Conventional Topology Optimization Research Articles

Maximum Stress Minimization via Data-Driven Multifidelity Topology Design

Abstract The maximum stress minimization problem is among the most important topics for structural design. The conventional gradient-based topology optimization methods require transforming the original problem into a pseudo-problem by relaxation techniques. Since their parameters significantly influence optimization, accurately solving the maximum stress minimization problem without using relaxation techniques is expected to achieve extreme performance. This paper focuses on this challenge and investigates whether designs with more avoided stress concentrations can be obtained by solving the original maximum stress minimization problem without relaxation techniques, compared to the solutions obtained by gradient-based topology optimization. We employ data-driven multifidelity topology design (MFTD), a gradient-free topology optimization based on evolutionary algorithms. The basic framework involves generating candidate solutions by solving a low-fidelity optimization problem, evaluating these solutions through high-fidelity forward analysis, and iteratively updating them using a deep generative model without sensitivity analysis. In this study, data-driven MFTD incorporates the optimized designs obtained by solving a gradient-based topology optimization problem with the p-norm stress measure in the initial solutions and solves the original maximum stress minimization problem based on a high-fidelity analysis with a body-fitted mesh. We demonstrate the effectiveness of our proposed approach through the benchmark of L-bracket. As a result of solving the original maximum stress minimization problem with data-driven MFTD, a volume reduction of up to 22.6% was achieved under the same maximum stress value, compared to the initial solution.

Nonlinear vibration analysis of sandwich plates with inverse-designed 3D auxetic core by deep generative model

Building on a deep generative model (DGM), this paper introduces an innovative sandwich plate structure featuring an inverse-designed auxetic 3D lattice core and conducts a detailed investigation of its nonlinear vibration characteristics and effective Poisson's ratios under various parameter settings. By incorporating a conditional estimator and quality loss evaluation functions, the enhanced conditional generative adversarial networks are capable of designing 3D truss auxetic topologies that achieve customized negative Poisson's ratios without reliance on subjective experience. Additionally, lattice specimens are created using 3D metal printing, and the mechanical properties of these DGM-based 3D auxetic structures are validated through vibration experiments and finite element models. These structures exhibit significantly superior natural frequencies compared to those obtained through conventional topology optimization methods reported in existing literature. The study also explores the impact of different functionally graded configurations, temperature variations, boundary conditions, and dimensional parameters on the natural frequency, nonlinear vibration response, and effective Poisson's ratio of the inverse designed auxetic sandwich plates.

Twice-topology optimized heat sinks for enhanced heat transfer performance: Numerical and experimental investigation

Since the heat dissipation problem is always confusing and hindering the computing power improvement of electronic chip, an effective thermal management strategy is critical to relieve these problems. In this work, a new twice topology optimization design method combining topology optimization and image processing to design heat sinks is presented, which extends topology optimization from 2Dimention (2D) to 3Dimention(3D). Firstly, on the horizontal design domain, the conventional topology optimization is conducted for the minimization of average temperature/standard deviation. Then the optimal shape of liquid domain is converted into 1D flow routine by thinning algorithm. After that, another topology optimization is performed on the flow channel cross-section plane to get the best cross-section shape of channels. The liquid domain of the final heat sink is then obtained by scanning the optimized flow channel cross-section along the 1 Dimension (1D) flow routine and solving the interference by introducing cylinder joints. Finally, two kinds of twice topology optimized heat sinks including TTOHS-1 with minimized temperature variation as optimal goal and TTOHS-2 with minimized average temperature as optimal goal are generated by combining the liquid domain and a cuboid using Boolean Operation. The performance of heat sinks is numerically investigated, and the results indicate that the thermal performance of TTOHS-1 and TTOHS-2 are much better than that of the traditional heat sink with straight channels (TSCHS). When Re = 689, the average temperature and the maximum temperature of the heat source surface of TTOHS-1 are decreased by 4.99 % and 6.29 % respectively, compared to the TSCHS. The Nusselt number is increased by 46.16 % while the thermal resistance is reduced by 33.13 %. At last, the thermal and flow performance of the TTOHS-1 is studied by conducting experiments, showing that the numerical results agree well with that of the experiment.

GYROID CELL USAGE IN TOPOLOGY OPTIMIZATION OF LOAD-CARRYING PARTS

This paper discusses the implementation and usage of a gyroid cell in topology optimization of load-carrying structural parts. Conventional topology optimization relies on a linear elastic model and the strain energy density field of the structure in order to optimally distribute the material within a given domain. This procedure may take place either on a completely unrestricted topological domain space or on a restricted preconfigured domain. The latter option is often chosen in order to enforce a cellular type structure of the part. In this context, surface-based cells like the gyroid cell may be an attractive option under special circumstances. For that reason, this paper addresses briefly the problem of numerical processing of the topological domain space in case of gyroid cell usage. In this context, a numerically efficient and stable procedure is proposed, suitable to be engaged on very large finite element meshes. Furthermore, an interesting numerical example demonstrates that conventional topology optimization of a linear model can even be used to tune the plastic dissipation of a structure under large deformations.

GYROID CELL USAGE IN TOPOLOGY OPTIMIZATION OF LOAD-CARRYING PARTS

This paper discusses the implementation and usage of a gyroid cell in topology optimization of load-carrying structural parts. Conventional topology optimization relies on a linear elastic model and the strain energy density field of the structure in order to optimally distribute the material within a given domain. This procedure may take place either on a completely unrestricted topological domain space or on a restricted preconfigured domain. The latter option is often chosen in order to enforce a cellular type structure of the part. In this context, surface-based cells like the gyroid cell may be an attractive option under special circumstances. For that reason, this paper addresses briefly the problem of numerical processing of the topological domain space in case of gyroid cell usage. In this context, a numerically efficient and stable procedure is proposed, suitable to be engaged on very large finite element meshes. Furthermore, an interesting numerical example demonstrates that conventional topology optimization of a linear model can even be used to tune the plastic dissipation of a structure under large deformations.

Latent Crossover for Data-Driven Multifidelity Topology Design

Abstract Topology optimization is one of the most flexible structural optimization methodologies. However, in exchange for its high level of design freedom, typical topology optimization cannot avoid multimodality, where multiple local optima exist. This study focuses on developing a gradient-free topology optimization framework to avoid being trapped in undesirable local optima. Its core is a data-driven multifidelity topology design (MFTD) method, in which the design candidates generated by solving low-fidelity topology optimization problems are updated through a deep generative model and high-fidelity evaluation. As its key component, the deep generative model compresses the original data into a low-dimensional manifold, i.e., the latent space, and randomly arranges new design candidates over the space. Although the original framework is gradient free, its randomness may lead to convergence variability and premature convergence. Inspired by a popular crossover operation of evolutionary algorithms (EAs), this study merges the data-driven MFTD framework and proposes a new crossover operation called latent crossover. We apply the proposed method to a maximum stress minimization problem in 2D structural mechanics. The results demonstrate that the latent crossover improves convergence stability compared to the original data-driven MFTD method. Furthermore, the optimized designs exhibit performance comparable to or better than that in conventional gradient-based topology optimization using the P-norm measure.

Bandgap design of 3D single-phase phononic crystals by geometric-constrained topology optimization

<abstract> <p>Phononic crystals (PnCs) possessing desired bandgaps find many potential applications for elastic wave manipulation. Considering the propagating essence of three-dimensional (3D) elastic waves and the interface influence of multiphase material, the bandgap design of 3D single-phase PnCs is crucial and appealing. Currently, the main approaches for designing 3D single-phase PnCs rely on less efficient trial-and-error approaches, which are heavily dependent on researchers' empirical knowledge. In comparison, topology optimization offers a dominant advantage by transcending the restriction of predefined microstructures and obtaining topologies with desired performance. This work targeted the exploration of various novel microstructures with exceptional performance by geometric-constrained topology optimization. To deal with high-dimensional design variables in topology optimization, the unit cell structure of a PnC was confined by pyramid symmetry to maximumly deduct the variable number of the unit cell. More importantly, to alleviate mesh dependence inherent in conventional topology optimization, node-to-node and edge-to-edge connection strategies were adopted, supplemented by the insertion of cylinders to ensure the stability of these connections. Finally, unstable PnC structures were filtered out using extra geometric constraints. Leveraging the proposed framework for the optimization of 3D single-phase PnCs, various novel structures were obtained. Particularly, our results demonstrate that PnC structures with only one type of mass lump exhibit significant potential to possess outstanding performance, and geometric configurations of the ultimately optimized structures are intricately linked to the particular sequence of the bandgaps.</p> </abstract>

Designing Porous Structure with Optimized Topology using Machine Learning

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.

DMF-TONN: Direct Mesh-free Topology Optimization using Neural Networks

We propose a direct mesh-free method for performing topology optimization by integrating a density field approximation neural network with a displacement field approximation neural network. We show that this direct integration approach can give comparable results to conventional topology optimization techniques, with an added advantage of enabling seamless integration with post-processing software, and a potential of topology optimization with objectives where meshing and Finite Element Analysis (FEA) may be expensive or not suitable. Our approach (DMF-TONN) takes in as inputs the boundary conditions and domain coordinates and finds the optimum density field for minimizing the loss function of compliance and volume fraction constraint violation. The mesh-free nature is enabled by a physics-informed displacement field approximation neural network to solve the linear elasticity partial differential equation and replace the FEA conventionally used for calculating the compliance. We show that using a suitable Fourier Features neural network architecture and hyperparameters, the density field approximation neural network can learn the weights to represent the optimal density field for the given domain and boundary conditions, by directly backpropagating the loss gradient through the displacement field approximation neural network, and unlike prior work there is no requirement of a sensitivity filter, optimality criterion method, or a separate training of density network in each topology optimization iteration.

Mixed topology optimization: A self-guided boundary-independent approach for power sources

As the use of electrochemical devices becomes more prevalent, advanced optimization techniques, such as topology optimization, are being employed to improve their performance. Among various electrochemical systems, power sources have an intrinsic best operating point that corresponds to the maximum output power. This study proposes a mixed topology optimization approach to enhance the performance of these systems by a simultaneous modification of electrode structure and the working condition. In contrast to the conventional approaches, the proposed method focuses on enhancement of the maximum power point. Thanks to its self-guidance feature, this technique outperforms conventional topology optimization methods and eliminates the need for a prior decision on the optimization starting point. Therefore, the proposed approach has a significant potential for adapting the material distribution to the best working condition. The proposed approach enables more effective topological optimization and takes the utilization of topology optimization in power sources to the next level.

Three-dimensional plasticity-based topology optimization with smoothed finite element analysis

AbstractThis paper presents a novel plasticity-based formulation for three-dimensional (3D) topology optimization of continuum structures. The proposed formulation addresses the optimization problem by combining mixed rigid-plastic analysis with density-based topology optimization, resulting in a volume minimization approach. Unlike conventional stress-constrained topology optimization methods that rely on linear elastic structural analysis, our developed formulation focuses on enhancing the loading capacity of the designed structures based on the plastic limit theory, leading to more cost-effective designs. To improve computational efficiency, we employ the smoothed finite element technique in our proposed method, enabling the utilization of linear tetrahedral elements for 3D mesh refinement. Moreover, the final formulation of our developed method can be efficiently solved using the advanced primal–dual interior point method, eliminating the need for a separate nonlinear finite element structural analysis. Numerical examples are presented to demonstrate the effectiveness of the proposed approach in offering enhanced design possibilities for continuum structures.

GPU-based mesh reduction strategy utilizing active nodes for structural topology optimization

This paper presents a novel mesh reduction strategy on graphics processing unit (GPU) that aims to reduce the computational complexity of conventional structural topology optimization. In the proposed strategy, the effective number of design variables is reduced by using the concept of active nodes and active elements in the finite element mesh. A novel mesh numbering scheme is also introduced to facilitate parallel identification of active nodes using a proposed GPU-based algorithm. The preconditioned conjugate gradient (PCG) solver is further developed using the proposed strategy and the numbering scheme. The proposed strategy is tested on three structural topology optimization problems using solid isotropic material with penalization method. Results of the proposed strategy demonstrate up to 8× speedup over the standard GPU implementation considering the entire mesh.

Constrained sensitivity filtering technique for topology optimization with lower computational expense

AbstractConstrained Sensitivity Filtering Method (CSFM) has been proposed to save computational expenses in topology optimization. The sensitivity filtering technique is widely adopted to avoid numerical instabilities. Because the filtered sensitivity values are recalculated from the normalized density values and the sensitivity values from within a fixed range of neighborhoods, the values are sometimes completely different from the original ones. Thus, the idea of the CSFM is to control the change of filtered sensitivity values based on the previous iterations. By controlling the changes of filtered sensitivity values within certain limitation, optimal layouts can be obtained with lower compliance and the computational expenses can also be reduced in comparison to that by conventional topology optimization. The computational expense with CSFM topology optimization could be reduced by up to 85%. The numerical examples established that CSFM topology optimization has improved the numerical efficiency and effectiveness.

Improving the manufacturability of highly materially restricted topology-optimized designs with Mixed Integer Linear Programming

This paper presents a new free-form topology optimization framework for highly materially restricted design situations. Highly materially restricted design situations are herein defined as being limited significantly by the combined demands on material use and manufacturability. The new framework uses the ground structure approach with frame elements and casts the design problem as a Mixed Integer Linear Program (MILP), ensuring a solution with a manufacturable discrete material distribution. This paper also presents an extension to hybrid mesh ground structures containing both frame and thin solid elements. In both cases, the user can easily tailor the resultant design to discrete fabrication requirements as e.g. relevant when using an extrusion-based Additive Manufacturing (AM) process that requires the design features to adhere to a discrete number of bead depositions. The new framework is numerically demonstrated on topology optimization benchmark examples. In addition, numerical and experimental comparisons are made to the conventional density-based topology optimization approach (with continuous density variables). When the design is highly restricted, the new MILP framework is in most tested cases found to generate solutions with improved numerical predictions on the compliance. For the experimentally validated case study, the numerical prediction is seen to significantly underestimate the experimentally observed performance gain. The experimental investigation additionally cements the high performance of density-based topology optimization in design situations with low levels of design restrictions. In these cases (6 out of 7 tested herein), the solutions generated with density-based topology optimization have comparable or preferable performance.

Learning topology optimization process via convolutional long‐short‐term memory autoencoder‐decoder

AbstractThis article proposed an autoencoder‐decoder architecture with convolutional long‐short‐term memory (ConvLSTM) cell for the purpose of learning topology optimization iterations. The overall topology optimization process is treated as time‐series data, with each iteration as a single step. The first few steps are fed into the encoder to generate encoder embedding, which is fed into the decoder. The decoder uses the encoder embedding as input and generates the result at each future step until the end of iteration. To train the proposed neural network, a large dataset is generated by a conventional topology optimization method, that is, solid isotropic material with penalization for intermediate densities, with randomly picked boundary conditions, load conditions, and volume constraints. Unlike other deep learning models introduced before, the proposed method can learn each topology optimization step iteratively and present the full optimization path. Furthermore, the proposed method can be extended to give solutions to unseen boundary and load conditions with a significant reduction in computation cost in a little sacrifice on the performance of the optimum design.

Topology optimization using super-resolution image reconstruction methods

This paper proposes a new topology optimization method to obtain super-resolution images without increasing mesh refinement by using various methods. For traditional process, low-resolution (LR) images are fed into the Solid Isotropic Material with Penalization (SIMP) and Optimality Criteria (OC) methods. Here, the trained super-resolution images are added to the inner loops to reconstruct the topology and used to obtain high-resolution (HR) images from the LR images at the end of each iteration. After finishing the reconstruction process, the main topology optimization method recovers the original size images from the HR images for the next iteration. Several examples are presented to demonstrate the effectiveness of the proposed method. The final topologies provide noticeably improvement over those of typical SIMP method and create a much sharper and higher contrast images. Moreover, the proposed strategy using the super-resolution image reconstruction methods can give valuable innovation for conventional topology optimization process.

Development of Deep Convolutional Neural Network for Structural Topology Optimization

This research develops a highly effective deep-learning-based surrogate model that can provide the optimum topologies of 2D and 3D structures. In general, structural topology optimization requires plenty of computations because of a large number of finite element analyses to obtain optimal structural layouts by reducing the weight and satisfying the constraints. Therefore, many researchers have developed a deep-learning-based model using the initial static analysis results to predict the optimum designs. However, these studies still considered relatively simple example problems, such as a cantilever plate and MBB beam, even though they required a large number of data to achieve an accurate surrogate model for the simple application. To overcome these limitations, we propose a new framework, which 1) efficiently uses limited data by normalizing it and 2) employs a surrogate model capable of handling more practical cases, such as a 2D panel and 3D stiffened panel subjected to a distributed load, and can be used for local–global structural optimization. In all cases, the developed surrogate models can predict the optimum layouts with structural performance levels equal to those of the structures considered to be ground truths. Also, when the optimal structures were obtained using the proposed method, the total calculation time was reduced by 98% as compared to conventional topology optimization once the convolutional neural network had been trained.

A Physics-Informed Neural Network-based Topology Optimization (PINNTO) framework for structural optimization

Physics-Informed Neural Networks (PINNs) have recently attracted exponentially increasing attention in the field of computational mechanics. This paper proposes a novel topology optimization framework: Physics-Informed Neural Network-based Topology Optimization (PINNTO). Unlike existing machine-learning based topology optimization frameworks, PINNTO employs an energy-based PINN to replace Finite Element Analysis (FEA) in the conventional structural topology optimization, to numerically determine the deformation states, which is a key novelty in the proposed methodology. A supervised neural network that respects governing physical laws defined via partial differential equations is trained to develop the corresponding network without any labelled data, with the intention of solving solid mechanics problems. To assess feasibility and potential of the proposed PINNTO framework, a number of topology-optimization-related case studies have been implemented. The subsequent findings illustrate that PINNTO has the ability to attain optimized topologies with neither labelled data nor FEA. In addition, it has the capability to generate comparable designs to those produced by the current successful approaches such as Solid Isotropic Material with Penalization (SIMP). Based on the results of this study, it can also be deduced that PINNTO can acquire optimal topologies for various types of complex domains given that the boundary conditions and loading configurations are correctly imposed for the associated energy-based PINN. Consequently, the proposed PINNTO framework has demonstrated promising capabilities to solve problems under conditions when the usage of FEA is challenged (if not impossible). In summary, the proposed PINNTO framework opens up a new avenue for structural design in this ‘data-rich’ age.

설계변수감소 위상최적설계기법을 활용한 자동차용 캘리퍼 강성 최대화 설계

A brake caliper is crucial for control in automotives. One of the main design factors is stiffness in terms of fatigue and robustness. The topology optimization technique is adopted to obtain a conceptual design for a brake caliper. However, topology optimization requires a high computational expense. RDVM topology optimization was proposed to overcome the restriction and demonstrate the efficiency in benchmarking problems. This study presents the effectiveness of RDVM topology optimization for a real structure (i.e., brake caliper). The objective function is defined as the minimization of compliance, which is the converse of stiffness, and volume constrained. The objective function values were compared among an original brake caliper, conventionally topology optimized, and RDVM topology optimized. The objective function value by topology optimization was approximately 30 % higher than the original one, which means the new design is 30 % stiffer. The computational expenses were also compared between conventional and RDVM topology optimization. Although the optimal layouts were almost the same, the RDVM topology optimization only cost 42 % of the conventional one.

A Review of Lightweight Design for Space Mirror Core Structure: Tradition and Future

With the continuous improvement of the imaging quality requirement of the space optical system, the large-aperture mirror becomes the research focus. However, the increase of the aperture will increase the whole weight which results in high launch cost and degrades the mirror surface figure accuracy. Therefore, the lightweight design method of the mirror structure is of great importance. In recent years, many space telescope system schemes have demonstrated the progress of the structural lightweight design of mirrors, such as Spitzer, SOFIA, JWST, etc. This article reviews the main content and innovations of the research on the structural designs of mirrors including conventional machining designs and topology optimization structures. Meanwhile, some emerging designs (e.g., lattices and Voronoi structures) considering additive manufacturing (AM) are also introduced. Several key elements of different structural design approaches for lightweight mirrors are discussed and compared, such as material, lightweight ratio, design methods, surface figure, etc. Finally, future challenges, trends, and prospects of lightweight design for mirrors are discussed. This article provides a reference for further related research and engineering applications.