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.

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.

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.

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.

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.

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.

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.

Concrete, as the most widely used construction material, is associated with a high environmental impact. Within the present study, structural optimization is the method of choice to counter this issue. The entire process, from optimization, to design, experiments and numerical simulation is outlined. Embedded in the framework of a design competition (Concrete Girder Optimization Competition 2021), a bridge between structural engineering and mathematical optimization is demonstrated. Two design concepts for optimized concrete girders, one with internal and one with external reinforcement, yet both based on strut-and-tie modeling, were investigated. Within the boundaries of the competition, several conclusions can be drawn: The results indicate the importance of an adequate structural interpretation of topology optimization results to obtain satisfying structural performance. The environmental evaluation outlines that the reinforcement mass has a substantial share in the total Global Warming Potential. A successful numerical re-simulation of selected girders can serve as a modeling base for other researchers. Compared to a conventionally designed girder an increase in resource efficiency, measured by load-carrying capacity versus environmental impact, of more than 30% was achieved.

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 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.

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 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.

The design of high-performance mechatronic systems is very challenging, as it requires delicate balancing of system dynamics, the controller, and their closed-loop interaction. Topology optimization provides an automated way to obtain systems with superior performance, although extension to simultaneous optimization of both topology and controller has been limited. To allow for topology optimization of mechatronic systems for closed-loop performance, stability, and disturbance rejection (i.e. modulus margin), we introduce local approximations of the Nyquist curve using circles. These circular approximations enable simple geometrical constraints on the shape of the Nyquist curve, which is used to characterize the closed-loop performance. Additionally, a computationally efficient robust formulation is proposed for topology optimization of dynamic systems. Based on approximation of eigenmodes for perturbed designs, their dynamics can be described with sufficient accuracy for optimization, while preventing the usual threefold increase of additional computational effort. The designs optimized using the integrated approach have significantly better performance (up to 350% in terms of bandwidth) than sequentially optimized systems, where eigenfrequencies are first maximized and then the controller is tuned. The proposed approach enables new directions of integrated (topology) optimization, with effective control over the Nyquist curve and efficient implementation of the robust formulation.

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.

Computational process modelling of metal additive manufacturing has gained significant research attention in recent past. The cornerstone of many process models is the transient thermal response during the AM process. Since deposition-scale modelling of the thermal conditions in AM is computationally expensive, spatial and temporal simplifications, such as simulating deposition of an entire layer or multiple layers, and extending the laser exposure times, are commonly employed in the literature. Although beneficial in reducing computational costs, the influence of these simplifications on the accuracy of temperature history is reported on a case-by-case basis. In this paper, the simplifications from the existing literature are first classified in a normalised simplification space based on assumptions made in spatial and temporal domains. Subsequently, all types of simplifications are investigated with numerical examples and compared with a high-fidelity reference model. The required numerical discretisation for each simplification is established, leading to a fair comparison of computational times. The holistic approach to the suitability of different modelling simplifications for capturing thermal history provides guidelines for the suitability of simplifications while setting up a thermal AM model.

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.

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.

A novel constraint to prevent local overheating is presented for use in topology optimization (TO). The very basis for the constraint is the Additive Manufacturing (AM) process physics. AM enables fabrication of highly complex topologically optimized designs. However, local overheating is a major concern especially in metal AM processes leading to part failure, poor surface finish, lack of dimensional precision, and inferior mechanical properties. It should therefore be taken into account at the design optimization stage. However, including a detailed process simulation in the optimization would make the optimization intractable. Hence, a computationally inexpensive thermal process model, recently presented in the literature, is used to detect zones prone to local overheating in a given part geometry. The process model is integrated into density-based TO in combination with a robust formulation, and applied in various numerical test examples. It is found that existing AM-oriented TO methods which rely purely on overhang control do not ensure overheating avoidance. Instead, the proposed physics-based constraint is able to suppress geometric features causing local overheating and delivers optimized results in a computationally efficient manner.

The design of high-precision motion stages, which must exhibit high dynamic performance, is a challenging task. Manual design is difficult, time-consuming, and leads to sub-optimal designs that fail to fully exploit the extended geometric freedom that additive manufacturing offers. By using topology optimization and incorporating all manufacturing steps (printing, milling, and assembly) into the optimization formulation, high-quality optimized and manufacturable designs can be obtained in an automated manner. With a special focus on overhang control, minimum feature size, and computational effort, the proposed methodology is demonstrated using a case study of an industrial motion stage, optimized for maximum eigenfrequencies. For this case study, an optimized design can be obtained in a single day, showing a substantial performance increase of around 15% as compared to a conventional design. The generated design is manufactured using laser powder-bed fusion in aluminum and experimentally validated within 1% of the simulated performance. This shows that the combination of additive manufacturing and topology optimization can enable significant gains in the high-tech industry.