In Metal Additive Manufacturing (MAM), support structures serve not only for mechanical supports but also for heat dissipation, preventing overheating in the melt zone. Although a high support volume aids heat dissipation, it significantly increases printing time, material wastage, and post-processing efforts. Additionally, contact area between the part and the supports often has higher surface roughness, which compromises part quality. This paper presents a novel density-based Topology Optimization (TO) technique for designing support structures optimized for efficient heat evacuation while keeping the part design fixed. First, a simplified MAM model, already established in the literature, is used to identify regions prone to overheating, referred to as ‘hotspots.’ This hotspot information is then used to formulate a TO problem that minimizes support volume while regulating the heat evacuation efficiency of the supports through thermal compliance which is defined as a constraint. For calculation of thermal compliance, a thermal load is defined using the hotspot information while the baseplate acts as a heat sink. To reduce post-processing costs, a concept of vicinity penalization is introduced, promoting the minimization of the part-support interface area. First, a set of 2D results is presented to demonstrate the method’s effectiveness and explain the influence of various parameters. Next, the TO algorithm is applied to a real-size 3D part and the results are discussed. Finally, the performance of the optimized supports is evaluated using a transient layer-by-layer AM simulation.

The quality factor (Q factor) of nanomechanical resonators is influenced by geometry and stress, a phenomenon called dissipation dilution. Studies have explored maximizing this effect, leading to softly-clamped resonator designs. This paper proposes a topology optimization methodology to design two-dimensional nanomechanical resonators with high Q factors by maximizing dissipation dilution. A formulation based on the ratio of geometrically nonlinear to linear modal stiffnesses of a prestressed finite element model is used, with its corresponding adjoint sensitivity analysis formulation. Systematic design in square domains yields geometries with comparable Q factors to literature. We analyze the trade-offs between resonance frequency and quality factor, and how these are reflected in the geometry of resonators. We further apply the methodology to optimize a resonator on a full hexagonal domain. By using the entire mesh—i.e., without assuming any symmetries—we find that the optimizer converges to a two-axis symmetric design comprised of four tethers.

In density-based topology optimization of flow problems, flow in the solid domain is generally inhibited using a penalization approach. Setting an appropriate maximum magnitude for the penalization traditionally requires manual tuning to find an acceptable compromise between flow solution accuracy and design convergence. In this work, three penalization approaches are examined, the Darcy (D), the Darcy with Forchheimer (DF), and the newly proposed Darcy with filtered Forchheimer (DFF) approach. Parameter tuning is reduced by analytically deriving an appropriate penalization magnitude for accuracy of the flow solution. The Forchheimer penalization is found to be required to reliably predict the accuracy of the flow solution. The state-of-the-art D and DF approaches are improved by developing the novel DFF approach, based on a spatial average of the velocity magnitude. In comparison, the parameter selection in the DFF approach is more reliable, as convergence of the flow solution and objective convexity are more predictable. Moreover, a continuation approach on the maximum penalization magnitude is derived by numerical inspection of the convexity of the pressure drop response. Using two-dimensional optimization benchmarks, the DFF approach reliably finds accurate flow solutions and is less prone to converge to inferior local optima.

A novel feature mapping topology optimization method is presented, allowing for the creation of features with highly flexible shapes. The method easily integrates with conventional density-based formulations. Feature shapes are implicitly described by NURBS control points. The feature shape dictates the locations of two sets of projection points to represent the solid void boundaries. At these projection points, density values are projected onto a finite element mesh. The method optimizes feature shapes in a gradient-based manner, while allowing more specific control of the feature shapes than classical level set methods. Several feature fields can be combined to create a final output design. It is found that the eminent flexibility of the NURBS-based feature definition is a benefit but also requires additional regularization to guarantee stability of the optimization.

A framework is proposed for geometric filters in density-based topology optimization. Most geometric filters feature density detection in a specified region of interest. In this method, this operation is decoupled from the finite element mesh by using interpolated densities. This allows for the filter configuration (e.g. tool orientation or printing direction) to be optimized simultaneously with the geometric layout. The framework is presented in a generic manner, and demonstrated on filters for: milling with simultaneous optimization of milling orientation; jetting with simultaneous optimization of jetting positions; and printing with simultaneous optimization of printing orientation. The performance of the framework is tested with numerical examples for compliance in 2D and 3D on a structured mesh, and in 2D on an unstructured mesh. The framework can extend the design freedom of existing filters, and can serve as a basis for the development of new geometric filters.

In topology optimization of transient problems, memory requirements and computational costs often become prohibitively large due to the backward-in-time adjoint equations. Common approaches such as the Checkpointing (CP) and Local-in-Time (LT) algorithms reduce memory requirements by dividing the temporal domain into intervals and by computing sensitivities on one interval at a time. The CP algorithm reduces memory by recomputing state solutions instead of storing them. This leads to a significant increase in computational cost. The LT algorithm introduces approximations in the adjoint solution to reduce memory requirements and leads to a minimal increase in computational effort. However, we show that convergence can be hampered using the LT algorithm due to errors in approximate adjoints. To reduce memory and/or computational time, we present two novel algorithms. The hybrid Checkpointing/Local-in-Time (CP/LT) algorithm improves the convergence behavior of the LT algorithm at the cost of an increased computational time but remains more efficient than the CP algorithm. The Parallel-Local-in-Time (PLT) algorithm reduces the computational time through a temporal parallelization in which state and adjoint equations are solved simultaneously on multiple intervals. State and adjoint fields converge concurrently with the design. The effectiveness of each approach is illustrated with two-dimensional density-based topology optimization problems involving transient thermal or flow physics. Compared to the other discussed algorithms, we found a significant decrease in computational time for the PLT algorithm. Moreover, we show that under certain conditions, due to the use of approximations in the LT and PLT algorithms, they exhibit a bias toward designs with short characteristic times. Finally, based on the required memory reduction, computational cost, and convergence behavior of optimization problems, guidelines are provided for selecting the appropriate algorithms.

The design of smart structures is challenging because of the integrated electromechanical modelling and optimization of actuators, sensors and load-bearing structures. To simplify the design process, it is common to decouple some of the components and physics and develop each part separately, which could lead to suboptimal systems. To improve the overall design of active structures, we propose an integrated and fully coupled design methodology for a certain class of smart structures. Specifically, this paper presents a numerical framework for the simultaneous application of density-based topology optimization of multi-material conductive compliant mechanisms and a composite multi-layered geometry-projection method for the optimization of the size, position and orientation of embedded piezoelectric stack actuators. Their electromechanical properties are represented in a continuum-based setting by an orientation- and geometry-dependent equivalent material model and their activation depends on the distribution of conductive material in the structure. Furthermore, a novel constraint on the polarization of the actuators is proposed to avoid unwanted designs that could cause their mechanical degradation. A set of numerical examples is analysed and discussed. The proposed framework exhibits promising results, with significant improvements in comparison to a benchmark problem.

Topology optimization methods are used to design high performance structural components that often have complex geometric layouts. In several industries, components are required to be cleanable, and for this research cleaning by jetting is considered. Thus, being able to ensure jet access on the entire surface of a structure is of interest in topology optimization. In this paper, a jetting filter is proposed, that turns a blueprint design into a jet accessible design. Two methods are considered to find an access field for each jet. These individual jet access fields are then combined into a total access field, to obtain a cleanable design. Consistent sensitivity analysis is used and the additional computational cost of the jetting filter is modest compared to the finite element analysis. The performance of the two methods is demonstrated with 2D and 3D numerical examples for mechanical and thermal topology optimization problems.

Soft grippers are ideal for grasping delicate, deformable objects with complex geometries. Universal soft grippers have proven effective for grasping common objects, however complex objects or environments require bespoke gripper designs. Multi-material printing presents a vast design-space which, when coupled with an expressive computational design algorithm, can produce numerous, novel, high-performance soft grippers. Finding high-performing designs in challenging design spaces requires tools that combine rapid iteration, simulation accuracy, and fine-grained optimization across a range of gripper designs to maximize performance, no current tools meet all these criteria. Herein, a diversity-based soft gripper design framework combining generative design and topology optimization (TO) are presented. Compositional pattern-producing networks (CPPNs) seed a diverse set of initial material distributions for the fine-grained TO. Focusing on vacuum-driven multi-material soft grippers, several grasping modes (e.g. pinching, scooping) emerging without explicit prompting are demonstrated. Extensive automated experimentation with printed multi-material grippers confirms optimized candidates exceed the grasp strength of comparable commercial designs. Grip strength, durability, and robustness is evaluated across 15,170 grasps. The combination of fine-grained generative design, diversity-based design processes, high-fidelity simulation, and automated experimental evaluation represents a new paradigm for bespoke soft gripper design which is generalizable across numerous design domains, tasks, and environments.

When employing the strut-and-tie modelling (STM) method in the conceptual design of reinforced concrete structures, a suitable strut-and-tie (ST) model indicating load transfer mechanisms first needs to be identified. Topology optimization (TO) methods have frequently been used for this purpose. However, although TO methods employing either a ground-structure or a continuum-based TO approach can be used, the performance and effectiveness of these two methods have not been systematically investigated and compared. To obtain a better understanding of the characteristics of both methods, a systematic comparison procedure is proposed to investigate the generation process and the resulting ST designs. Three aspects, relating to structural performance, economic issues, and method applicability are considered in the comparison, with six metrics formulated to quantify these aspects. Based on investigation of designs for three reinforced concrete elements incorporating typical discontinuity regions (two 2D cases and a 3D case), the performance of the two methods is assessed. It is found that both methods result in safe and efficient ST designs, with comparable structural performance, while some differences in terms of computation time and usability are observed.

Modeling of fluid flows in density-based topology optimization forms a longstanding challenge. Methods based on the Navier–Stokes equations with Darcy penalization (NSDP equations) are widely used in fluid topology optimization. These methods use porous materials with low permeability to represent the solid domain. Consequently, they suffer from flow leakage in certain areas. In this work, the governing equations for solid/fluid density-based topology optimization are reevaluated and reinterpreted. The governing equations are constructed using the volume averaged Navier–Stokes (VANS) equations, well known in the field of porous flow modeling. Subsequently, we simplify, interpret and discretize the VANS equations in the context of solid/fluid topology optimization, and analytically derive lower bounds on the Darcy penalization to sufficiently prevent flow leakage. Based on both the NSDP and VANS equations, two flow solvers are constructed using the Finite Volume method. Their precision and the lower bound on the Darcy penalization are investigated. Subsequently, the solvers are used to optimize flow channels for minimal pressure drop, and the resulting designs and convergence behavior are compared. The optimization procedure using the VANS equations is found to show less tendency to converge to inferior local optima for more precise flow solutions and is less sensitive to its parameter selection.

This paper presents a density based topology optimization method for infinite fatigue life constraints of non-proportional load cases, with a specific focus on parts with cyclic symmetry. Considering non-proportional loads in topology optimization significantly broadens the types of design problems that can be handled. The method estimates the local variation in Signed von Mises stress using a smooth min/max function and constrains the resulting stress amplitude using established stress based topology optimization methods. Accounting for non-proportionality of loading significantly increases the computation cost with respect to existing proportional methods, as the time-varying stress field needs to be computed. Inertia effects are neglected in the structural analysis. Therefore, a quasi-static analysis is used to obtain the stress history. To reduce the computational cost, advantage is taken of cyclic symmetric properties to reduce the number of necessary time steps to evaluate. This reduces the computational cost roughly proportional to the number of unique load time steps present in the repeated segments as opposed to a standard implementation. The method is tested on numerical examples in 2D and 3D for both proportional and non-proportional loads and was found to be locally accurate up to the accuracy of the constraint aggregation.

Soft robotic grasping has rapidly spread through the academic robotics community in recent years and pushed into industrial applications. At the same time, multimaterial 3D printing has become widely available, enabling the monolithic manufacture of devices containing rigid and elastic sections. We propose a novel design technique that leverages both technologies and can automatically design bespoke soft robotic grippers for fruit-picking and similar applications. We demonstrate the novel topology optimisation formulation that generates multi-material soft grippers, can solve internal and external pressure boundaries, and investigate methods to produce air-tight designs. Compared to existing methods, it vastly expands the searchable design space while increasing simulation accuracy.

Compliant mechanisms actuated by pneumatic loads are receiving increasing attention due to their direct applicability as soft robots that perform tasks using their flexible bodies. Using multiple materials to build them can further improve their performance and efficiency. Due to developments in additive manufacturing, the fabrication of multi-material soft robots is becoming a real possibility. To exploit this opportunity, there is a need for a dedicated design approach. This paper offers a systematic approach to developing such mechanisms using topology optimization. The extended SIMP scheme is employed for multi-material modeling. The design-dependent nature of the pressure load is modeled using the Darcy law with a volumetric drainage term. Flow coefficient of each element is interpolated using a smoothed Heaviside function. The obtained pressure field is converted to consistent nodal loads. The adjoint-variable approach is employed to determine the sensitivities. A robust formulation is employed, wherein a min-max optimization problem is formulated using the output displacements of the eroded and blueprint designs. Volume constraints are applied to the blueprint design, whereas the strain energy constraint is formulated with respect to the eroded design. The efficacy and success of the approach are demonstrated by designing pneumatically actuated multi-material gripper and contractor mechanisms. A numerical study confirms that multiple-material mechanisms perform relatively better than their single-material counterparts.

Additive manufacturing (AM) processes have proven to be a perfect match for topology optimization (TO), as they are able to realize sophisticated geometries in a unique layer-by-layer manner. From a manufacturing viewpoint, however, there is a significant likelihood of process-related defects within complex geometrical features designed by TO. This is because TO seldomly accounts for process constraints and conditions and is typically perceived as a purely geometrical design tool. On the other hand, advanced AM process simulations have shown their potential as reliable tools capable of predicting various process-related conditions and defects. Thus far, geometry design by topology optimization and multiphysics manufacturing simulations have been viewed as two mostly separate paradigms, whereas one should really conceive them as one holistic computational design tool. More specifically, AM process models provide input to physics-based TO, where consequently, not only the designed component will function optimally, but also will have near-to-minimum manufacturing defects. In this regard, we aim at giving a thorough overview of holistic computational design tool concepts applied within AM. First, literature on TO for performance optimization is reviewed and then the most recent developments within physics-based TO techniques related to AM are covered. Process simulations play a pivotal role in the latter type of TO and serve as additional constraints on top of the primary end-user optimization objectives. As a natural consequence of this, a comprehensive and detailed review of non-metallic and metallic additive manufacturing simulations is performed, where the latter is divided into micro-scale and deposition-scale simulations. Material multi-scaling techniques, which are central to the process-structure-property relationships, are reviewed next, followed by a subsection on process multi-scaling techniques, which are reduced-order versions of advanced process models and are incorporable into physics-based TO due to their lower computational requirements. Finally the paper is concluded and suggestions for further research paths discussed.

This paper presents a method to consider uncertainties in the distortion prediction of additive manufacturing processes within robust topology optimization. The random variable of the stochastic additive manufacturing process is the inherent thermomechanical strain, typically determined by process characterization experiments. The value of the inherent strain per se encompasses uncertainty due to differences between characterization and production geometries, uncontrolled process variations, hatching pattern choices, and other effects not captured in layer-by-layer part-scale additive manufacturing simulation. These effects can be represented by different inherent strains for each realized layer, therefore, model the variability in part distortion. Instead of employing a more detailed simulation approach, requiring significantly more process data and computation time, our method aims at generating a robust design in this setting, to obtain parts exhibiting reduced distortion regardless of uncertainties in distortion prediction. The formulation benefits from the superposition potential within the employed process simulation. For robust optimization, the expected part distortion and its estimated variance are included in the standard density-based topology optimization algorithm's objective function. The effectiveness of the approach is demonstrated by simultaneously optimizing structural performance combined with a minimized additive manufacturing part distortion under uncertain process conditions.

Overheating is a major issue especially in metal Additive Manufacturing (AM) processes, leading to poor surface quality, lack of dimensional precision, inferior performance and/or build failures. A 3D density-based topology optimization (TO) method is presented which addresses the issue of local overheating during metal AM. This is achieved by integrating a simplified AM thermal model and a thermal constraint within the optimization loop. The simplified model, recently presented in literature, offers significant computational gains while preserving the ability of overheating detection. The novel thermal constraint ensures that the overheating risk of optimized designs is reduced. This is fundamentally different from commonly used geometry-based TO methods which impose a geometric constraint on overhangs. Instead, the proposed approach takes the process physics into account. The proposed method is validated via an experimental comparative study. Optical tomography (OT) is used for in-situ monitoring of process conditions during fabrication and obtained data is used for evaluation of overheating tendencies. The novel TO method is compared with two other methods: standard TO and TO with geometric overhang control. The experimental data reveals that the novel physics-based TO design experienced less overheating during the build as compared to the two classical designs. A study further investigated the correlation between overheating observed by high OT values and the defect of porosity. It shows that overheated regions indeed show higher defect of porosity. This suggests that geometry-based guidelines, although enhance printability, may not be sufficient for eliminating overheating issues and related defects. Instead, the proposed physics-based method is able to deliver efficient designs with reduced risk of overheating.

In metal Additive Manufacturing (AM), the deposited material is subjected to a series of heating and cooling cycles. The locally occurring temperature extremes and cooling rates determine solid-state phase fractions, material microstructure, texture, and ultimately the local material properties. As the shape of a part determines the local thermal history during AM, this offers an opportunity to influence these material properties through design. In this paper, we present a way to obtain desired properties by controlling the local thermal history. This is achieved through topology optimization of the printed part while considering its entire transient thermal history. As an example of this approach, this work focuses on high strength low alloy steels, where resulting phase fractions significantly influence mechanical properties such as yield strength and ductility. These solid-state phase fractions depend on cooling rates in a particular critical temperature range. The phase composition and hence the local yield strength in target regions can be controlled by constraining the cooling time in this range. Numerical examples illustrate the capability of the proposed approach in adapting part designs to achieve various desired material properties.

Topology optimization has seen increased interest with the rise of additive manufacturing (AM) as a fabrication method, because of its ability to exploit the geometric complexity that AM offers. However, AM still imposes some geometric restrictions on the design, most notably on minimum feature size, overhang angles, and enclosed voids. Enclosed voids are problematic because for many AM methods it is impossible to remove supports, unmelted powder or uncured liquid from them. This paper introduces a filter based on a cumulative sum flood fill algorithm to alleviate this issue in a flexible manner. This filter produces a density field where every enclosed void element is rendered solid. It successfully eliminates enclosed voids in both 2D and 3D problems, with low computational cost due to its geometric nature. In addition we demonstrate direct control over the location, amount, and size of powder removal features by varying boundary conditions for the filter, running additional flood fills, and adding morphology operators, respectively.

In design optimization of bulk handling equipment (BHE) we generally focus on the mean performance of the equipment. However, granular materials behave stochastic due to irregularities in particle shape and size which leads to stochastic performance of the equipment. To include the stochastic performance we propose robust metamodel-based design optimization (MBDO). The used metamodels are trained with stochastic performance data from randomly repeated discrete element method (DEM) simulations and predict mean and variance of the equipment performance. This method is compared to the conventional deterministic optimization method by means of a case study of a discharging hopper including verification and validation. The robust MBDO shows more distinctive optimal designs compared to the deterministic approach. In addition, the DEM-based metamodel is a relatively accurate method to predict DEM-model simulation results. However, the validation indicates that differences between DEM-model and experimental results highly affect the reliability of the found optima.