Structural Topology Optimization Research Articles

An efficient GPU solver for 3D topology optimization of continuous fiber-reinforced composite structures

An efficient GPU solver for 3D topology optimization of continuous fiber-reinforced composite structures

Structural topology optimization of aircraft wing leading edge fabricated of multilayer composites

Structural topology optimization of aircraft wing leading edge fabricated of multilayer composites

Integrating moving morphable components and plastic layout optimization: a two-stage approach for enhanced structural topology optimization

Integrating moving morphable components and plastic layout optimization: a two-stage approach for enhanced structural topology optimization

Optimization, analysis, and thermal performance enhancement of the cooling flow channel for a condenser mirror

Condenser mirrors with the ellipsoidal surface type are widely used in laser illuminating systems. Nonetheless, thermal absorption in optical components is unavoidable because of high-energy lasers, leading to a decline in surface shape accuracy. In extreme instances, this can shorten the operational longevity or impair the system’s focusing capabilities. Currently, water cooling is a major technical approach for controlling the thermal deformation of condenser mirrors. This paper proposes an efficient cooling flow channel based on topology optimization methods for high-gradient ellipsoidal optical mirrors. Firstly, topology optimization of the cooling flow channel was performed with the objective function of minimizing average temperature and entransy dissipation. Next, the influence of different design parameters on the optimization results was investigated, and the optimal topological structure was obtained. Then, a thermal–fluid–solid coupled simulation was carried out for a three-dimensional model of the water-cooled condenser mirror to verify the topology optimization design. The results show that when the inlet flow rate is 2.82×10−4m3/s, the surface shape accuracy of the water-cooled condenser mirror (RMS 213.79 nm) equipped with the topology optimization cooling flow channel is reduced by 22.96% compared to that of the water-cooled condenser mirror (RMS 277.66 nm) with the traditional spiral cooling flow channel. Finally, the manufacturability of the optimized model was verified by selective laser melting technology and x-ray detection.

Topology optimization of structures with steady-state heat conduction using an improved parameterized level set method

This article proposes an improved parameterized level set method to handle topology optimization design of structures with steady-state heat conduction. In this method, the level set function (LSF) is interpolated using compactly-supported radial basis functions. Thus, it is more convenient and efficient to evolve the LSF, while ensuring the smoothness of the optimized boundary. The shape sensitivity constraint factor is used to improve computational efficiency. Furthermore, an approximate re-initialization scheme is adopted after each of iteration to keep the gradient of the LSF boundary stable, thereby improving the numerical stability and convergence speed of the structural topology optimization process.

Multipatch IGA for stress-constrained minimum weight structural topology optimization

In this article, an isogeometric analysis (IGA) formulation with various patches (multipatch approach) is proposed to solve the structural topology optimization (STO) problem. The multipatch formulation enables the solution of STO problems with geometries not equivalent to rectangles by using IGA. For this purpose, a minimum weight with stress constraints (MWSC) problem is stated. A quadratic B-splines basis defined for each patch is used to model the material distribution. The structural analysis is computed with IGA. The introduction of all of the stress constraints in the formulation of the problem is made with an overweight constraint (OC). Finally, the multipatch approach is validated with the solution of some benchmark problems.

A parameterized level set method for structural topology optimization using the approximate re-initialization scheme

This article proposes an efficient parameterized level set method (PLSM) for structural topology optimization design with minimum compliance as the objective function and volume fraction as the constraint condition. In the stage of establishing the optimization model, the level set function (LSF) is interpolated using compactly-supported radial basis functions (CS-RBFs) to transform the Hamilton-Jacobi partial differential equation (PDE) into ordinary differential equations (ODEs), thereby making the evolution of the LSF more convenient and efficient, and ensuring the smoothness of the optimization result boundary. The method of moving asymptotes (MMA) is used for solving the established optimization model, and meanwhile the shape sensitivity constraint factor is added to improve computational efficiency. During the evolution of the LSF, an approximate re-initialization scheme is employed to prevent the gradient of the LSF boundary from being too large or too small, thereby improving the numerical stability and the convergence speed of structural topology optimization process. Furthermore, the proposed method is also extensible and applicable to topology optimization of multi-material structures. The feasibility and effectiveness of this method have been verified through several typical numerical examples involving topology optimization of single-material structures and multi-material structures within the framework of minimum compliance design. HIGHLIGHTS An efficient parameterized level set method using the approximate re-initialization scheme is proposed for structural topology optimization. The approximate re-initialization scheme is employed when solving the parameterized level set function via the MMA algorithm. This scheme can prevents the gradient of the level set function boundary from being too large or too small, making the level set function update more stable and accelerating the convergence speed of structural topology optimization. The effectiveness and feasibility of the proposed method are demonstrated through examples of single-material and multi-material structural topology optimization.

Structural topology optimization in linear and nonlinear elasticity using a discontinuous Galerkin finite element method

Abstract A discontinuous Galerkin finite element method is developed for structural topology optimization with the level set method. The discontinuous Galerkin finite element method is employed to discretize and solve both the elasticity system, possible adjoint, and the transport equation of the level set function. Structural compliance and compliant mechanisms are considered for linear and nonlinear elastic structures. Numerical examples are provided to verify the effectiveness of the algorithm presented.

Featured Cover

The cover image is based on the article On the Use of Fidelity Transformation Method for Stress‐Constrained Reliability‐Based Topology Optimization of Continuum Structure With High Accuracy by Peng Hao et al., https://doi.org/10.1002/nme.7602. image

Structural topology and parameter optimization of torsional dampers used in parallel hybrid electric vehicles based on the working conditions

Hybrid electric vehicles (HEVs) are equipped with multiple power sources and involve complex mode-switching processes, which lead to intricate torsional vibration characteristics in their powertrains. This paper presents a novel clutch torsional damper with arc springs (CTD-AS) that combines the advantages of traditional clutch torsional dampers (CTDs) and dual-mass flywheels (DMFs). The structure and working principle of the CTD-AS are introduced in the paper, and a torsional damper parameter design method is discussed. During the study, a 13-degree-of-freedom concentrated mass model was established for an HEV powertrain, and optimization schemes based on multiple sets of operating conditions were obtained for a CTD, a DMF, and the CTD-AS. The optimized simulation results demonstrated that the average torsional vibration transmissibility value of the CTD-AS under the three working conditions was approximately 13.8% and 29.7% lower than that of the DMF and the CTD, respectively, and the overall performance is the best. The novel structural topology and parameter optimization method for the torsional damper of a parallel HEV proposed in this paper can effectively enhance driving smoothness under a variety of working conditions.

Extending the Meshless Natural-Neighbour Radial-Point Interpolation Method to the Structural Optimization of an Automotive Part Using a Bi-Evolutionary Bone-Remodelling-Inspired Algorithm

Topological structural optimization is a powerful computational tool that enhances the structural efficiency of mechanical components. It achieves this by reducing mass without significantly altering stiffness. This study combines the Natural-Neighbour Radial-Point Interpolation Method (NNRPIM) with a bio-inspired bi-evolutionary bone-remodelling algorithm. This combination enables non-linear topological optimization analyses and achieves solutions with optimal stiffness-to-mass ratios. The NNRPIM discretizes the problem using an unstructured nodal distribution. Background integration points are constructed using the Delaunay triangulation concept. Nodal connectivity is then imposed through the natural neighbour concept. To construct shape functions, radial point interpolators are employed, allowing the shape functions to possess the delta Kronecker property. To evaluate the numerical performance of NNRPIM, its solutions are compared with those obtained using the standard Finite Element Method (FEM). The structural optimization process was applied to a practical example: a vehicle’s suspension control arm. This research is divided into two phases. In the first phase, the optimization algorithm is applied to a standard suspension control arm, and the results are closely evaluated. The findings show that NNRPIM produces topologies with suitable truss connections and a higher number of intermediate densities. Both aspects can enhance the mechanical performance of a hypothetical additively manufactured part. In the second phase, four models based on a solution from the optimized topology algorithm are analyzed. These models incorporate established design principles for material removal commonly used in vehicle suspension control arms. Additionally, the same models, along with a solid reference model, undergo linear static analysis under identical loading conditions used in the optimization process. The structural performance of the generated models is analyzed, and the main differences between the solutions obtained with both numerical techniques are identified.

Evolutionary topology optimization for elastoplastic structures via isogeometric analysis

In this article, an evolutionary isogeometric topology optimization method for elastoplastic materials while minimizing compliance is proposed. The material and constitutive models are grounded in the framework of finite strain nonlinear isotropic hardened plasticity, and the yield surfaces undergo updates through an explicit numerical scheme of elastic prediction/plasticity correction. The application of isogeometric analysis is intended to meet the requirements of high-order continuity between adjacent elements during transitional states. For evolutionary-based optimization, adjoint sensitivity expressions are developed under displacement-loaded control, and the isogeometric realization is performed. Numerical results demonstrate that the proposed method performs well with different models and is effective for scenarios with various displacement-loaded specifications. The comparison with finite element results shows that the proposed technique yields fast yet accurate solutions.

Topology optimization of thermoelastic structures with single and functionally graded materials exploring energy and stress-based formulations

Topology optimization problem formulations have lately included stresses, besides compliance, to ensure mechanical strength feasibility, which is of utmost importance in structural engineering practice. A mechanically induced stress field has often been considered in optimal structural design. However, one realizes that thermal stresses can also greatly influence efficient designs, especially when addressing highly constrained structures. Moreover, stress mitigation has been achieved by enlarging the design domain to multi-material solutions. This motivates to pursue stress-based topology optimization of thermoelastic structures and the extension of the multi-material setting to Functionally Graded Materials (FGMs), with greater potential in stress mitigation. Two optimization problems are investigated: (1) elastic strain energy minimization and (2) maximum von Mises stress minimization. In the former, the single-material problem is revisited, but in the frame of a multi-objective formulation, weighting mechanical and thermal strain energy terms, as they can be decoupled. Insights into thermal stresses allow to propose a well-posed stress-based formulation for the topology optimization thermoelastic problem. In the latter, stress mitigation is sought on account of optimizing the spatial mixture (composition) of two solids amidst prescribed or predicted voids. It is assumed that the RAMP interpolation scheme has the physical meaning of rendering the thermoelastic properties for the continuous variation of composition. Linear thermoelasticity and plane stress benchmarks are used. In the multi-objective energy-based problem, the trade-offs between the conflicting design objectives, in the Pareto sense, are highlighted. Regarding the stress-based problem, lower stress peaks are obtained in FGM solutions, as stresses are more evenly distributed.

Corrigendum to “Topology optimization of lattice structures for target band gaps with optimum volume fraction via Bloch-Floquet theory” [Comput. Struct. 307 (2025) 107601

Corrigendum to “Topology optimization of lattice structures for target band gaps with optimum volume fraction via Bloch-Floquet theory” [Comput. Struct. 307 (2025) 107601

Thermo-elastic topology optimization and experimental characterization for multiphase structure with high thermal stiffness invariability

Thermo-elastic topology optimization and experimental characterization for multiphase structure with high thermal stiffness invariability

Topology optimization of lattice structures for target band gaps with optimum volume fraction via Bloch-Floquet theory

Topology optimization of lattice structures for target band gaps with optimum volume fraction via Bloch-Floquet theory

Topology optimization of periodic heat transfer structure with anisotropic multi-material based on element-free Galerkin method

Topology optimization of periodic heat transfer structure with anisotropic multi-material based on element-free Galerkin method

A novel digital unit cell library generation framework for topology optimization of multi-morphology lattice structures

A novel digital unit cell library generation framework for topology optimization of multi-morphology lattice structures

Level set method for structure topology optimization with asymmetrical microstructure model

Level set method for structure topology optimization with asymmetrical microstructure model

A Critical Review of Structural Topology Optimization Algorithms

In the past 30 years , the field of structural topology optimization has developed rapidly, and many representative algorithms such as homogenization algorithm, solid isotropic material with penalization algorithms and evolutionary structural optimization algorithms have emerged. In this paper, the above three representative algorithms’ principles and development history are briefly introduced. Secondly, with the classic example of long cantilever beams, the three methods are compared in all aspects of the optimisation process, and their similarities and differences in terms of optimisation objectives, constraints, and characteristics of the results are analysed. Finally, the above algorithms are summarized, and their advantages, disadvantages and applicable scenarios are listed, which will provide reference for future designers to a certain extent.