Topology Optimization Method Research Articles

Topology optimization of porous structures by considering acoustic and mechanical characteristics

Porous structures are widely found in nature and have been extensively studied due to their high stiffness-to-weight ratio, excellent sound absorption, and robustness regarding loading variation. This paper proposes a new topology optimization approach for the design of porous acoustic-mechanical structures based on the three-field floating projection topology optimization (FPTO) method. In order to capture the change of ambiguous structural boundary during topology optimization, the mixed displacement/pressure (u/p) finite element formulation with the linear material interpolation scheme is adopted. The artificial porous features of the structures are generated by imposing the local volume constraint defined by a constant or adaptive filter radius. The 0/1 constraints of the design variables are simulated by the floating projection constraint so that the final design has a clear topology. To verify the effectiveness of the proposed method, some interesting 2D and 3D numerical examples considering their mechanical and acoustic characteristics simultaneously are presented to achieve porous structures by minimizing dynamic compliance, possibly with an additional acoustic constraint. The results also show that the resulting porous features are useful in improving the acoustic performance of the optimized designs.

Topology Structural Design and Thermal Characteristics Analysis of High-Efficiency Heat Conductive Path for the Spindle System

In order to enhance the heat dissipation of the spindle under working condition, thermal conductivity paths were designed based on the topology optimization method. The heat conductive path was proposed to be constructed in the bearing housing and the spindle housing, which was simplified as a toroidal model. Taking the heat dissipation weakness as the optimization objective, the topological structure with the highest thermal conductivity was obtained based on the OC and IPTO algorithms. In order to analyze the influence of the heat conductive path on the circumferential heat distribution of the spindle, the thermal characteristic of the model with heat conductive paths filled with copper was investigated. Compared with the general model, the heat conductive path could reduce the temperature of the spindle from 47 °C to 33 °C when the volume proportion of the high thermal conductivity material was 40%. At the same time, the strength of the heat conductive path was analyzed, and the size of the stress was not more than 3MPa, which verified the effectiveness of the heat conductive path for efficient heat conduction.

Quasi-Newton methods for topology optimization using a level-set method

The ability to efficiently solve topology optimization problems is of great importance for many practical applications. Hence, there is a demand for efficient solution algorithms. In this paper, we propose novel quasi-Newton methods for solving PDE-constrained topology optimization problems. Our approach is based on and extends the popular solution algorithm of Amstutz and Andrä (J Comput Phys 216: 573–588, 2006). To do so, we introduce a new perspective on the commonly used evolution equation for the level-set method, which allows us to derive our quasi-Newton methods for topology optimization. We investigate the performance of the proposed methods numerically for the following examples: Inverse topology optimization problems constrained by linear and semilinear elliptic Poisson problems, compliance minimization in linear elasticity, and the optimization of fluids in Navier–Stokes flow, where we compare them to current state-of-the-art methods. Our results show that the proposed solution algorithms significantly outperform the other considered methods: They require substantially less iterations to find a optimizer while demanding only slightly more resources per iteration. This shows that our proposed methods are highly attractive solution methods in the field of topology optimization.

An effective phase field method for topology optimization without the curvature effects

An effective phase field method for topology optimization without the curvature effects

Computational synthesis of wheeled vehicles via multi-layer topology optimization

In current engineering practice, computer-aided design (CAD) tools play a key role in the design and fabrication of most mechanical systems, including the design of most vehicles. This software tends to rely heavily on human designers to provide the basic design concept, with the software being used to computationally render an existing design, or to perform modifications to a design to achieve incremental improvements in performance. However, an emerging class of computational methods, known as topology optimization methods, offers the potential for true black box computational design. Under this general framework, practitioners provide the algorithm with the constitutive properties of the design materials, and the mechanical function being designed for (e.g. maximum stiffness under a given loading condition), and the algorithm autonomously generates a description of the corresponding structure. With some exceptions, existing topology optimization methods are limited to generating static, single-body designs. In this study, we present a novel method that builds upon the current state of the art by combining multiple collocated planar design domains to achieve automated computational synthesis of multi-body wheeled vehicles. This capability represents an important step on the path toward automated computational design of increasingly complex, innovative and impactful mechanical systems.

Research on topology optimization method of surface support structure based on leaf vein growth process

In this paper, a biomimetic topology optimization design method that simulates the growth pattern of leaf veins is proposed for the design of the support structure of ultra-light airfoil-like solar cells in the solar powered unmanned aerial vehicle. This method simulates the optimal growth process of main vein morphology through the topology change of dynamic point groups to obtain an optimized topological main support structure and then generates a Voronoi grid structure in the area surrounded by the main support structure to increase the local support for the battery. The whole process is combined with genetic algorithm to simulate the optimal distribution strategy of leaf vein growth by inputting a small number of parameters. Compared with the traditional grid support structure, the support structure obtained by simulating the leaf vein growth optimization strategy can provide more efficient support for the solar panel and avoid damage to the solar cell.

An enhanced proportional topology optimization with virtual elements: Formulation and numerical implementation

This paper presents an improved non-sensitivity structural topology optimization method incorporating virtual elements with unstructured polygonal meshes. Specifically, we employ the recently developed gradient-free proportional topology optimization (PTO) approach, for the first time, together with a new material distribution formula suitable for both minimum compliance and compliant mechanism problems. In order to improve performance, we integrate a linear virtual element method (VEM) module into the PTO algorithm. The linear VEM has a desirable characteristic: it does not require numerical integration and, more importantly, is less sensitive to small-edge elements, thus, significantly reducing computational time. Additionally, we utilize virtual elements with unstructured polygonal meshes inside PTO to suppress one-node connection instabilities. Furthermore, the Heaviside-type operator in the main PTO algorithm loop enhances the optimized results by encouraging the density variables to approach discrete (0/1) solutions more effectively. We demonstrate the performance of our developed method in terms of computational speed, diversity of applications, and improved black-and-white (0/1) structures through several benchmark examples of compliance and compliant mechanism designs.

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.

Dynamic response-oriented multiscale topology optimization for geometrically asymmetric sandwich structures with graded cellular cores

Compared with conventional symmetric sandwich structures with two identical face-sheets and uniform core, geometrically asymmetric sandwich structures (GASSs) enable better dynamic performance due to the expanded design space provided by two unidentical face-sheets and graded cellular cores (GCCs). This paper proposes a dynamic response-oriented multiscale topology optimization method for the GASSs, which is capable of designing the thicknesses of two solid face-sheets, graded distribution of GCCs and their topological configurations to minimize dynamic compliance. Specifically, at macroscale, a variable thickness sheet method is employed to optimize the thicknesses of two solid face-sheets and then generate an overall free distribution of cellular cores within sandwich layers. At microscale, a parametric level set method combining with a numerical homogenization approach is adopted to progressively optimize multiple representative cellular cores (RCCs), achieving their similar topological configurations. Benefitting from the level set-based topology description of RCCs, a shape interpolation technology is conveniently applied to interpolate the shapes of these RCCs to generate the configurations of GCCs. Moreover, a Kriging metamodel constructed by some cellular cores as sample points is adopted to predict the effective properties of each cellular core within sandwich layers, significantly reducing the computational burden. Several 2D and 3D numerical examples are illustrated to show the validity of the proposed method. The results indicate that the optimized GASSs show superior dynamic performances over the conventional sandwich structures designed by microscale and macroscale topology optimization, as well as filled with the commonly applied lattice and honeycomb cores.

Shape and Generalized Topology Optimization of Curved Grid Stiffeners Through the Level Set-Based Density Method

Abstract A shape and generalized topology optimization method based on the level set-based density method is proposed to design the curved grid stiffeners. The overall layout of the stiffeners is described by combining many single stiffeners, and each single stiffener is described by a level set function parameterized by using the compactly supported radial basis functions (CS-RBFs). The curvilinear path of each stiffener is described by the zero iso-contour of each level set function, and the width of each stiffener is described by applying an interval projection to each level set function. The combination operation that is similar to the Boolean operation “union” is achieved by using the p-norm method. The expansion coefficients of CS-RBFs are taken as part of the design variables of the optimization, and they are responsible for changing the shape of curved stiffeners. A topology design variable is assigned to each single stiffener, and it is responsible for changing the existence of single stiffeners. The proposed method is validated through several numerical examples, and the results demonstrate that the shape and topology of stiffeners can be effectively changed during the optimization.

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.

Sequential conservative integer programming method for multi-constrained discrete variable structure topology optimization

Sequential conservative integer programming method for multi-constrained discrete variable structure topology optimization

Lightweight Design and Analysis of Steering Knuckle of Formula Student Car Using Topology Optimization Method

The steering knuckle is a crucial component of student racing vehicles, designed by the Formula Society of Automotive Engineers (FSAE). Developing a lightweight (LW) vehicle that meets the requirements of the student formula car presents a challenge. This study presents a LW design of the steering knuckle using the Topology Optimization (TO) approach for the Formula Society of Automotive Engineers (FSAE) competition considering two different mass constraints (40% and 48%). Moreover, the research includes Stress–Life (SN) curves for three materials, structural steel, 4130 steel, and AISI 1020 steel, providing essential insights into the fatigue characteristics of the model. The results compare the three materials and two mass reduction levels, with steel 4130 achieving a significant mass reduction of 42.70%. Additionally, steel 4130 exhibits superior performance in weight reduction, stress, deformation, and safety aspects. The optimized design meets the criteria for strength, stiffness, and safety under various conditions. The fatigue analysis reveals that AISI 1020 and steel 4130 have superior endurance (1 × 105 and 2 × 105 cycles, respectively). This research provides significant contributions to the development of a LW, high-performance steering knuckle for student formula racing vehicles, highlighting the significance of TO and material selection in achieving optimal outcomes.

Origami Chomper‐Based Flexible Gripper with Superior Gripping Performances

Flexible grippers with superior gripping capabilities are essential for carrying objects. Herein, an origami chomper‐based flexible gripper is designed using a combination of the origami technique and a newly developed nonlinear topology optimization method. This novel origami chomper‐based flexible gripper exhibits superior gripping performance, as revealed by a series of experiments, including gripping range capability under an identical input load, maximum gripping ratio, gripping adaptability, and achieving richer gripping characteristics by size scaling. The origami chomper‐based flexible gripper can handle a wide range of object irregularities in textures and uneven shapes and can enable effective gripping of objects across scales from millimeters to centimeters to decimeters through size scaling. This study paves the way for innovative high‐performance designs of flexible grippers.

Topology optimization for reducing stress shielding in cancellous bone scaffold

In this paper, a topology optimization method is proposed to design bone scaffold structures that match the anisotropic elasticity tensors of cancellous bone. Grid point density and boundary error are introduced in the optimization model to achieve smooth boundaries of scaffold topology and control the distribution of intermediate elements. Combined with finite element analysis, the effects of scaffolds with different levels of elasticity tensors on the stress transfer and distribution of the scaffold-cancellous bone structure are investigated. It is found that scaffolds with the same or slightly lower elastic properties (0.9 times) than cancellous bone transmitted more uniform stresses into the cancellous bone. Finally, we demonstrate that optimized scaffolds can be fabricated by Stereolithography (SLA).

Design of Radial Flow Channel Proton Exchange Membrane Fuel Cell Based on Topology Optimization

In this paper, the flow channel of the radial proton exchange membrane fuel cell (PEMFC) is optimized by the topological optimization method. Using the SNOPT algorithm, a two-dimensional stable constant temperature model is freely constructed in the cyclic sector design domain. Topology optimization aims to maximize the efficiency of PEMFC and minimize the energy dissipation of reaction gas. We analyze radial topology flow channels’ mass transfer capacity and cell performance with different maximum volume constraints. The results show that under high current density, the performance of the optimized channel is significantly better than that of the traditional channel. Increasing the maximum volume constraint is beneficial for improving the mass transfer of PEMFC. At 0.6 V, the cell performance of Scheme 4 is 14.9% higher than the serpentine flow channel and 9.5% higher than the parallel flow channel. In addition, in the optimal selection, 3D simulation modeling is carried out for more accurate verification.

A Two-scale Topology Optimization Method for Functionally Graded Lattice Structures using Three Families of Micro-Structures

A Two-scale Topology Optimization Method for Functionally Graded Lattice Structures using Three Families of Micro-Structures

Multiscale topology optimisation for porous composite structures with stress-constraint and clustered microstructures

While porous composites are drawing growing attention for their excellent lightweight and multifunctional characteristics, inherent stress concentration in these porous composites often presents a main concern of structural integrity. This study aims to develop a multiscale topology optimisation (MTO) method for design of porous composites with clustered microstructures under a prescribed stress constraint. First, the concurrent topology optimisation (TO) for both macrostructures and microstructures are implemented via a multiscale algorithm. Meanwhile, a clustering technique is implemented based on a so-called k-means method to simultaneously determine the allowable volume fraction and microstructural configuration. Second, a consistent density-and-strain based clustering technique is developed for both 2D and 3D multiscale TO. Finally, two benchmark design examples, namely Messerschmitt–Bölkow–Blohm (MBB) and L-bracket structures, are implemented using the presented MTO method by considering either 2D or 3D situations to demonstrate the design effectiveness. The results indicate that, when optimising a high-stiffness porous composites subject to the stress constraint, the maximum von Mises stresses of the 2D MBB and L-bracket structures are well restrained, which are respectively 20% and 29% lower than those without the stress-constraint. In design of a 3D L-bracket, the present MTO method can achieve around 19% reduction in the maximum stress. The study demonstrates the importance of stress constraint to the topological design of multiscale porous composite structures.

Bi-EvoGAN: Bi-level Evolutionary Approach for Generative Adversarial Networks

Generative Adversarial Networks (GANs) are an adversarial approach to generative modeling using deep learning methods, which have become one of the most relevant topics in the last years. Despite producing interesting outputs, recent studies have demonstrated that GANs remain difficult to control and suffer from training problems, such as instability and mode collapse, as well as several aspects of their models are designed by hand. Neuroevolution is a recent evolution strategy that uses Evolutionary Algorithms (EAs) in order to provide an automatic design of deep neural networks architectures. Many recent efforts have been dedicated to contributing on GANs by developing different single-level EAs approaches, however they could not solve their common issues completely which are still open problems. In this paper, we propose a new design of evolutionary algorithms in the context of GANs, consisting of dividing the evolution search space into two complementary levels, modeling a Bi-level Evolutionary Approach called Bi-EvoGAN searching to surpass their adversarial optimization difficulties and also to demonstrate the performance of considering two levels of optimization in comparison to a single optimization level. To the best of our knowledge, this work presents the first application of the bi-level optimization in the context of generative adversarial networks. The upper level uses an Evolutionary Algorithm-based Topology Optimization method named “EA-TO” to evolve a population of GAN networks as a set of individuals in order to find the best network topology. The lower level applies an Evolutionary Algorithm-based Decomposition for Hyperparameter Optimization termed “EA/D-HO” in order to select the best hyperparameters of each GAN individual. The performance of Bi-EvoGAN is explained by the double optimization of the GAN topology and their hyperparameters through the new bilevel optimization design allowing to evolve a GAN population in its higher fitness which will improve the quality of the search method and consequently to accelerate the convergence. Experimental studies are carried out based on four well-known benchmark datasets, MNIST, Fashion-MNIST, CelebA and LSUN-Bedroom allowing to show the efficiency of our approach in comparison to the other state-of-the-art approaches.

DESIGN AND OPTIMIZATION OF THE VARIABLE-DENSITY LATTICE STRUCTURE BASED ON LOAD PATHS

Lattice structure is more and more widely used in engineering by replacing solid structure. But its mechanical performances are constrained by the external shape if the unit cells are directly filled in the design domain, and the traditional topology optimization methods are difficult to give the explicitly mechanical guidance for the distribution of internal unit cells. In this paper, a novel design and optimization method of variable-density lattice structure is proposed in order to simultaneously optimize the external shape and the internal unit cells. First of all, the envelope model of any given structure should be established, and the load paths need to be visualized by the theory of load path. Then, the design criteria of external shape are established based on the principle of smoother load paths in the structure. An index of load flow capacity is defined to indicate the load paths density and to control the density distribution of unit cells, and a detailed optimization strategy is given. Finally, three examples of a cantilever plate, an L-shaped bracket and a classical three-point bending beam are used to verify the method. The results show that the models designed by the proposed method have better mechanical performances, lower material usage and less printing time.