When drilling for oil or gas, wells are typically constructed using a conventional or telescopic well design. After a section of the well has been drilled, a steel casing (or liner) is inserted into the hole preventing the collapse of the hole. The next well section has a smaller diameter as it’s casing must pass through the previously installed casing. This process leads to a stepwise reduction of the well diameter which, especially in deep or complicated wells, restricts the maximum production rate of oil and gas. Mono-diameter technology utilizes casings which are plastically deformed after they have been placed in the well. This plastic deformation is done by pulling a conically shaped tool, known as the cone, through the newly installed casing. The plastic deformation increases the diameter of the new casing to (nearly) the same as that of the previous casing, therefore the well diameter no longer decreases with every new section. The expansion requires a force in the order of 1000-2500[kN]. The work done by this force leads to high local heat generation due to friction and plastic deformation. This heat, poses a risk for the expansion process as the lubricant (RPSLF) decomposes above 250[C]. Decomposition of the lubricant leads to an increase of the friction, inducing more heat release and further decomposition of the lubricant. The expansion force may then exceed the pulling capacity of the drill rig or strength of the drill string, leaving the cone stuck in the well. Previous research provides the distribution of pressure on the contact surface of the cone, the strain distribution inside the liner and the temperature dependent friction coefficient of the lubricant, by combining these the frictional heat is calculated. Heat generation from plastic deformation is a complex phenomenon especially at low strain (-rates). The Taylor-Quinney coefficient defines the ratio between the work done on a material and the heat generated. A strain-dependent model for the Taylor-Quinney coefficient, developed by Zehnder, is used to determine the heat release from plastic deformation. A numerical heat transfer model is built in Matlab, based on the finite volume method. The model uses a mesh based on skewed quadrilateral cells. Numerical stability of the model is verified for the cell size, time step and time integration method. Movement of the cone and the plastic deformation of the casing are modeled by taking a reference frame fixed relative to the motion of the cone and adding a ”convective” term inside the liner. Heat transfer phenomena at all boundaries are investigated using thermal resistance models. A series of experiments is executed to verify the numerical model. The experiments consist of full-scale expansion test using a cone equipped with 30 thermocouples placed just below the contact surface. Additionally also the temperature of the liner, expansion speed and expansion force are measured and recorded. Comparison of the experimental and numerical results leads to the observation that the pressure profile determined in previous work is likely valid at the first onset of expansion. Over time, the forming of a lubricant film however leads to the re-distribution of roughly 20% of the force from the rear of the cone to the front. When the pressure profile is corrected for this effect; the temperatures inside the cone, temperature of the liner, expansion force and overall heat balance show a good match between the numerical and experimental results with an error of around 5%. From the heat balance based on the experimental results, it follows that between 54% - 60% of the work done on the system is converted into heat. As all work done in the form of friction is converted into heat the remaining energy must be lost in the work done to plastically deform the casing, this provides indirect evidence for the validity of the Zehndermodel. The validated numerical model is used to simulate a reference case field expansion, the maximum contact temperature here is 164.4[C]. This value is well below the lubricant decomposition temperature of 250[C], which leads to the conclusion that the process is safe and the expansion speed could even be increased from a thermal point of view.

Origami structures have become of increasing importance in the field of engineering, due to their lightweight, compact and stiff properties. To design these structures, progress is being made into incorporating origami modeling in the Finite Element Method. To implement an arbitrarily located fold on an existing mesh, either re-meshing or enriched finite elements are required. In fold pattern optimisation of origami structures, re-meshing each intermediate design would not be time efficient, whereas enriched elements may be very time efficient. In this thesis foldable Kirchhoff-Love plate elements are derived using a mixed/hybrid element formulation in combination with an enriched Finite Element formulation. The use of a mixed/hybrid element formulation enables great simplification of the enrichment functions, since the discontinuous rotation field is evaluated at the boundaries of the enriched plate elements, instead of the element domain. Six foldable plate elements are derived and tested for accuracy and stability. The stability is improved by either local condensation of the enriched elements or by applying a precondition matrix.

Origami has become a source of inspiration in engineering for structural design and the creation of mechanical metamaterials. In the often used analytic geometric and energy methods, it is difficult to incorporate deformation of the faces in non-rigid origami. However, deformation of the faces can play a significant role in their mechanical behaviour. This thesis aims to investigate and improve the design of non-rigid origami structures by using the Finite Element Method (FEM), which is well suited to model all deformations of these structures. In collaboration with the Bertoldi Group at Harvard University, FEM is applied on the new bistable non- rigid origami structure called the Star bellow. The suitable building blocks of the FEM approach, are finite rotation shell elements to model the faces of the structure, torsional spring elements to model the crease lines, and a Newton-Raphson arc-length control solution procedure. In addition to the numerical analysis, experimental work is performed. A parametric study, FEM simulations, and physical load tests of prototypes, are performed to understand the mechanical properties of the Star bellow structure and to improve its bistable behaviour. In addition, the Star bellow structure was considered as a unit cell and tessellated into a 1D-array to create a Star bellow metamaterial. Simulations and physical load tests were performed to investigate the influence of the tessellation on the bistable properties of the metamaterial. A design improvement was successfully proposed with a decrease of the minimum force value of 0.11 [N]. The tessellated Star bellow metamaterial into a 1D-array is feasible and keeps its bistable proper- ties, although the bistability is reduced compared to a non-tessellated, single Star bellow structure. The application of FEM to study the Star bellow structure enhances the design process of the Star bellow. It has been shown that a parametric study using FEM is a way to gain understanding of the structure’s mechanical properties. Furthermore, a design change of the Star bellow was proposed which improved its bistable properties. It is also found that the results of the FEM simulations, for the force values, did not match the results of the physical load tests for various reasons. To improve this, another load testing setup and a more advanced implementation of the torsional spring elements to model the crease lines is advised.

We perform a study on acoustic metasurfaces, aiming to achieve simultaneously low resonance frequencies (below 400 Hz), high attenuation bandwidth (greater than 200 Hz), and high attenuation coefficient magnitudes (above 0.8), while maintaining a surface-like structure. We propose the implementation of geometrical optimization through genetic algorithms, as well as the incorporation of a chamber to induce resonator coupling in a supercell hexagonal Helmholtz resonator metasurface, to achieve the stated objectives simultaneously. Results show that genetic algorithms can effectively increase the attenuation bandwidth while maintaining a moderate attenuation coefficient magnitude. Incorporating a chamber induces resonator coupling, causing frequency locking and pulling phenomena. A narrow chamber can effectively lower the resonance frequencies and enhance the attenuation coefficients at those frequencies, while maintaining a surface-like structure. However, incorporating a chamber may lead to a reduction in bandwidth. By combining the genetic algorithm optimization with chamber integration, we observe a significant reduction in bandwidth narrowness, while the benefits of frequency locking and pulling are maintained. In conclusion, genetic algorithms have the potential to achieve wide attenuation bandwidths, while chamber incorporation holds promise for attaining low resonance frequencies with high attenuation coefficients. Using both methods simultaneously may enable the achievement of all objectives.

Nanophotonics is the study of structures’ interaction with light with features at or below the nanometer scale. It has gained the interest of many researchers, as it can be used to control the flow of light very effectively in the design of, e.g., solar cells, highly efficient biosensors or lasers. The design of such devices can be non-intuitive and complex and therefore computational tools like topology optimization techniques have been used to improve their designs. However, the topology optimization methods used in the literature often use a density-based representation of the geometry, which often leads to jagged edges. It has been shown in the literature that jagged edges can deteriorate the accuracy of simulation results. Using a level-set method in combination with an enriched finite element method offers a smoother boundary representation than the often used density-based methods. This work aims to develop an analysis and level set optimization for 2D electromagnetic scattering and eigenvalue problems using an enriched finite element method. Furthermore, we showcase that even for a non-conforming discretization, the enriched finite element method achieves the same convergence properties as the standard finite element method with fitted meshes. Finally, we perform topology optimization on the design of both a 2D meta lens and 2D reflector, maximizing their ability to focus light onto a point, using a level set method to define the geometry in combination with the enriched method used in the analysis.

inPhocal, a startup company specialized in laser marking, developed a novel optical module to make the depth of focus more than 50mm, and wants to replace ink marking by this laser marking system in the production line when marking information on products. Distortion will always happen when marking 2D patterns onto 3D objects with laser, so deforming the 2D patterns beforehand to make marked pattern keep its shape is necessary. This process is called shape correction. Nowadays, the way to do this shape correction is very complicated and time- consuming. This thesis is focused on providing a new method that can do shape correction easily and fast. In this research, Non-Uniform Rational B-Spline (NURBS) is used in reconstructing the 3D surfaces and the shape correction will be based on these NURBS surfaces. With this NURBS-based shape correction, the pattern can be mapped on to 3D object fast without distortion.

From the motion of electrons in an atom to the orbits of celestial bodies in the cosmos, governing equations are essential to the characterisation of dynamical systems. They facilitate an understanding of the physics of a system, which enables the development of useful techniques such as predictive control. An increasingly popular method to obtain these equations is Symbolic Regression, where governing laws are discovered from observations of the system. In this work, we extend the Deep Symbolic Regression package to the identification of dynamical systems. Preliminary tests revealed the limits of the method as applied to dynamical systems, and new methods of incorporating domain knowledge to constrain the expression space are added. We test the extended package on 3 strongly nonlinear ODEs that exhibit different dynamics as their parameterisation varies. Finally, we demonstrate the working of this method in practice by discovering the governing equation of a pendulum, from a video of its oscillation. This method achieved a 100% equation recovery rate on our tests, and was able to consistently retrieve the correct equation from datasets representing a diverse range of dynamics.

In this 3D fracture-based topology optimization framework, the author extended the 2D framework on tailoring fracture resistance for brittle materials (Zhang et al., 2022) to 3D. In the optimization, the topology is described by radial basis functions interpolated level set function, and the problem is solved by the Interface-enriched Generalized Finite Element Method (IGFEM). Cracks are assumed to exist on enriched nodes that are added on the boundary of the geometry to increase the accuracy of approximation. The first part of the work assumes cracks to be semi-circular with the crack plane perpendicular to the boundary, and the crack opening direction to be either parallel to the 𝑋𝑍- or 𝑌𝑍-plane of the global coordinates. An extended framework that assumes crack opening direction perpendicular to the surface first principal stress is also developed at the end. The energy release rates (ERRs) of the cracks are evaluated with the topological derivative method, which requires only a stress field of the geometry and weight functions that relate the stress and stress intensity factors (SIFs). The weight functions are found by a finite element analysis on a cuboid with a crack. This approach is computationally efficient because it eliminates the need of actually modeling and meshing the crack planes in the geometry during optimization. Moreover, a 3D stress recovery technique (or stress improvement procedure, SIP) is used to recover the nodal stress non-locally to improve the accuracy. The objective function is then established with the 𝑝-mean aggregation of the ERRs. Finally, Numerical examples in 3D, including the famous L-bracket benchmark problem, are performed to prove the correctness and capacity of the framework. In conclusion, this extended framework shows more flexibility and provides more information to the optimized design than the 2D framework by considering an added dimension both in analyzed geometry and crack shape, i.e., the effect of the anisotropy of cracks can be captured.

In this report a new enriched finite volume method is introduced. This method will be particularly useful for fluid-structure interaction problems. In engineering many problems are in the domain of fluidstructure interaction. Examples of these are water in sea locks, blood flowing in vessels and sailing ships. Fluid problems are usually solved with the finite volume method (FVM), and structures in this fluid flow are handled by discretizing the fluid flow around this structure. The mesh therefore needs to be conforming around the structure, and remeshing is needed when the the structure is moving over time. Remeshing is a computationally expensive process, therefore in FEM a method called enriched FEM is developed, which removes the need for remeshing. Enriched FEM uses so-called enrichment functions; these enrichment functions decouple the structure from the mesh. This concept is implemented in the finite volume method to get an enriched FVM. In order to come up with this method; FVM and enriched FEM are compared to see if the concepts of enriched FEM can be implemented in FVM. The FE method that is used is the discontinuous Galerkin (DG) method, which is a method that uses components of FEM and FVM. It discretizes equations as in FEM, but the elements are connected using flux functions as in FVM. DG is used to develop a high-order FVM and to introduce enrichments in FVM. The result of this thesis is a method which can implement enrichment functions in FVM, such that remeshing is no longer needed. The method is compared with conforming FVM and enriched DG, and it uses less computational power than both methods. The method also recovers the optimal convergence rate for a non-conforming FVM discretization. The enrichment functions are decoupled from the FVM discretization, therefore the method can be added to existing FVM solvers without changing the non-enriched part. The method is tested on a problem where waves are generated in a box.

The predominant influence of geometry and tensile stress on the Q factor of nanomechanical resonators is a phenomenon commonly described as dissipation dilution. In recent years, a variety of studies has looked into maximizing this effect, resulting in an assortment of softly-clamped resonator designs. This paper proposes a methodology that uses topology optimization (TO) to design nanomechanical structures with very high Q factors, by maximizing the effects of dissipation dilution. A novel equation, based on the tensile and bending energies of a prestressed finite element model, is proposed to capture this effect. Through adjoint sensitivity analysis, the sensitivity of this function with respect to (changes in) element-level design parameters was determined, which is a capability that is not available in commercial finite element packages. Furthermore, the absence of information required a priori to the optimization makes the proposed methodology versatile and easy to use. After verification of the equation and its sensitivity, it is used as an objective in TO to optimize resonator geometries inspired by state-of-the-art resonator designs. Given a thickness of 340nm and prestress of 1GPa, the final designs show a numerical Q × f0 that competes with optimized designs found in literature.

It is relevant for various applications to seek a material that could be used for the active control of wave propagation. In this study, we explore tunablemetamaterials based on foldable origami sheets where the size of the bandgap can be tuned by the rigid folding along predefined crease lines. A combination of out-of-plane components and a crease results in the coupling and separation of bands in the band structure and eventually in a (modal) bandgap. The location, size, and vibration isolation performance are optimized and analyzed for a set of geometrical and material parameters, resulting in a potential design of aMiura-Ori structure. The methods used in this paper could be used for any kind of origami structure, which may lead to various new applications in the field of vibrations and acoustics.

Current service and installation activities for offshore wind turbines are carried out by jack-up vessels, which eliminate wave disturbances to a large extent. The use of these vessels imposes several disadvantages, including high operational costs and the limitation of operating in restricted water depths. An alternative is a crane mounted on a floating vessel (monohull), which is quicker in operation and multi-deployable. With these vessels, however, a motion compensator is needed to eliminate most of the hydrodynamic disturbances. The purpose of this graduation assignment is to develop a concept design for a passive motion compensator (PMC) to isolate the vessel motion from the payload. This goal is achieved by the implementation of a multi-objective optimization algorithm based on genetic programming (GP) that constructs a two-dimensional PMC based on the principle of quasi-zero stiffness. The GP employs a set of genetic operators to explore the design space in terms of topology and design variables, which effectively mimics Darwin’s Theory of Evolution. The better a mechanism performs, the higher the fitness, and thus the higher the chance this design appear in future generations. Each design is a composition of cylinders and nodes that are assembled into a mechanism. During the fitness evaluation, all mechanisms are examined by a nonlinear finite element method to extract the force-displacement relations. The arc-length control method is used due to the large displacements and rotations of the members in the mechanism, whereby both the nodal displacement vector and external load vector are varied to follow an equilibrium path in an incremental-iterative way. To provide sufficient support to the payload, the mechanism is prestressed, which is applied by using the arc-length procedure as well. Static and dynamic results show that the GP is suitable for constructing a high-level planar QZS mechanism for the intended application in various sea states. From multiple runs, it can be concluded that the optimizer generally produces designs with the same topology. Dynamic analyses in the time domain show that motions are effectively mitigated in the horizontal and vertical directions for the chosen designs. In addition, analysis in the frequency domain shows that the mechanisms effectively attenuate motions in the frequencies of interest.

This thesis introduces the Discontinuity-Enriched Finite Element Method (DE-FEM) for the modeling of dynamic multiple crack growth problems including branching and merging, as an alternative to eXtended/Generalized Finite Element Method (X/GFEM). DE-FEM differs from X/GFEM by placing the enriched degrees of freedom (DOFs) directly along the discontinuities, and the enrichment functions vanish at standard mesh nodes. This approach allows DE-FEM to preserve the physical meaning of standard mesh nodes and avoid the issues associated with blending elements. Moreover, by adding enrichment directly along the discontinuities, DE-FEM is more straightforward in computer implementation. These properties of DE-FEM facilitate its modeling of complex crack configurations such as the dynamic crack propagation problems with multiple cracks. Here we propose a scheme for dynamic multiple crack propagation using DE-FEM, which covers crack initiation, propagation, and interaction. Numerical examples are provided to validate the effectiveness of DE-FEM in capturing crack patterns that are similar to those observed in other studies. Meanwhile, the reasons for the numerical instabilities observed during crack propagation and methods to mitigate them are also discussed.

In recent years, the increased need for renewable energy has put more interest in wind energy and therefore in making wind turbines more efficient and building them as efficiently and cheap as possible. Delft Offshore Turbines (DOT) is developing a drivetrain that replaces the heavy and expensive parts in the nacelle of a wind turbine and makes these parts more accessible and aims to improve the reliability of the wind turbines by replacing the parts that are most prone to failure.  Due to the innovative design of their drivetrain, several unknowns still have to be answered since this has never been tried before. One of the most important parts of this drivetrain requires rolling contacts that endure high contact stresses and have to operate for a long time in harsh conditions. These rolling contacts have to be tested and for this, DOT created the Roller Test Bench (RTB) to test different materials and material combinations until failure and to see what type of failure is occurring and what the lifetime of these rollers is. The rollers are a lot smaller compared to the rollers found in the drivetrain to reduce cost and testing time. The scaling of the dimensions has been done several times in different fields of research but it is unclear how this affects the results and how the results translate to the original rollers. In literature some papers have stated that the results scale in a certain way but this has not been proven or the statements have not been argumented in a clear way such that these statements hold no ground.  A rolling contact has several ways that it can fail; wear, deformation, corrosion or fatigue are most commonly found. From the literature study performed in this thesis it has been noted that the main mode of failure in the RTB is rolling contact fatigue since the rollers are smooth, have no lubrication applied, are free of external contaminants and have no significant amount of friction on the surface. With the stress applied and the material used it is also noted that the fatigue will occur after a high amount of cycles and in literature this is also called high-cycle rolling contact fatigue. Experimental testing of such problems takes a very long time, even if the rollers are smaller and are run faster through the load cycles.  With both problems stated, the lack of information on the influence of scaling on fatigue life and the testing of high cycle fatigue, the goal of this thesis was found and it was to find a method to predict the lifetime and wear mechanisms of rolling contacts in the DOT Direct Drive Pump. This method could then be used to figure out how the scaling affects the fatigue life for rolling contacts and make a possible statement of its influence.  From the literature study a numerical modelling method was found that incorporated the microstructure and included both crack initiation and propagation and was able to model high cycle fatigue. This model suited the problem the best and was proven to provide results that agree well with previously performed experiments and their experimental results. This method implemented a Voronoi tessellation to reproduce the microstructure and applied continuum damage mechanics to calculate the damage evolution and apply the damage to the microstructure. A jump-in-cycle method was applied to improve the efficiency of the model and greatly reduce the time to model until failure. The created model is able to reproduce subsurface initiated fatigue and with that produce a scatter and L10 life comparable with previous models and experimental results. The model was validated by comparing the stress distribution, crack formation and the initiation and total lives with other models and data. The model was off the required range since the models uses an homogeneous isotropic material which causes the scatter to be lower.  With the model created and validated, it was applied to several different half-widths to test how the scaling affects the fatigue life. From the results it was noted that for a larger roller size the fatigue life decreases but it has to be noted that further tests, experimental and numerical, have to be done and improvements to the model have to be made such that at some point a correlation can be made between the scaling and the fatigue life. Further recommendations were provided on improving the model and with that creating more reliable results such that a better prediction can be made on how the fatigue life is affected but also to predict the life of a rolling contact.

The computational modeling of crack propagation is important in aerospace and automotive industries because cracks play a significant role in structural failure. In comparison with the quasi-static case, inertial effects are significant in dynamic crack propagation. The classical numerical tool for modeling dynamic crack propagation is the standard finite element method (FEM). However, the method suffers from problem of mesh-dependency. Enriched finite element procedures such as the eXtended/Generalized finite element method (X/GFEM) are able to solve this issue by adding enriched degrees of freedom (DOFs) to nodes of the original mesh, thereby providing full decoupling between the mesh and cracks. Yet, X/GFEM suffers from other issues that are inherent to the formulation such as the need for more complicated methods for applying non-zero Dirichlet boundary condition, and an intricate computer implementation. In the thesis, the Discontinuity-Enriched Finite Element Method (DE-FEM) is used to simulate dynamic crack propagation as an alternative to X/GFEM. DE-FEM also decouples cracks from the background mesh while solving X/GFEM’s aforementioned issues. This is achieved by adding enriched DOFs along cracks. Prescribing non-zero essential boundary conditions is as straightforward as in standard FEM. Moreover, DE-FEM’s enrichment strategy provides simplicity on crack propagation, as the crack tip node can be transformed into a crack segment node directly with little effort. Also, fewer enriched DOFs than in X/GFEM are appended while advancing cracks. In the numerical examples of either stationary crack with dynamic loading or dynamically propagating cracks, DE-FEM is able to reproduce analytical and/or experimental results. Both Bathe’s time integration method and the classical Newmark constant average acceleration method are applied and compared. Results show DE-FEM is a suitable candidate to solve dynamic fracture problems.

High-dimensional optimization problems with expensive and non-convex cost functions pose a significant challenge, as the non-convexity limits the viability of local optimization, where the results are sensitive to initial guesses and often only represent local minima. But as the number of expensive cost function evaluations required for a full exploration of the search space grows exponentially with the increasing number of dimensions, the use of standard global optimization algorithms is also not practical. To overcome this obstacle and to lower the dimensionality of the problem, the use of an autoencoder for model order reduction is proposed. In the resulting lower dimensional space, standard global optimization methods can then be utilized, as fewer cost functions evaluations are necessary. For problems with comparatively more expensive cost functions, this optimization includes the employment of a surrogate model, which reduces the necessary number of these computationally expensive evaluations further. This proposed method is then tested firstly on a number of benchmark functions, where it shows the ability to find global optima under certain conditions. Secondly, the proposed method is used to solve a compliance minimization problem, where it shows the ability to improve upon a large number of designs generated by local optimization.

Extensive computational resources are required to solve large-scale nonlinear problems having a finite element mesh with a large number of degrees of freedom (DOFs). Model order reduction (MOR) is a technique used to reduce these DOFs, facilitating a faster solution with reasonable accuracy. This work proposes a method for constructing a finite element-based Reduced order model (ROM) by extending the method of modal derivatives (MDs) to analyse nonlinear vibrations of geometrically complex thin-walled structures. We show that the use of MDs is an effective method to capture the geometric nonlinearities that are present in the system. After validating results with the literature, the proposed ROM is applied to the analysis of a Miura-Ori patterned origami structure and the results of the numerical simulation are compared to that of experiments.