesis a proof-of-principle demonstration is developed that uses the heat flux between a probe and a sample as a proxy for their separation. The proposed architecture uses a probe that consists of a bilayer cantilever with an attached sphere at its free end. The deflection of the cantilever that is caused by the heat input is measured using the optical beam deflection method. To eliminate temperature dependent effects the temperatures of the probe and the sample are kept constant. Moreover, a total internal reflection microscopy is included to provide an independent measurement of the separation between the probe and the sample. This architecture allows the measurement of the heat flux as a function of only the separation.
An equation is derived that relates the output signal of the instrument directly to the heat flux that is absorbed by the probe. It couples the top-level design parameters to the system output and is used to study and design the separate elements. In addition to the design of the instrument, the research contributes a detailed study of the influences of the microsphere and the microcantilever on the heat flux measurement.
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An equation is derived that relates the output signal of the instrument directly to the heat flux that is absorbed by the probe. It couples the top-level design parameters to the system output and is used to study and design the separate elements. In addition to the design of the instrument, the research contributes a detailed study of the influences of the microsphere and the microcantilever on the heat flux measurement.
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In this thesis a proof-of-principle demonstration is developed that uses the heat flux between a probe and a sample as a proxy for their separation. The proposed architecture uses a probe that consists of a bilayer cantilever with an attached sphere at its free end. The deflection of the cantilever that is caused by the heat input is measured using the optical beam deflection method. To eliminate temperature dependent effects the temperatures of the probe and the sample are kept constant. Moreover, a total internal reflection microscopy is included to provide an independent measurement of the separation between the probe and the sample. This architecture allows the measurement of the heat flux as a function of only the separation.
An equation is derived that relates the output signal of the instrument directly to the heat flux that is absorbed by the probe. It couples the top-level design parameters to the system output and is used to study and design the separate elements. In addition to the design of the instrument, the research contributes a detailed study of the influences of the microsphere and the microcantilever on the heat flux measurement.
An equation is derived that relates the output signal of the instrument directly to the heat flux that is absorbed by the probe. It couples the top-level design parameters to the system output and is used to study and design the separate elements. In addition to the design of the instrument, the research contributes a detailed study of the influences of the microsphere and the microcantilever on the heat flux measurement.
Cracks, which could nucleate and propagate in engineering structures, could have an adverse effect on mechanical performance and even lead to catastrophic failure. Thus, it is critical to investigate structural behavior under fracture, which requires an appropriate modeling methodology for fracture analysis. Furthermore, designing structures that are resilient to fracture is highly desired, where it is necessary to find a computational design technique for improving the structural fracture resistance. This thesis focuses on realizing these two goals....
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Cracks, which could nucleate and propagate in engineering structures, could have an adverse effect on mechanical performance and even lead to catastrophic failure. Thus, it is critical to investigate structural behavior under fracture, which requires an appropriate modeling methodology for fracture analysis. Furthermore, designing structures that are resilient to fracture is highly desired, where it is necessary to find a computational design technique for improving the structural fracture resistance. This thesis focuses on realizing these two goals....
This thesis a method is described to include manufacturing constraints of the additive manufacturing process into topology optimization. Topology optimization often results in complex structures, which can only be produced by additive manufacturing. Although additive manufacturing has much fewer design restrictions compared to conventional manufacturing methods, it has its own limitations. The most prominent limitation is the overhang constraint, which causes the need for support structures. In this thesis front propagation is utilized to crudely mimic the printing process. Making use of existing numerical methods for front propagation, a numerically efficient algorithm is produced that can identify parts of the structure that do not adhere to the overhang constraint, during the topology optimization process. Since the sensitivities of the algorithm are available, it can be used in the gradient based topology optimization to ensure printability of the final part. Due to the continuous description of the constraint, it can be applied to unstructured meshes and for variable overhang angles. Furthermore, it is shown that the constraint can be parallelized which is demonstrated on large scale 3D problems.
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This thesis a method is described to include manufacturing constraints of the additive manufacturing process into topology optimization. Topology optimization often results in complex structures, which can only be produced by additive manufacturing. Although additive manufacturing has much fewer design restrictions compared to conventional manufacturing methods, it has its own limitations. The most prominent limitation is the overhang constraint, which causes the need for support structures. In this thesis front propagation is utilized to crudely mimic the printing process. Making use of existing numerical methods for front propagation, a numerically efficient algorithm is produced that can identify parts of the structure that do not adhere to the overhang constraint, during the topology optimization process. Since the sensitivities of the algorithm are available, it can be used in the gradient based topology optimization to ensure printability of the final part. Due to the continuous description of the constraint, it can be applied to unstructured meshes and for variable overhang angles. Furthermore, it is shown that the constraint can be parallelized which is demonstrated on large scale 3D problems.
Stiffened shells and plates are widely used in engineering, but their performance is highly influenced by the arrangement, or layout, of stiffeners on the base shell or plate and the geometric features, or topology, of these stiffeners. Moreover, structures with modules are beneficial, since it allows for increased quality control and more accessible mass production. The aim of this work is to develop a method that simultaneously optimizes the topology of the modular stiffeners and their layout on a base shell or plate. This is accomplished by introducing a fixed number of module stiffeners which are subject to density based topology optimization and a mapping of these modules to a ground structure of stiffeners. To illustrate potential applications, several stiffened plates and shell examples are presented. After optimization, these examples were converted to three-dimensional physical structures using additive manufacturing. All examples demonstrated that the proposed method is able to generate clear topologies for any number of modules and a distinct layout on the base.
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Stiffened shells and plates are widely used in engineering, but their performance is highly influenced by the arrangement, or layout, of stiffeners on the base shell or plate and the geometric features, or topology, of these stiffeners. Moreover, structures with modules are beneficial, since it allows for increased quality control and more accessible mass production. The aim of this work is to develop a method that simultaneously optimizes the topology of the modular stiffeners and their layout on a base shell or plate. This is accomplished by introducing a fixed number of module stiffeners which are subject to density based topology optimization and a mapping of these modules to a ground structure of stiffeners. To illustrate potential applications, several stiffened plates and shell examples are presented. After optimization, these examples were converted to three-dimensional physical structures using additive manufacturing. All examples demonstrated that the proposed method is able to generate clear topologies for any number of modules and a distinct layout on the base.
Computational efficient robustness analysis of aircraft component distortion
Accounting for stochastic pre-stressed stock material in reductive manufacturing processes
Master thesis
(2019)
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Yannick Janssens, Fred van Keulen, Dirk Munro, Marcel Tichem, Sjoerd van der Veen
In this thesis, a methodology is developed that allows for both reliable and computational efficient robustness analysis of aircraft component distortion. This research applies to dis- tortion caused by reductive manufacturing processes that are used to obtain monolithic components from pre-stressed stock material. With the developed methodology, orienta- tions of any component within rolled plate stock material can be found where distortion is most robust. Part distortion is defined as a deviation in shape of an aircraft component from original intent as a result of the component’s reductive manufacturing process. As extreme precision is required in aircraft component assembly, the distortion phenomenon is highly undesired. The developed methodology in this thesis contributes to AIRBUS’ objectives to minimize part distortion related issues. In this thesis, the fundamentals of part distortion are studied. It is found that aircraft com- ponents distort as a result of residual stresses that are present in stock material from which the components are manufactured. As residual stress in rolled plate is subjected to substan- tial variation, part distortion is stochastic in nature. Positions of the components in rolled plate are searched for where distortion is most robust. The robustness of distortion refers to the insensitivity of distortion to uncertainty in residual stress. A mathematical stochastic representation of residual stress in rolled plate is developed showing high coherence with experimental measurement data provided by AIRBUS. For elementary geometries, the rela- tionship between distortion robustness and residual stress is derived analytically. The developed method for predicting distortion robustness is more than one hundred times more efficient in terms of computation cost compared to state-of-the-art methods and al- lows for reliable robustness predictions. In the developed method, three-dimensional po- sitioning of a component in rolled plate can be simulated where state-of-the-art distortion modeling tools usually stick to one dimension. The developed methodology is put to the test in a case study concerning an aircraft stiffener component. The case study emphasizes the significance of robustness predictions; distor- tion dispersion is found to be relatively large compared to the distortion magnitude and significant correlation is found between the component’s orientation in rolled plate and the level of robustness. Positions of components in rolled plate can be found where distortion is extremely robust. Moreover, a relationship is found between the component’s degree of symmetry and the level of robustness.
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In this thesis, a methodology is developed that allows for both reliable and computational efficient robustness analysis of aircraft component distortion. This research applies to dis- tortion caused by reductive manufacturing processes that are used to obtain monolithic components from pre-stressed stock material. With the developed methodology, orienta- tions of any component within rolled plate stock material can be found where distortion is most robust. Part distortion is defined as a deviation in shape of an aircraft component from original intent as a result of the component’s reductive manufacturing process. As extreme precision is required in aircraft component assembly, the distortion phenomenon is highly undesired. The developed methodology in this thesis contributes to AIRBUS’ objectives to minimize part distortion related issues. In this thesis, the fundamentals of part distortion are studied. It is found that aircraft com- ponents distort as a result of residual stresses that are present in stock material from which the components are manufactured. As residual stress in rolled plate is subjected to substan- tial variation, part distortion is stochastic in nature. Positions of the components in rolled plate are searched for where distortion is most robust. The robustness of distortion refers to the insensitivity of distortion to uncertainty in residual stress. A mathematical stochastic representation of residual stress in rolled plate is developed showing high coherence with experimental measurement data provided by AIRBUS. For elementary geometries, the rela- tionship between distortion robustness and residual stress is derived analytically. The developed method for predicting distortion robustness is more than one hundred times more efficient in terms of computation cost compared to state-of-the-art methods and al- lows for reliable robustness predictions. In the developed method, three-dimensional po- sitioning of a component in rolled plate can be simulated where state-of-the-art distortion modeling tools usually stick to one dimension. The developed methodology is put to the test in a case study concerning an aircraft stiffener component. The case study emphasizes the significance of robustness predictions; distor- tion dispersion is found to be relatively large compared to the distortion magnitude and significant correlation is found between the component’s orientation in rolled plate and the level of robustness. Positions of components in rolled plate can be found where distortion is extremely robust. Moreover, a relationship is found between the component’s degree of symmetry and the level of robustness.
Dynamic analysis of large-size finite element models has been commonly applied by mechanical engineers to simulate the dynamic behavior of complex structures. The ever-increasing demand for both detailed and accurate simulation of complex structures forces mechanical engineers to pursue a balance between two conflicting goals during the simulations: low computational cost and high accuracy. These goals become extremely difficult for geometric nonlinear structural dynamical problems. When geometrical nonlinearities are introduced, the internal force vector and Jacobians are configuration dependent, and the corresponding updates are computationally expensive. This thesis presents nonlinear model order reduction techniques that aim to perform detailed dynamic analysis of multi-component structures with reduced computational cost, without degrading the accuracy too much. Special attention is given to flexible multibody system dynamics.
For multi-component structures featuring many interface degrees of freedom, standard substructuring dynamics can be combined with interface reduction techniques to obtain compact reduced order models. Chapter~2 summarized a variety of interface reduction techniques for the well-known Craig-Bampton substructuring method. These approaches are reviewed and compared in terms of both computational cost and accuracy. A multilevel interface reduction method is presented as a more generalized approach, where a secondary Craig-Bampton reduction is performed when the subsystems are assembled within localized subsets. The multilevel interface reduction method provides an accurate representation of the full linear model with significantly lower computational cost.
In Chapter~3, we extend the Craig-Bampton method to geometric nonlinear problems by augmenting the system-level interface modes and internal vibration modes of each substructure with their corresponding modal derivatives. The modal derivatives are capable of describing the bending-stretching coupling effects exhibited by geometric nonlinear structures. Once the reduced order model is constructed by Galerkin projection, the upcoming challenge is the computation of the reduced nonlinear internal force vectors and tangent matrices during the time integration. The evaluation of these objects scales with the size of the full order model, and it is therefore expensive, as it needs to be repeated multiple time within every time step of the time integration. To address this problem, we directly express the reduced nonlinear vectors and matrices as a polynomial function of the modal coordinates, using substructure-level higher-order tensors with much smaller size. This enhanced Craig-Bampton method offers flexibility for reduced modal basis construction, as modal derivatives need to be computed only for substructures actually featuring geometrical nonlinearities, and do not need the prior knowledge of the nonlinear response of the full system with training load cases.
For flexible multibody systems, each body undergoes both overall rigid body motion and flexible behavior. To describe the dynamic behavior of each body accurately, the floating frame of reference is commonly applied. In Chapter~4, the enhanced Craig-Bampton method, as proposed in Chapter~3, is embedded in the floating frame of reference. We consider here structures modeled with von-Karman beam elements. Interface reduction methods are in this context unnecessary since the adjacent bodies are connected through a single node. The proposed reduction method constitutes a natural and effective extension of the classical linear modal reduction in the floating frame.
For more complex geometries, like wind turbine blades, extremely simplified beam models can not capture the complexity of the real three-dimensional structure, and therefore the dynamic behavior might not be accurately modeled. In Chapter~5, we present an enhanced Rubin substructuring method for three-dimensional nonlinear multibody systems. The standard Rubin reduction basis is augmented with the modal derivatives of both the free-interface vibration modes and the attachment modes to include bending-stretching coupling effects triggered by the nonlinear vibrations. When compared to the enhanced Craig-Bampton method proposed in Chapter~4, the enhanced Rubin method better reproduces the geometrical nonlinearities occurring at the interface, and, as a consequence, higher accuracy can be achieved.
In Chapter~6, the overall conclusions are drawn and recommendations for further study are provided.
...
For multi-component structures featuring many interface degrees of freedom, standard substructuring dynamics can be combined with interface reduction techniques to obtain compact reduced order models. Chapter~2 summarized a variety of interface reduction techniques for the well-known Craig-Bampton substructuring method. These approaches are reviewed and compared in terms of both computational cost and accuracy. A multilevel interface reduction method is presented as a more generalized approach, where a secondary Craig-Bampton reduction is performed when the subsystems are assembled within localized subsets. The multilevel interface reduction method provides an accurate representation of the full linear model with significantly lower computational cost.
In Chapter~3, we extend the Craig-Bampton method to geometric nonlinear problems by augmenting the system-level interface modes and internal vibration modes of each substructure with their corresponding modal derivatives. The modal derivatives are capable of describing the bending-stretching coupling effects exhibited by geometric nonlinear structures. Once the reduced order model is constructed by Galerkin projection, the upcoming challenge is the computation of the reduced nonlinear internal force vectors and tangent matrices during the time integration. The evaluation of these objects scales with the size of the full order model, and it is therefore expensive, as it needs to be repeated multiple time within every time step of the time integration. To address this problem, we directly express the reduced nonlinear vectors and matrices as a polynomial function of the modal coordinates, using substructure-level higher-order tensors with much smaller size. This enhanced Craig-Bampton method offers flexibility for reduced modal basis construction, as modal derivatives need to be computed only for substructures actually featuring geometrical nonlinearities, and do not need the prior knowledge of the nonlinear response of the full system with training load cases.
For flexible multibody systems, each body undergoes both overall rigid body motion and flexible behavior. To describe the dynamic behavior of each body accurately, the floating frame of reference is commonly applied. In Chapter~4, the enhanced Craig-Bampton method, as proposed in Chapter~3, is embedded in the floating frame of reference. We consider here structures modeled with von-Karman beam elements. Interface reduction methods are in this context unnecessary since the adjacent bodies are connected through a single node. The proposed reduction method constitutes a natural and effective extension of the classical linear modal reduction in the floating frame.
For more complex geometries, like wind turbine blades, extremely simplified beam models can not capture the complexity of the real three-dimensional structure, and therefore the dynamic behavior might not be accurately modeled. In Chapter~5, we present an enhanced Rubin substructuring method for three-dimensional nonlinear multibody systems. The standard Rubin reduction basis is augmented with the modal derivatives of both the free-interface vibration modes and the attachment modes to include bending-stretching coupling effects triggered by the nonlinear vibrations. When compared to the enhanced Craig-Bampton method proposed in Chapter~4, the enhanced Rubin method better reproduces the geometrical nonlinearities occurring at the interface, and, as a consequence, higher accuracy can be achieved.
In Chapter~6, the overall conclusions are drawn and recommendations for further study are provided.
...
Dynamic analysis of large-size finite element models has been commonly applied by mechanical engineers to simulate the dynamic behavior of complex structures. The ever-increasing demand for both detailed and accurate simulation of complex structures forces mechanical engineers to pursue a balance between two conflicting goals during the simulations: low computational cost and high accuracy. These goals become extremely difficult for geometric nonlinear structural dynamical problems. When geometrical nonlinearities are introduced, the internal force vector and Jacobians are configuration dependent, and the corresponding updates are computationally expensive. This thesis presents nonlinear model order reduction techniques that aim to perform detailed dynamic analysis of multi-component structures with reduced computational cost, without degrading the accuracy too much. Special attention is given to flexible multibody system dynamics.
For multi-component structures featuring many interface degrees of freedom, standard substructuring dynamics can be combined with interface reduction techniques to obtain compact reduced order models. Chapter~2 summarized a variety of interface reduction techniques for the well-known Craig-Bampton substructuring method. These approaches are reviewed and compared in terms of both computational cost and accuracy. A multilevel interface reduction method is presented as a more generalized approach, where a secondary Craig-Bampton reduction is performed when the subsystems are assembled within localized subsets. The multilevel interface reduction method provides an accurate representation of the full linear model with significantly lower computational cost.
In Chapter~3, we extend the Craig-Bampton method to geometric nonlinear problems by augmenting the system-level interface modes and internal vibration modes of each substructure with their corresponding modal derivatives. The modal derivatives are capable of describing the bending-stretching coupling effects exhibited by geometric nonlinear structures. Once the reduced order model is constructed by Galerkin projection, the upcoming challenge is the computation of the reduced nonlinear internal force vectors and tangent matrices during the time integration. The evaluation of these objects scales with the size of the full order model, and it is therefore expensive, as it needs to be repeated multiple time within every time step of the time integration. To address this problem, we directly express the reduced nonlinear vectors and matrices as a polynomial function of the modal coordinates, using substructure-level higher-order tensors with much smaller size. This enhanced Craig-Bampton method offers flexibility for reduced modal basis construction, as modal derivatives need to be computed only for substructures actually featuring geometrical nonlinearities, and do not need the prior knowledge of the nonlinear response of the full system with training load cases.
For flexible multibody systems, each body undergoes both overall rigid body motion and flexible behavior. To describe the dynamic behavior of each body accurately, the floating frame of reference is commonly applied. In Chapter~4, the enhanced Craig-Bampton method, as proposed in Chapter~3, is embedded in the floating frame of reference. We consider here structures modeled with von-Karman beam elements. Interface reduction methods are in this context unnecessary since the adjacent bodies are connected through a single node. The proposed reduction method constitutes a natural and effective extension of the classical linear modal reduction in the floating frame.
For more complex geometries, like wind turbine blades, extremely simplified beam models can not capture the complexity of the real three-dimensional structure, and therefore the dynamic behavior might not be accurately modeled. In Chapter~5, we present an enhanced Rubin substructuring method for three-dimensional nonlinear multibody systems. The standard Rubin reduction basis is augmented with the modal derivatives of both the free-interface vibration modes and the attachment modes to include bending-stretching coupling effects triggered by the nonlinear vibrations. When compared to the enhanced Craig-Bampton method proposed in Chapter~4, the enhanced Rubin method better reproduces the geometrical nonlinearities occurring at the interface, and, as a consequence, higher accuracy can be achieved.
In Chapter~6, the overall conclusions are drawn and recommendations for further study are provided.
For multi-component structures featuring many interface degrees of freedom, standard substructuring dynamics can be combined with interface reduction techniques to obtain compact reduced order models. Chapter~2 summarized a variety of interface reduction techniques for the well-known Craig-Bampton substructuring method. These approaches are reviewed and compared in terms of both computational cost and accuracy. A multilevel interface reduction method is presented as a more generalized approach, where a secondary Craig-Bampton reduction is performed when the subsystems are assembled within localized subsets. The multilevel interface reduction method provides an accurate representation of the full linear model with significantly lower computational cost.
In Chapter~3, we extend the Craig-Bampton method to geometric nonlinear problems by augmenting the system-level interface modes and internal vibration modes of each substructure with their corresponding modal derivatives. The modal derivatives are capable of describing the bending-stretching coupling effects exhibited by geometric nonlinear structures. Once the reduced order model is constructed by Galerkin projection, the upcoming challenge is the computation of the reduced nonlinear internal force vectors and tangent matrices during the time integration. The evaluation of these objects scales with the size of the full order model, and it is therefore expensive, as it needs to be repeated multiple time within every time step of the time integration. To address this problem, we directly express the reduced nonlinear vectors and matrices as a polynomial function of the modal coordinates, using substructure-level higher-order tensors with much smaller size. This enhanced Craig-Bampton method offers flexibility for reduced modal basis construction, as modal derivatives need to be computed only for substructures actually featuring geometrical nonlinearities, and do not need the prior knowledge of the nonlinear response of the full system with training load cases.
For flexible multibody systems, each body undergoes both overall rigid body motion and flexible behavior. To describe the dynamic behavior of each body accurately, the floating frame of reference is commonly applied. In Chapter~4, the enhanced Craig-Bampton method, as proposed in Chapter~3, is embedded in the floating frame of reference. We consider here structures modeled with von-Karman beam elements. Interface reduction methods are in this context unnecessary since the adjacent bodies are connected through a single node. The proposed reduction method constitutes a natural and effective extension of the classical linear modal reduction in the floating frame.
For more complex geometries, like wind turbine blades, extremely simplified beam models can not capture the complexity of the real three-dimensional structure, and therefore the dynamic behavior might not be accurately modeled. In Chapter~5, we present an enhanced Rubin substructuring method for three-dimensional nonlinear multibody systems. The standard Rubin reduction basis is augmented with the modal derivatives of both the free-interface vibration modes and the attachment modes to include bending-stretching coupling effects triggered by the nonlinear vibrations. When compared to the enhanced Craig-Bampton method proposed in Chapter~4, the enhanced Rubin method better reproduces the geometrical nonlinearities occurring at the interface, and, as a consequence, higher accuracy can be achieved.
In Chapter~6, the overall conclusions are drawn and recommendations for further study are provided.
Master thesis
(2017)
-
Hari Mohanachandran, Fred van Keulen, Max van der Kolk, Dennis Heck, Patrick Smulders, R. Delfos, S.H. Hossein Nia Kani
An active fluid heat exchanger can be controlled effectively using Peltier elements to condition the temperature of the fluid flowing through the heat exchanger. The thermal resistance of the heat exchanger can be reduced to increase the speed of controlling the fluid's temperature. Topology optimization is used in this study to find the geometry of a heat exchanger with reduced thermal resistance.
The design of a heat exchanger using topology optimization requires the coupling of the fluid flow equations and the energy equation in a finite element model with a continuous design variable. The existing optimization models perform well when the goal of the optimization problem is to minimize viscous dissipation. A weighted sum multi-objective function is however necessary to optimize the thermal performance of a design, and the correct choice of weights to meet design specifications is difficult to arrive at.
The drawback in the existing model is that the conductivity distribution is defined as a function of the design variable of the optimization problem. This results in infeasible designs when the goal of the optimization problem is to minimize only thermal resistance, and this is demonstrated with several numerical examples along with a motivation for a new formulation.
A new formulation for conductivity distribution is proposed in this thesis. The new formulation defines the conductivity distribution in terms of the velocity field in the design domain. The new formulation is capable of significantly reducing the thermal resistance of the heat exchanger, and this is demonstrated with a numerical example. Finally, a 3d design case is implemented, the results of the optimization routine are post-processed and the performance of the baseline design from ASML is compared with the topology optimized design.
...
The design of a heat exchanger using topology optimization requires the coupling of the fluid flow equations and the energy equation in a finite element model with a continuous design variable. The existing optimization models perform well when the goal of the optimization problem is to minimize viscous dissipation. A weighted sum multi-objective function is however necessary to optimize the thermal performance of a design, and the correct choice of weights to meet design specifications is difficult to arrive at.
The drawback in the existing model is that the conductivity distribution is defined as a function of the design variable of the optimization problem. This results in infeasible designs when the goal of the optimization problem is to minimize only thermal resistance, and this is demonstrated with several numerical examples along with a motivation for a new formulation.
A new formulation for conductivity distribution is proposed in this thesis. The new formulation defines the conductivity distribution in terms of the velocity field in the design domain. The new formulation is capable of significantly reducing the thermal resistance of the heat exchanger, and this is demonstrated with a numerical example. Finally, a 3d design case is implemented, the results of the optimization routine are post-processed and the performance of the baseline design from ASML is compared with the topology optimized design.
...
An active fluid heat exchanger can be controlled effectively using Peltier elements to condition the temperature of the fluid flowing through the heat exchanger. The thermal resistance of the heat exchanger can be reduced to increase the speed of controlling the fluid's temperature. Topology optimization is used in this study to find the geometry of a heat exchanger with reduced thermal resistance.
The design of a heat exchanger using topology optimization requires the coupling of the fluid flow equations and the energy equation in a finite element model with a continuous design variable. The existing optimization models perform well when the goal of the optimization problem is to minimize viscous dissipation. A weighted sum multi-objective function is however necessary to optimize the thermal performance of a design, and the correct choice of weights to meet design specifications is difficult to arrive at.
The drawback in the existing model is that the conductivity distribution is defined as a function of the design variable of the optimization problem. This results in infeasible designs when the goal of the optimization problem is to minimize only thermal resistance, and this is demonstrated with several numerical examples along with a motivation for a new formulation.
A new formulation for conductivity distribution is proposed in this thesis. The new formulation defines the conductivity distribution in terms of the velocity field in the design domain. The new formulation is capable of significantly reducing the thermal resistance of the heat exchanger, and this is demonstrated with a numerical example. Finally, a 3d design case is implemented, the results of the optimization routine are post-processed and the performance of the baseline design from ASML is compared with the topology optimized design.
The design of a heat exchanger using topology optimization requires the coupling of the fluid flow equations and the energy equation in a finite element model with a continuous design variable. The existing optimization models perform well when the goal of the optimization problem is to minimize viscous dissipation. A weighted sum multi-objective function is however necessary to optimize the thermal performance of a design, and the correct choice of weights to meet design specifications is difficult to arrive at.
The drawback in the existing model is that the conductivity distribution is defined as a function of the design variable of the optimization problem. This results in infeasible designs when the goal of the optimization problem is to minimize only thermal resistance, and this is demonstrated with several numerical examples along with a motivation for a new formulation.
A new formulation for conductivity distribution is proposed in this thesis. The new formulation defines the conductivity distribution in terms of the velocity field in the design domain. The new formulation is capable of significantly reducing the thermal resistance of the heat exchanger, and this is demonstrated with a numerical example. Finally, a 3d design case is implemented, the results of the optimization routine are post-processed and the performance of the baseline design from ASML is compared with the topology optimized design.