Search

Additive manufacturing (AM) has enabled the production of intricate lattice structures with excellent performance and minimal mass. Design approaches that consider static loading, including lattice-based topology optimization (TO), have been well-researched recently. However, to date, there appears to be no widely accepted method of optimizing lattice structures for high-strain rate loading, especially when the design for additive manufacturing (DFAM) principles are considered. This study proposes a computational framework for the design of lattice structures under specified impact loading. To manage dimensionality while achieving sufficient generality, a heuristic design space is developed that relies on traditional TO to govern the design's macrostructure and standard dimensioning to govern its mesostructure. DFAM principles are then incorporated into a Bayesian optimization scheme wrapped around traditional TO to achieve manufacturable designs that absorb high-impact loading. Because this approach does not require analytical gradient information, the framework can be used to optimize directly on complex objectives, such as injury metrics calculated from the acceleration curve. A series of case studies is formulated around a mass-performance tradeoff and involves individual unit cell design as well as full-part design. The proposed design parameterization is found to enable sufficient flexibility to achieve consistently good performance regardless of AM build orientation. [ABSTRACT FROM AUTHOR]

Objectives: The objective of this paper was to compare the effectiveness of different materials for mouthguards in preventing oral and maxillofacial injuries during sports activities. The present study compares the stress-reduction and energy absorption capabilities of two other fused filament materials — poly(lactic-acid plus) (PLA+) and polycarbonate (PC), with Ethylene-vinyl acetate (EVA), which is the most commonly used material for mouthguard fabrication. Materials and methods: Two human skulls were modelled, and a boxing glove simulated punches along the x, y, and z-axes with 5 mm displacement with 1 kN force. Firstly, the maximum principal stress curve in the skull was compared for forces along the three perpendicular directions. Furthermore, the present study examines materials energy absorption properties, including their specific energy absorption characteristics and initial peak von Mises stresses. Additionally, a topology optimization approach is used to create an alternative design for a mouthguard to improve specific energy absorption. Results: The model without a mouthguard showed the highest stress concentration of 32.298 MPa in the teeth, followed by the EVA material, which resulted in a maximum principal stress of 28.525 MPa. Fused filament 3D materials, such as PLA + and PC, on the other hand, showed better mechanical effectiveness in both lower jaw dislocation and lower maximum principal stress by 30.82% and 51.25% in the mandibular and maxillary teeth. Though EVA comparatively shows better specific energy absorption capability at 2.24 kJ/kg post-optimization than PLA + and PC, the peak principal stress experienced in the mandibular region was comparatively higher. The topology optimization, however, improved the energy-absorbing capabilities of PLA + by 4.5 times, reaching 1.37 kJ/kg and PC from 0.165 kJ/kg to 0.38 kJ/kg. Conclusions: This study demonstrates that PLA + and PC have better stress reduction capabilities than EVA and could be promising materials for the fabrication of mouthguards in sports activities. This study highlights the importance of topology optimization in dental materials science and engineering to develop safer and more effective mouthguard designs. [ABSTRACT FROM AUTHOR]

• Reliability-based non-probabilistic multiscale topology optimization (NRBMTO) with stress constrained is proposed. • The p-norm function aggregates global unit stresses. • Mechanical and thermo-mechanical loads are considered as non-probabilistic uncertain parameters. • Ellipsoid modeling describes uncertainty in non-probabilistic random variables. • NRBMTO results in more security than the traditional deterministic multiscale topology optimization (DMTO) approach. A reliability-based non-probabilistic multiscale topology optimization (NRBMTO) method with stress constraints is proposed for thermo-mechanical continuous structures with uncontrollable stresses. The physical parameters, external loads and temperature values at the macro scale, are regarded as non-probabilistic uncertain parameters in the optimization of structural topologies with complex physical fields at multi-scale. The homogenization-based finite element method is employed to quantify thermo-mechanical structures with multi-scale uncertain parameters in the established multi-scale topology model. The ellipsoid model is applied to describe the uncertainty of non-probabilistic random variables, and the non-probabilistic reliability index is obtained by estimating the failure probability based on the first-order reliability method (FORM). The unit stresses are aggregated to the global maximum stresses with the normalized p-norm function, taking into account the mechanical and thermal stresses. The sensitivity information of the compliance and stress constraint to the macro- and micro-design variables and uncertain variables are derived simultaneously. The macro- and micro- design variables are solved by the method of moving asymptotes (MMA), respectively. Several numerical examples are given to verify the effectiveness and feasibility of the proposed NRBMTO method. The results demonstrate that the optimized structure based on the NRBMTO method provides better security with reliability index β =3 and minimum compliance (244.39) while stress is controlled below 235 MPa compared to the classical deterministic multiscale topology optimization (DMTO) method. [ABSTRACT FROM AUTHOR]

Flow boiling in microchannels has attracted wide attention due to its excellent heat transfer capability, but flow boiling instability is a huge challenge limiting its application. Instability can lead to a series of problems, such as uneven flow distribution, temperature and pressure drop oscillations. This work proposes a novel asymmetric check microvalve (ACMV) structure, exhibiting high ratio of resistance between the reverse and forward flow. The results show the reverse pressure drop of the ACMV structure is 2.06 times that of the forward pressure drop, and the forward flow resistance of the ACMV structure is 16% smaller than that of the conventional inlet restrictor. In addition, bubble dynamics of an isolated bubble in the generated channel under dual outlet condition was numerically investigated. It is found that the bubble grows symmetrically in the rectangular channel upstream and downstream. The distance of bubble movement downstream in the microchannel with ACMV is three times that of the microchannel with inlet restrictor. The microchannel with ACMV can suppress the backflow of isolated bubble better than microchannel with inlet restrictor. Moreover, the growth of the bubble downstream extends the effective evaporation domain, which contributes to the enhanced bubble growth rate. The ACMV is expected to be a potential replacement for the conventional inlet restrictor, which provides a novel and efficient solution for future heat dissipation from high power devices. [ABSTRACT FROM AUTHOR]

Multi-material lattice structures demonstrate superior mechanical advantages and lightweight potential, enabling it preferable in many engineering fields, especially with the rise of additive manufacturing. However, employing multi-scale topology optimization inherently involves computational complexities of designing the macromaterial distribution and microlattice geometric size simultaneously. In this paper, a modified relative density mapping (MRDM) method is proposed, which generates a multi-material lattice structure by projecting the continuum multi-material topology optimization results. The proposed method extends the standard relative density mapping (RDM) method to multi-material problem and improves the performance. To achieve such purpose, a new mapping relation considering multi-material density and stress information is introduced to generate mapping weight of materials, which is the most novel contribution. Second, to avoid intersection of different materials, two types of material mapping strategies, namely continuous mapping strategy, and discrete mapping strategy, are introduced to generate multi-material lattice structure using the mapping weight of materials. Several numerical examples are exhibited, which demonstrate that the proposed method is capable of generating a multi-material lattice structure with clear material interface and good performance. [ABSTRACT FROM AUTHOR]

By analyzing the results of compliance minimization of thermoelastic structures, we observed that microstructures play an important role in this optimization problem. Then, we propose to use a multiple variable cutting (M–VCUT) level set-based model of microstructures to solve the concurrent two–scale topology optimization of thermoelastic structures. A microstructure is obtained by combining multiple virtual microstructures that are derived respectively from multiple microstructure prototypes, thus giving more diversity of microstructure and more flexibility in design optimization. The effective mechanical properties of microstructures are computed in an off-line phase by using the homogenization method, and then a mapping relationship between the design variables and the effective properties is established, which gives a data-driven model of microstructure. In the online phase, the data-driven model is used in the finite element analysis to improve the computational efficiency. The compliance minimization problem is considered, and the results of numerical examples prove that the proposed method is effective. [ABSTRACT FROM AUTHOR]

The moving morphable components (MMC) method has been widely used for topology optimization due to its ability to provide an explicit description of topology. However, the MMC method may encounter the instability issue during iteration. Specifically, the iteration history is highly sensitive to parameters of the optimizer, that is, the move limits in the method of moving asymptotes (MMA). Additionally, the final topology obtained from the MMC method usually depends on the initial values. To address these issues and improve the stability of the MMC method in practical applications, this article introduces two strategies. The first strategy is based on the time‐series MMC (TSMMC) method, which proposes a unified description of curved components. However, the use of control‐points‐based design variables may introduce instability into the iteration process due to the strong locality associated with these variables. To mitigate this, global design variables have been incorporated into the formulation. Numerical examples demonstrate that this mixed formulation, combining global and local design variables, can enhance stability significantly. To further enhance stability, the second strategy involves using the trust region‐based moving asymptotes (TRMA) method as the optimizer instead of MMA. The TRMA method incorporates an accuracy control mechanism, resulting in stable and fast convergence behavior, as demonstrated in the numerical examples. [ABSTRACT FROM AUTHOR]

Bidirectional controllable propagation of waterborne sound holds significant importance in developing multifunctional underwater acoustic and mechanical devices. However, the existing waterborne acoustic metasurfaces have rarely explored the bidirectional sound modulations. Here, a class of Janus waterborne acoustic metasurface, enabling two‐faced arbitrarily asymmetric wavefront manipulations is reported. A three‐degree‐of‐freedom mechanical system facilitated by acoustic‐structure interaction underwater is proposed to introduce bianisotropic responses of unit cells. Monolayer ultrathin Janus metasurface is inversely designed by utilizing a function‐structure integrated topology optimization framework. Distinct underwater acoustic functionalities, including axial and oblique focusing, beam splitting, and sound diffusion, are successfully demonstrated. Underwater experiments are further conducted to validate the concept of Janus metasurface. The good consistency between experimental and simulated results confirms the excellent two‐faced asymmetric acoustic focusing performance. The proposed Janus metasurface opens up a new dimension for designing advanced waterborne acoustic devices with two‐faced multifunctional wavefront manipulations. [ABSTRACT FROM AUTHOR]

This article extends recently developed finite variation sensitivity analysis (FVSA) approaches to an inverse homogenization problem. The design of metamaterials with prescribed mechanical properties is stated as a discrete density‐based topology optimization problem, in which the design variables define the microstructure of the periodic base cell. The FVSA consists in estimating the finite variations of the objective and constraint functions after independently switching the state of each variable. It is used to properly linearize the functions of binary variables so the optimization problem can be solved through sequential integer linear programming. Novel sensitivity expressions were developed and it was shown that they are more accurate than the ones conventionally used in literature. Referred to as the conjugate gradient sensitivity (CGS) approach, the proposed strategy was quantitatively evaluated through numerical examples. In these examples, metamaterials with prescribed homogenized Poisson's ratios and minimal homogenized Young's moduli were obtained. A hexagonal base cell with dihedral D3$$ {D}_3 $$ symmetry was used to produce only metamaterials with isotropic properties. It was shown that, by using the CGS approach instead of the conventional sensitivity analysis, the sensitivity error was substantially reduced for the considered problem. The proposed developments effectively improved the stability and robustness of the discrete optimization procedures. In all the considered examples, when more accurate sensitivity analyses were performed, the parameters of the topology optimization method could be tuned more easily, yielding effective solutions even if the settings were not ideal. [ABSTRACT FROM AUTHOR]

AbstractThis article proposes an enhanced proportional topology optimization (EPTO) method to solve the structural topology optimization problem of minimizing compliance under material volume constraints. In the proposed method, a new filtering weight function based on the improved Heaviside threshold function is adopted to filter element density during the optimization process. The optimization process of the EPTO method consists of an inner loop and an outer loop. In the inner loop, density distribution is modified in combination with a new filtering weight function. By locally averaging the weighted element compliance, an improved density distribution function in the inner loop is put forward to make the topology configuration of the optimized structure more reasonable. In addition, the projection method is used to reduce the number of intermediate density elements, thereby obtaining optimization results with clear boundaries. In the outer loop, a new termination criterion is adopted, which terminates the optimization process by determining that the relative error of the objective function in several consecutive iterations is less than the specified value. The effectiveness and efficiency of the proposed method are demonstrated through several numerical examples involving two-dimensional (2D) and three-dimensional (3D) topology optimization problems. The results of numerical examples show that the proposed method can not only accelerate the convergence of optimization iterations, but also obtain optimized structures with smaller objective function values and better topology configurations. HIGHLIGHTSA new density filtering weight function is proposed based on an improved Heaviside threshold function.An improved inner loop density distribution formula is proposed by combining a new filtering weight function.Using projection based methods to suppress the appearance of intermediate density elements.Verify the effectiveness of the proposed algorithm by comparing the optimization results with existing algorithms such as top88 and PTO.A new density filtering weight function is proposed based on an improved Heaviside threshold function.An improved inner loop density distribution formula is proposed by combining a new filtering weight function.Using projection based methods to suppress the appearance of intermediate density elements.Verify the effectiveness of the proposed algorithm by comparing the optimization results with existing algorithms such as top88 and PTO. [ABSTRACT FROM AUTHOR]

AbstractThis work proposes topology optimization for steel I-beams, including consideration of bolted beam-column connections with geometric and material nonlinear analysis. The aim is to assess and compare the topological configurations influenced by different connections, examining their stress distribution and rotational stiffness to illustrate the potential of structural optimization. The bi-directional evolutionary structural optimization (BESO) approach is implemented. Furthermore, several bolted steel beam-column configurations were validated based on experimental tests. Subsequently, a series of finite element models were developed, contributing to a comprehensive understanding of the plastic-limit behavior of I-beams under different loading conditions. The proposed method could potentially use a lesser quantity of material while maintaining the same level of structural performance. The results indicate that the implementation of structural topology optimization on I-beams while considering various beam-column connections, yields structural performance similar to that of solid web configurations, achieved through material reduction. [ABSTRACT FROM AUTHOR]

This paper presents a level-set topology optimization approach that uses conformal meshes for the analysis of the displacement field. The structure’s boundary is represented by the iso-contour of a level-set field discretized on a fixed background design mesh. The conformal mesh is updated for each design iteration via a PDE based mesh morphing process that identifies the set of facets in the background mesh that are homeomorphic to the boundary and relaxes the homeomorphic mesh to conform to the structure’s boundary and ensure high element quality. The conformal mesh allows for a more accurate computation of the response versus density and some level-set based methods which interpolate material properties using the volume fraction. Numerical examples illustrate the proposed approach by optimizing linear-elastic two- and three-dimensional structures, wherein insight into the performance of the mesh morphing process is provided. The examples also highlight the scalability of the approach. [ABSTRACT FROM AUTHOR]

As a method of lightweight design, multi-material design aims to make targeted use of materials in order to reduce CO2 emissions. In this context, it can be described as one of the product development methods used to meet the challenges of climate change. However, since the design of structures in multi-material design is complex, topology optimization can be used to support the product developer. In this article, a multi-material topology optimization method is developed that combines the Velocity Field Level Set method with the Reconciled Level Set method. Furthermore, the current design is explicitly resolved in each iteration by means of multi-material remeshing. The edge collapse phase in the remeshing process is achieved by applying the producer consumer pattern. The developed method is then validated using known examples from the state of research, and the influence of the parameters of the method on the result is analyzed by means of studies. [ABSTRACT FROM AUTHOR]

In order to effectively achieve the optimization design of the aircraft cargo rack, based on finite element modal simulation, the structure was redesigned and analyzed using two schemes of surrogate model size optimization and topology optimization, ensuring the strength requirements while improving the natural frequency and reducing the weight. According to the modal shape of vibration, additional bridge structures were added at the weak points to improve the dynamic stiffness of the structure. According to the optimization design requirements, the response surface function was constructed, and the particle swarm optimization algorithm was applied in the size optimization and surrogate model solution. A multi-objective optimization model was established for flexibility and low-order natural frequencies, and topology optimization was carried out in HyperWorks. The structural dynamic modification of the topology optimization model was performed using the modal strain energy analysis method. The research results show that both optimization methods can achieve good lightweight design. The static performance of the optimized structure is stable, and the overall modal frequency is improved. [ABSTRACT FROM AUTHOR]

A means of reducing the computational cost in robust topology optimization is discussed. Without proper countermeasures, topology optimization can lead to artificially well-performing solutions for certain design problems, with unrealistic hinges that would break in reality. Enforcement of minimum length scales in both solid and void phases of the optimized designs mitigates this problem. The robust approach to topology optimization has been shown to produce designs that have such a two-phase minimum length scale. However, a drawback of the robust approach is the fact that multiple finite element analyses are needed per iteration step of the optimization, which slows down the optimization process. We therefore investigate the possibility of speeding up the computations by replacing some of the calculations based on finite element analyses with Taylor series approximations. Specifically, we consider first-, second-, third- and fourth-order Taylor series approximations of the objective functions of the dilated and eroded designs as a function of the projection threshold parameter. This robust approach with Taylor series approximations is tested by applying it to a compliant gripper design problem. It is shown that Taylor series approximations can be used to speed up the optimization process in robust topology optimization. [ABSTRACT FROM AUTHOR]

In order to solve the loosening problem caused by stress shielding of femoral stem prostheses in clinical practice, an optimization design method of a personalized porous titanium alloy femoral stem is proposed. According to the stress characteristics of the femur, the porous unit cell structures (TO-C, TO-T, TO-B) under three different loads of compression, torsion, and bending were designed by topology optimization. The mechanical properties and permeability of different structures were studied. Combined with the porous structure optimization, a personalized radial gradient porous titanium alloy femoral stem was designed and manufactured by selective laser melting (SLM) technology. The results show that the TO-B structure has the best comprehensive performance among the three topologically optimized porous types, which is suitable for the porous filling structure of the femoral stem, and the SLM-formed porous femoral stem has good quality. The feasibility of the personalized design and manufacture of porous titanium alloy implants is verified, which can provide a theoretical basis for the optimal design of implants in different parts. [ABSTRACT FROM AUTHOR]

Traditional topology optimization methods only consider a limited number of loads in the optimization procedure, neglecting load variations common in real-world scenarios. To incorporate real load scenarios, robust topology optimization considers uncertainties in load directions while minimizing compliance, generating structures capable of withstanding variations in the load. This paper incorporates the angles of the load directions as parameters into the optimization formulation to design structures that perform well under a range of load directions. Additionally, the formulation is extended to incorporate local volume constraints to balance the solution distribution throughout a domain, achieving more complex designs with proper material distribution as the angle of the loads and the number of sub-regions increases while maintaining consistency in the worst-case scenario. Two and three-dimensional examples demonstrate that topology-optimized designs are susceptible to loads that vary in direction and magnitude, and by considering realistic loading conditions, this formulation yields robust, reliable designs, markedly enhancing their suitability for actual engineering applications. [ABSTRACT FROM AUTHOR]

This paper introduces a novel method for optimal shape design of thick shells. We consider shells based on the Reissner-Mindlin theory, with the assumption of linear elastic material behavior. The goal is to find the optimal material distribution within the shell’s mid-surface. This is achieved using a cost function that minimizes the volume while considering stress-based constraints, with the material distribution represented by a level set function. The evolution of the shape is driven by the gradient of the cost function within the framework of a Hamilton–Jacobi equation. Both the level set and the displacement fields are described using computer aided design compatible tools, within the framework of isogeometric analysis. This allows for precise definition of the optimal shape and straightforward export of the resulting design to commercial software for manufacturing. Furthermore, the proposed method handles complex, non-conforming multi-patch geometries thanks to an augmented Lagrangian formulation. The latter guarantees strong compatibility with real-world engineering applications. The effectiveness of the method is demonstrated through its application to various three-dimensional multi-patch geometries under different loading conditions. [ABSTRACT FROM AUTHOR]

To improve the efficiency of topology optimization for piezoelectric energy harvesters (PEHs), this paper proposes a discrete level set method enhanced by conformal mapping. By mapping the PEH onto a 2D regular domain, the original 3D topology optimization problem is simplified as a 2D problem by using a scalar function. Then re-meshing and barycentric interpolation theory are used to simplify the solution of the driving equation and resolve the issue of inconsistent discretization between the level set function and the finite element model. Moreover, based on the proposed method, the finite element expression of the piezoelectric shell element is derived, taking into account the piezoelectric material coupling effect and polarization direction. This leads to an accurate numerical solution for the optimization process. Resultantly, numerical examples demonstrate that proposed method enables the optimization using a simple discretization, while effectively preserving surface characteristics of PEHs. Hence, this method offers a new approach for the structural optimization of PEHs. [ABSTRACT FROM AUTHOR]

In this study the optimum topology distribution of the magnetorheological elastomer (MRE) layer in an adaptive sandwich plate is investigated. The adaptive sandwich plate consists of an MR elastomer layer embedded between two thin elastic plates. A finite element model has been first formulated to derive the governing equations of motion. A design optimization methodology incorporating the developed finite element model has been subsequently developed to identify the optimum topology treatment of the MR layer to enhance the vibration control in wide-band frequency range. For this purpose, the dynamic compliance and density of each element are defined as the objective function and design variables in the optimization problem, respectively. The method of the solid isotropic material with penalization (SIMP), is extended for material properties interpolation leading to a new MRE-based penalization (MREP) model. Method of moving asymptotes (MMA) has been subsequently utilized to solve the optimization problem. The developed finite element model and design optimization method are first validated using benchmark problems. The proposed design optimization methodology is then effectively utilized to investigate the optimal topologies of the magnetorheological elastomer (MRE) core layer in MRE-based sandwich plates under various boundary and loading conditions. Results show the effectiveness of the proposed design optimization methodology for topology optimization of MRE-based sandwich panels to mitigate the vibration in wide range of frequencies. [ABSTRACT FROM AUTHOR]

To design a patient-specific subperiosteal implant for a severely atrophic maxillary ridge using yttria-stabilized additively manufactured zirconia (3YSZ) and evaluate its material properties by applying topology optimization (TO) to replace bulk material with a lattice structure. A contrast-based segmented skull model from anonymized computed tomography data of a patient was used for the initial anatomical design of the implant for the atrophic maxillary ridge. The implant underwent finite element analysis (FEA) and TO under different occlusal load-bearing conditions. The resulting implant designs, in bulk material and lattice, were evaluated via in-silico tensile tests and 3D printed. The workflow produced two patient-specific subperiosteal designs: a) an anatomically precise bulk implant, b) a TO lattice implant. In-silico tensile tests revealed that the Young's modulus of yttria-stabilized zirconia is 205 GPa for the bulk material and 83.3 GPa for the lattice. Maximum principal stresses in the implant were 61.14 MPa in bulk material and 278.63 MPa in lattice, both tolerable, indicating the redesigned implant can withstand occlusal forces of 125–250 N per abutment. Furthermore, TO achieved a 13.10 % mass reduction and 208.71 % increased surface area, suggesting improved osteointegration potential. The study demonstrates the planning and optimization of ceramic implant topology. A further iteration of the implant was successfully implanted in a patient-named use case, employing the same fabrication process and parameters. • Novel ceramic maxillary subperiosteal implant design. • Topology optimization of occlusal stresses. • Osseoconductive custom-lattice for light weight implant. • 3D printed yttria-stabilized zirconia ceramic. • Implant successfully placed into a patient-named use case. [ABSTRACT FROM AUTHOR]

Electroactive polymers (EAPs) deform when subject to an electric field, which is generated by two or more electrodes. To ensure proper function of the EAP, these electrodes are connected to a source and they are therefore required to be continuous such that no isolated islands exist. Increasing an EAP's performance using topology optimization while ensuring electrode connectivity is the goal of this work. A topology optimization formulation is introduced where electrode connectivity is ensured using the virtual temperature method. Numerical experiments demonstrate that this is an efficient method to guarantee connectivity. [ABSTRACT FROM AUTHOR]

Component sequence preservation is an intrinsic requirement in typical engineering applications, such as deployable chain-like structures, 3D printing structures with contour-parallel toolpaths, additive manufacturing of continuous fibre-reinforced polymer structures, customized stents, and soft robotics parts. This study presents a feature-driven method that preserves component sequences accounting for engineering requirements. The chain-of-bars design variables setting scheme is developed to realize the sequential component's layout, which sets the current bar's end point as the next bar's start point. The total length of the printing path is constrained to reduce the consumption of material accurately. Also, the angle between adjacent bars is constrained to avoid sharp angles at the turning point of the 3D printing path. Next, the sensitivity analysis considering the inter-dependence of substructures is performed. Several numerical examples are given to demonstrate the validity and merits of the proposed method in designing structures preserving component sequences. [ABSTRACT FROM AUTHOR]

Biomedical engineering relies on topology optimization to refine material distribution, crucial for lightweight, high-performance prostheses and orthoses. Advanced manufacturing techniques like additive manufacturing can then be used to create these intricate designs layer by layer, ensuring precision and customization. However, conventional numerical simulation-based topology optimization methods can be time-consuming and resource-intensive, especially as the design domain expands. To overcome this issue, machine learning models are investigated for their ability to perform topology optimization. The results indicate a significant decrease in computation time, along with comparable optimization performance to conventional methods. [ABSTRACT FROM AUTHOR]

Technological progress is leading to the incorporation of digital twinning and artificial intelligence, causing engineering design and scientific procedures to transition into an AI-driven age. Digital twinning and modeling have been increasingly included into engineering design optimization, particularly via processes like topology optimization and generative design, to provide modern design solutions efficiently. The integration of topology optimization with additive manufacturing is revolutionizing the design optimization process in the automotive industry, where there is a pressing demand for lightweight design and improving production efficiency. A design optimization methodology has been developed to optimize an Automotive Seatbelt Bracket subjected to dynamic load and fatigue. The innovative design is lighter and consolidates the entire assembly into a single body that can be manufactured using additive manufacturing. [ABSTRACT FROM AUTHOR]

Recently, CAD environments have integrated topology optimization (TO) tools, enabling rapid development and manufacturing of parts with optimized mechanical properties. However, different CAD platforms incorporate TO differently, making a comparative analysis necessary. This study aims to systematically compare the efficiency, material usage, and design quality of five commonly used CAD/TO platforms when applied to the topology optimization of a six degrees of freedom robotic arm. The objective is to identify the key differences in how these platforms influence the final design and manufacturing outcomes. Practical validation of results is provided by printing and assembling optimized components into a fully functional robotic arm. Our findings indicate differences in optimization efficiency, material usage, and print time between analyzed platforms. Strengths and weaknesses of each platform are indicated and recommendations for optimization parameters are provided. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Shenyang Agricultural University is the property of Journal of Shenyang Agricultural University Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Xi'an Jiaotong University is the property of Editorial Office of Journal of Xi'an Jiaotong University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

With the advancement of deep-sea exploration, the demand for underwater manipulators capable of long-duration heavy-duty operations has intensified. Water-hydraulic systems exhibit less viscosity variation with increasing depth than oil-based systems, offering better adaptability to deep-sea conditions. Using seawater as the driving medium inherently eliminates issues such as oil contamination by water, frequent maintenance limiting underwater operation time, and environmental pollution caused by oil leaks. This paper introduces a deep-sea manipulator directly driven by seawater from the deep-sea environment. To address the challenges of weak lubrication and high corrosion associated with water hydraulics, a reciprocating plunger seal was adopted, and a water-hydraulic actuator was developed. The installation positions of actuator hinges and maximum output force requirements were optimized using particle swarm optimization (PSO), effectively reducing the manipulator's self-weight. Through kinematic and inverse kinematic analyses and joint performance tests, a six-degree-of-freedom water-hydraulic manipulator was designed with a maximum reach of 2.5 m, a lifting capacity of 5000 N, and end-effector positioning accuracy within 18 mm. [ABSTRACT FROM AUTHOR]

Additive manufacturing (AM) and topology optimization (TO) emerge as vital processes in modern industries, with broad adoption driven by reduced expenses and the desire for lightweight and complex designs. However, iterative topology optimization can be inefficient and time-consuming for individual products with a large set of parameters. To address this shortcoming, machine learning (ML), primarily neural networks, is considered a viable tool to enhance topology optimization and streamline AM processes. In this work, a machine learning (ML) model that generates a parameterized optimized topology is presented, capable of eliminating the conventional iterative steps of TO, which shortens the development cycle and decreases overall development costs. The ML algorithm used, a conditional generative adversarial network (cGAN) known as Pix2Pix-GAN, is adopted to train using a variety of training data pairs consisting of color-coded images and is applied to an example of cantilever optimization, significantly enhancing model accuracy and operational efficiency. The analysis of training data numbers in relation to the model's accuracy shows that as data volume increases, the accuracy of the model improves. Various ML models are developed and validated in this study; however, some artefacts are still present in the generated designs. Structures that are free from these artefacts achieve 91% reliability successfully. On the other hand, the images generated with artefacts may still serve as suitable design templates with minimal adjustments. Furthermore, this research also assesses compliance with two manufacturing constraints: the limitations on build space and passive elements (voids). Incorporating manufacturing constraints into model design ensures that the generated designs are not only optimized for performance but also feasible for production. By adhering to these constraints, the models can deliver superior performance in future use while maintaining practicality in real-world applications. [ABSTRACT FROM AUTHOR]

The fast charge and discharge of a battery will significantly increase the overall temperature and thermal difference of the battery, which will further affect the working performance and safety of the battery. Therefore, a heat–fluid coupling topology optimization pipeline for developing radiation performance of the cooling plate is presented to ensure the thermal homogeneity of the battery in this paper. First, the Brinkman penalty model is utilized to construct the solid and fluid structures. Then, a local volume constraint is introduced to create the lattice structure to reduce the temperature difference of the cooling plate. Furthermore, a functionally graded lattice structure via a variable influence radius is presented to improve the radiation performance of the cooling plate when the thermal load is uneven. Numerical experiments are carried out to evaluate the performance of the presented methods on the optimization of the cooling plate, which indicates that the designed cooling plate by the proposed method improves the radiation performance when compared against a traditional straight channel and a SIMP-based optimal design. [ABSTRACT FROM AUTHOR]

The growing use of additive manufacturing to obtain finished components has led scientific research to increase the studies on topological optimization methods. Thanks to this it is possible to reduce the weight of the components, guaranteeing the desired mechanical properties. In this paper, a new algorithm of parametric optimization is used. Using the Finite Element Analysis, the algorithm uses a grid of prefixed points on the optimizable piece to hollow it. The stresses coming from the Finite Element Analysis are used to parametrize the hollowing process varying the size of the hole. The software used in this work are Grasshopper (a Rhinoceros plug-in) to implement the algorithm and Ansys Workbench to carry out the Finite Element Analysis. The used algorithm directly modifies the original CAD with the optimised one. This is the greatest potential of the method. Furthermore, this method can be used with both additive and subtractive manufacturing. The case study is a plate for structural application. It has been designed and tested with the Finite Element Analysis. After the optimization with the proposed algorithm, a new Finite Element Analysis has been carried out on the optimised plate to compare the two behaviours. Both the plates have been printed using a Fused Deposition Modeling technique also to evaluate the differences between the printing time. The optimised plate can still resist to the imposed loads without achieving the yield stress. [ABSTRACT FROM AUTHOR]

An area of interest in orthopaedics is the development of efficient customized neck orthoses, considered that pathologies which affect the neck area are widespread. Advanced acquisition and modelling approaches combined with Additive Manufacturing (AM) can potentially provide customized orthoses with improved performance and complexity. However, in the design of these devices, besides functional and structural requirements, benefit and comfort of the patient should be a main concern, in particular, at the early stage of design during the acquisition of the body's part, and while using the printed orthosis. In this paper, a scanning system with three sensors was developed which allows a fast, about 5 s, and accurate acquisition of the neck area with minimum discomfort for the patient. A neck orthosis with a ventilation pattern obtained by Topology Optimization (TO), lightened by about 35%, was also established. In fact, a main role for comfort is played by the ventilation pattern which contributes both to lightness and breathability. Its structural and comfort performance was evaluated in comparison with an orthosis with a ventilation pattern configured by Voronoi cells. Structural assessment was carried out by means of finite element analysis under main loading conditions. An evaluation of neck temperatures in relation to wearing 3D printed prototypes, manufactured with Hemp Bio-Plastic® filament, was finally conducted by means of a thermal imaging camera. TO orthosis prototype showed a better performance regarding thermal comfort, with a maximum increase of neck temperature less than 1 °C, which makes the proposed configuration very promising for user's comfort. [ABSTRACT FROM AUTHOR]

This paper intends to provide an application example of using metamaterials for elastic wave manipulation inside a nonlinear waveguide. The concept of phase-gradient metasurfaces, in the form of artificially architectured structures/materials, is adopted in nonlinear-guided-wave-based structural health monitoring (SHM) systems. Specifically, the second harmonic lowest-order antisymmetric Lamb waves (2nd A0 waves), generated by the mutual interaction between primary symmetric (S) mode and antisymmetric (A) mode waves, show great promise for local incipient damage monitoring. However, the mixing strength is adversely affected by the wave beam divergence, which compromises the 2nd A0 wave generation, especially in the far field. To tackle this problem, a metasurface is designed to tactically enhance the 2nd A0 waves through manipulating the phases and amplitudes of both primary waves simultaneously. After theoretically revealing the features of the 2nd A0 wave generation in a weakly nonlinear plate, an inverse-design strategy based on topology optimization is employed to tailor-make the phase gradient while ensuring the high transmission of the primary waves, thus converting the diverging cylindrical waves into quasi-plane waves. The efficacy of the design is tested in a 2nd-A0-wave-based SHM system for material degradation monitoring. Results confirm that the manipulated S and A mode waves can propagate in a quasi-planar waveform after passing the surface-mounted metasurface. Changes in material properties inside a local region of the host plate can be sensitively captured through examining the variation of the 2nd A0 wave amplitude. The concept presented here not only showcases the potential of metamaterial-enhanced 2nd A0 waves for material degradation monitoring, but also illuminates the promising direction of metamaterial-aided SHM applications in nonlinear waveguides. [ABSTRACT FROM AUTHOR]

AbstractResearch in topology optimization with stress constraints has shown that defining the stress constraint locally yields better performance compared to global methods. However, an examination of the formulas for local stress constraints reveals a limitation - the constraint is only satisfied at points where it is explicitly defined, failing to guarantee satisfaction across the entire design domain. To address this shortcoming, this paper proposes utilizing an integral form of the stress constraint. The integral formulation theoretically ensures that the stress constraint is satisfied over whole design domain. The objective is to minimize the mass of plane stress structures using reaction-diffusion level set method while incorporating local stress constraints in this integral form. The methodology utilizes finite element approximations for geometry and displacements, defining local stress constraints through an integral formulation. A Lagrangian function combines objective and constraint functions, with sensitivity analysis performed during optimization based on level set function changes. Structural boundaries are updated using the Hamilton-Jacobi equation. The paper presents numerical examples with varying loads and support conditions to demonstrate the effectiveness of this integral stress constraint approach. Results illustrate the capability of the proposed method to generate optimal topologies while satisfying stress constraints across the entire design space. [ABSTRACT FROM AUTHOR]

The design of continuum structures often presents challenges related to stress concentration, which can cause significant structural damage. To address this issue, the current study presents a new stress minimization method that utilizes the Windowed Evolutionary Structural Optimization (WESO) framework. The method aims to improve algorithm stability by optimizing design variables with an intermediate density. The use of a P‐norm stress aggregation method improves the assessment of global stress levels and enhances computational efficiency. Furthermore, a stable element sensitivity formulation, derived from the adjoint sensitivity analysis of the global stress measure, effectively handles the nonlinear stress behavior. Mesh filtering techniques are utilized to convert sensitivity from elements to nodes, and the structural topological solution is represented using the level set function (LSF) based on element‐node sensitivity. This method addresses the singularity issue commonly found in density‐based optimization methods and facilitates the achievement of smooth topological solutions. Through 2D and 3D benchmark designs, the proposed method's feasibility, stability, and superiority are thoroughly demonstrated. A parametric study is conducted to identify the optimal parameter range for the algorithm, leading to the development of a rational method for parameter selection. The optimized topology, with its smooth boundaries, can guide the design of structures without the need for redesign or post‐processing, helping to drive innovation and development in engineering. [ABSTRACT FROM AUTHOR]

For the fabrication of structures in complex environments and to improve device performance, this paper presents a thermoelastic topology optimization formulation for the design of support structures in layer-by-layer printed additive manufacturing. The formulation is written in the form of structural compliance minimization with two competing constraint functions, one related to mechanical performance (stress) considering mechanical stress and thermal stress and one related to thermal performance (temperature). The optimization problem is solved by applying the p-norm function to handle global stress constraints and overall temperature constraints, separately. The sensitivity information of the objective function and constraints is derived using the adjoint variable method. The design variables are updated using the Method of Moving Asymptotes (MMA). We present several examples that explore the ability of the formulation to obtain optimized support structures for additive manufacturing under different volume constraints, various performance constraints, and print orientations, which addresses the issues of mechanical and thermal stress concentration when considering thermoelastic coupled effect, thus validating the effectiveness of the proposed method. In comparison with previous works, thermal performance-related constraints are introduced in this study, which effectively solves the optimization problem under thermoelastic coupling effect. [ABSTRACT FROM AUTHOR]

Functionally Graded Materials (FGMs) can outperform their homogeneous counterparts. Advances in digitalization technologies, mainly additive manufacturing, have enabled the synthesis of materials with tailored properties and functionalities. Joining dissimilar metals to attain compositional grading is a relatively unexplored research area and holds great promise for engineering applications. Metallurgical challenges may arise; thus, a theoretical critical analysis is presented in this paper. A multidisciplinary methodology is proposed here to unify optimal design, multi-feed Wire-Arc Additive Manufacturing (WAAM), and image-based characterization methods to create structure-specific oriented FGM parts. Topology optimization is used to design FGMs. A beam under pure bending is used to explore the layer-wise FGM concept, which is also analytically validated. The challenges, limitations, and role of WAAM in creating FGM parts are discussed, along with the importance of numerical validation using full-field deformation data. As a result, a conceptual FGM engineering workflow is proposed at this stage, enabling digital data conversion regarding geometry and compositional grading. This is a step forward in processing in silico data, with a view to experimentally producing parts in future. An optimized FGM beam, revealing an optimal layout and a property gradient from iron to copper along the build direction (bottom–up) that significantly reduces the normal pure bending stresses (by 26%), is used as a case study to validate the proposed digital workflow. [ABSTRACT FROM AUTHOR]

The imperative for lightweighting technologies, paramount in mission-critical cyber-physical systems (CPSs) including aerospace, automotive and allied sectors, hinges upon optimizing energy efficiency and curbing product weight. Honeycomb structures, celebrated for their exceptional strength-to-weight ratio, have indisputably guided the pursuit of lightweight design. This paper expounds upon the versatility of honeycomb structures by scrutinizing their in-plane mechanical attributes. Leveraging finite element simulations and polynomial fitting, we enhance the prevailing equivalent elastic modulus model for uniform honeycomb structures, expanding its domain to encompass a broader spectrum of relative density values. Deliberations ensue concerning the model's constraints and its inapplicability to nonuniform honeycomb structures. The investigation introduces nodes as pivotal influencers in the mechanical comportment of nonuniform honeycomb structures, delineating the nexus between the equivalent elastic modulus and node dimensions through a fusion of finite element simulations and mechanical experimentation. Furthermore, this research delves into the tenets and constructs of density-based variable density methodologies within the ambit of topology optimization, with an overarching goal of maximizing stiffness. We furnish a holistic design protocol for optimizing honeycomb structures, underscored by a pragmatic instantiation of the density-based variable density approach. Scrutinizing the geometric interplay between honeycomb structures and design spaces, we posit an innovative paradigm employing concentric circles to approximate cellular envelopes, streamlining numerical cartography and the conversion of optimization outputs into variable density honeycomb configurations. Evaluation of the in-plane mechanical attributes of variable density honeycomb structures reveals that TPU material augments the resilience of both uniform and variable density honeycomb structures, whereas topology optimization amplifies specific stiffness and resilience modulus in variable density honeycomb structures relative to their uniform counterparts. This study sheds light on the complexities of honeycomb structures, providing valuable insights for their optimization in lightweight applications. [ABSTRACT FROM AUTHOR]

Copyright of Machine Tool & Hydraulics is the property of Guangzhou Mechanical Engineering Research Institute (GMERI) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A novel material‐constrained method for the design of liquid crystal optical devices – computer‐generated liquid crystal‐based holograms – and their manufacture using photo‐patterning is demonstrated. The developed topology optimization method is compared to the Gerchberg‐Saxton algorithm, and key advantages and disadvantages are outlined. The key novelties and advantages of the method are that it accounts for the natural relaxation and material properties of the liquid crystal and that it can account for different material or manufacturing constraints, such as maximum optical axis gradients. The viability of the method is applied for different binary and greyscale target images of varying complexity, target image sizes, and algorithms that account for the material properties of the liquid crystal. Finally, with the topology optimization design approach and photo‐patterning, it is possible to produce high‐accuracy and high‐contrast liquid crystal‐based computer‐generated holograms. [ABSTRACT FROM AUTHOR]

Data-driven models that act as surrogates for computationally costly 3D topology optimization techniques are very popular because they help alleviate multiple time-consuming 3D finite element analyses during optimization. In this study, one such 3D CNN-based surrogate model for the topology optimization of Schoen's gyroid triply periodic minimal surface unit cell is investigated. Gyroidlike unit cells are designed using a voxel algorithm and homogenization-based topology optimization codes in MATLAB. A few such optimization data are used as input-output for supervised learning of the topology-optimization process via the 3D CNN model in Python code. These models could then be used to instantaneously predict the optimized unit cell geometry for any topology parameters. The high accuracy of the model was demonstrated by a low mean square error metric and a high Dice coefficient metric. The model has the major disadvantage of running numerous costly topology optimization runs but has the advantages that the trained model can be reused for different cases of TO and that the methodology of the accelerated design of 3D metamaterials can be extended for designing any complex, computationally costly problems of metamaterials with multi-objective properties or multiscale applications. The main purpose of this paper is to provide the complete associated MATLAB and PYTHON codes for optimizing the topology of any cellular structure and predicting new topologies using deep learning for educational purposes. [ABSTRACT FROM AUTHOR]

AbstractThis study investigates the integration of modal analysis and topology optimization in the design of a robotic arm to enhance both its reliability and efficiency. The primary objectives are to reduce the weight and minimize the vibration of the robotic arm. Initially, the kinematics and dynamics of the robotic arm were examined to identify the joint experiencing the highest torque. Finite element analyses (FEA) were then conducted on this critical joint to assess its vibration characteristics and redesign the joint for improved performance through topology optimization. Comparative analysis of the initial and optimized designs has highlighted significant improvements in weight reduction and vibration control. The selected robot arm component was manufactured using fused deposition modeling (FDM). Experimental modal analysis validated the theoretical predictions, demonstrating the effectiveness of the optimized design. The selected component of the robotic arm was redesigned using three different topology geometries and two different unit cell sizes for each, resulting in a maximum weight reduction of 29.37%. Stresses were reduced by 41% under critical operating conditions, which contributed significantly to the system’s reliability. The improvements in efficiency were measured through reductions in weight and vibration, demonstrating the enhanced dynamic performance of the robotic arm. The optimized design was validated through experimental modal analysis, confirming the effectiveness of the redesign. This study underscores the synergy of modal analysis and topology optimization in advancing robotic arm technology, providing a comprehensive approach to design optimization for enhanced reliability. [ABSTRACT FROM AUTHOR]

Aiming at the requirements of strong mobility and high flexibility of rescue and relief mobile pump trucks, this paper designs a new type of mobile pump truck frame based on existing mobile vehicle frame models. The materials used for the frame are 40Cr and Q235, and the finite element method is utilized to carry out static mechanical analysis and dynamic characteristic analysis. Simultaneously utilizing topology optimization and multi-objective genetic algorithm to optimize the design of the frame structure. The results show that the optimized pump truck frame can meet the strength design requirements of four typical working conditions: full load bending, full load torsion, emergency turning and emergency braking, while avoiding resonance phenomena caused by road surface and diesel engine vibration. Compared with the original frame model, the weight of the optimized frame is reduced by 87.88 kg, with a weight reduction rate of 10.89%, realizing the lightweight design requirements. [ABSTRACT FROM AUTHOR]

The aeroengine bracket is a vital connector, which plays a key role in supporting and transmitting loads. In this paper, a bracket with variable stiffness for vibration control of aeroengine accessory is designed. Firstly, the topology optimization for the initial model of the aeroengine bracket is carried out, and the quality of the bracket was reduced by 84.78% while meeting the strength requirements. After that, part of the material of the bracket was replaced by shape memory alloy (SMA) to design the bracket with variable stiffness. It is found that with the increase in temperature, the stiffness of the designed bracket with variable stiffness increases by about 36%, and maximum von Mises stress and deformation of the bracket have decreased. Finally, the integrated modeling of aeroengine casing-bracket-accessory is carried out. Under single and coupled fault frequencies, the amplitude of the accessory is reduced by 57.5% and 63.1%, respectively. The frequency sweep at different temperatures shows that as the temperature increases, the resonance frequency changed from 74.6 Hz to 89.1 Hz and the resonance peak amplitude decreased by 17.7%. [ABSTRACT FROM AUTHOR]

Topology optimization is an influential technique engineers and designers employ to achieve desirable material distribution within a designated domain. This educational article introduces a concise and efficient Matlab code, comprising only 262 lines, developed explicitly for the Level Set topology optimization based on the estimated Gradient Field (GFLS) in the body-fitted mesh. Unlike conventional level set methods that rely on the upwind scheme employed in the structured meshes, the proposed algorithm adopts the per-cell linear estimation of the discrete gradient vectors in the body-fitted mesh framework to obtain the velocity field and update the level set function. The Matlab code, named GFLS262, consists of a 62-line main program, 41-line finite element analysis function, and 48-line sub-functions, enabling the implementation of the GFLS method in 2D scenarios. Additionally, a 111-line function describes an improved mesh generator incorporated in the code to facilitate the generation of body-fitted meshes. The superiority of this innovative approach over the previous optimization methods with invariant meshes is demonstrated through various benchmark examples. For ease of access and further learning, the educational Matlab code is available on the website and can also be found in the Appendix section of this article. [ABSTRACT FROM AUTHOR]

In the design optimization of fiber-reinforced composites, spatial material discontinuity is considered intractable within the manufacturing reality imposed by advanced technologies. This paper presents a topological optimization framework based on truss-like material to design composite structures with continuous fiber. Specifically, the fiber morphology at the scattered design points, which controls the orientation and volume fraction, is taken as design variables. Using the Shepard interpolant scheme, the fiber morphology at any given computational point is interpolated by scattered design variables within a certain circular influence domain. The employed interpolation inherently ensures the spatial continuity and range-restricted of the physical field in an element-independent manner. Since separating the design variable field and analysis mesh on two independent sets of points, this method is well suited for using a sparse design variable field. The computational savings are compelling due to the reduced number of design variables without significantly restricting the design freedom. Numerical instability such as checkerboard and mesh dependencies vanished as no intermediate densities are suppressed in optimization. The continuous fiber-reinforced composites (CFRCs) in the form of truss-like continua are ready to be manufactured with the aid of a simple post-processing. Several numerical examples are investigated to demonstrate the feasibility and effectiveness of the proposed formulation and numerical techniques. [ABSTRACT FROM AUTHOR]

This paper presents two MATLAB codes for topology optimization of multi-material piezoelectric actuators and energy harvesters. These codes provide the extensions of the previously published 2D topology optimization codes for piezoelectric actuators and energy harvesters (Struct Multidisc Optim 63 (2), 983–1014) with two major contributions: (1) extension to the third dimension, (2) combination of piezoelectric (active) and non-piezoelectric (passive) materials in the design domain. The codes are written in the most flexible form to be compatible with different optimization problems and practical case studies of piezoelectricity that exist in the literature. The codes address unique challenges that emerge by introducing the third dimension to non-isotropic piezoelectric materials including the polarization direction and definition of electrodes. The finite element discretization has been done with two different types of 3D hexahedral elements: (1) 8-node trilinear elements, (2) 20 node quadratic elements. The users are free to choose between these element types for the finite element model of the structure based on having preferences for accuracy or computation time. A new method of indexing the elements, nodes, and degrees of freedom is introduced to facilitate the definition of loads, boundary conditions, electrodes, etc. The inclusion of piezoelectric material and non-piezoelectric material in the design domain is by default. In comparison to previously published 2D codes, the codes in this paper benefit from the latest advancements in optimization algorithms, filtering methods, and speed-up techniques. The codes are independent and hence can be run without calling any external code. Different parts of the codes are explained in detail to make them comprehensive for newcomers in the field of topology optimization of piezoelectric structures. [ABSTRACT FROM AUTHOR]

This paper proposes a Topology Optimization (TO) method for the design of microstructures within All-Solid-State Batteries (ASSBs), using the homogenization method. ASSBs have attracted significant attention because of their possibilities to surpass the problems of conventional liquid lithium-ion batteries regarding safety, energy density, and longevity. To improve the performance of ASSBs, many experimental research results based on costly trial-and-error approaches have previously been presented. In order to mitigate the cost and time involved in trial-and-error, several numerical approaches have also been proposed to deal with the multiple materials in various batteries. TO is one of the most flexible structural optimization methods that can allow topological changes as well as boundary changes, and has the potential to provide high-performance structures. TO methods have also been successfully applied to the design of several kinds of batteries, such as Solid Oxide Fuel Cells (SOFC) and Redox flow batteries. However, to the best of our knowledge, research concerning the structural optimization of ASSBs has not been found. In this paper, we propose the TO method targeting microstructure designs of ASSBs using the homogenization method to associate microstructural configurations and macroscopic properties. First, we define a new objective function that can appropriately evaluate the performance of ASSBs and can reduce computational costs in the optimization process. Next, the design sensitivities addressing the time-dependent and nonlinear aspects of the problem are derived using the Lagrange and continuous adjoint methods. Finally, we provide several numerical results under various conditions, including different C-rates, to confirm the validity and efficiency of our proposed method. [ABSTRACT FROM AUTHOR]