Zhao Li¹, Hongyu Xu^1,*, Shuai Zhang², Jintao Cui¹, Xiaofeng Liu¹

CMC-Computers, Materials & Continua, Vol.86, No.1, pp. 1-18, 2026, DOI:10.32604/cmc.2025.068763 - 10 November 2025

Abstract The moving morphable component (MMC) topology optimization method, as a typical explicit topology optimization method, has been widely concerned. In the MMC topology optimization framework, the surrogate material model is mainly used for finite element analysis at present, and the effectiveness of the surrogate material model has been fully confirmed. However, there are some accuracy problems when dealing with boundary elements using the surrogate material model, which will affect the topology optimization results. In this study, a boundary element reconstruction (BER) model is proposed based on the surrogate material model under the MMC topology optimization… More >

Kangjie Li, Wenjing Ye^*

CMES-Computer Modeling in Engineering & Sciences, Vol.145, No.2, pp. 1665-1688, 2025, DOI:10.32604/cmes.2025.072447 - 26 November 2025

Abstract Recent progress in topology optimization (TO) has seen a growing integration of machine learning to accelerate computation. Among these, online learning stands out as a promising strategy for large-scale TO tasks, as it eliminates the need for pre-collected training datasets by updating surrogate models dynamically using intermediate optimization data. Stress-constrained lightweight design is an important class of problem with broad engineering relevance. Most existing frameworks use pixel or voxel-based representations and employ the finite element method (FEM) for analysis. The limited continuity across finite elements often compromises the accuracy of stress evaluation. To overcome this… More >

Fei Wu¹, Ziyang Zeng^1,2, Kunliang Xie¹, Yuqiang Liu¹, Jiang Ding^1,2,3,*

CMES-Computer Modeling in Engineering & Sciences, Vol.145, No.2, pp. 1689-1710, 2025, DOI:10.32604/cmes.2025.071256 - 26 November 2025

Abstract The level set method (LSM) is renowned for producing smooth boundaries and clear geometric representations, facilitating integration with CAD environments. However, its inability to autonomously generate new holes during optimization makes the results highly dependent on the initial design. Although topological derivatives are often introduced to enable hole nucleation, their conversion into effective shape derivatives remains challenging, limiting topological evolution. To address this, a level set topology optimization method with autonomous hole formation (LSM-AHF) is proposed, integrating the material removal mechanism of the SIMP (Solid Isotropic Material with Penalization) method into the LSM framework. First,… More >

Tao Liu¹, Yang Liu², Jianbin Du^1,*

The International Conference on Computational & Experimental Engineering and Sciences, Vol.33, No.4, pp. 1-2, 2025, DOI:10.32604/icces.2025.011595

Abstract Currently, the application of the Boundary Penalty (BP) method in acoustic-structural coupled multiphysics optimization problems remains unexplored. Within the theoretical framework of BP developed previously, we address acoustic-structural coupled topology optimization problems by proposing a BP-based acoustic-structural coupled topology optimization model. A systematic solution strategy is developed to tackle the challenges encountered during model solving.
The proposed model employs a mixed u/p formulation for finite element analysis and the adjoint method for sensitivity analysis to minimize the acoustic pressure within a specified region (Fig.1 A). During optimization iterations, issues such as topological discretization and iteration oscillations… More >

Rui Xu¹, Chaogan Gao¹, Jiale Shi², Guorui Yu¹, Quhao Li^2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.145, No.1, pp. 1-16, 2025, DOI:10.32604/cmes.2025.071942 - 30 October 2025

Abstract To address the design challenges of helicopter hub central components under high-performance requirements, this paper conducts safe-life topology optimization design research considering fatigue performance for rotor hub central components under multi-load conditions, combined with helicopter fatigue strength engineering design theory. For dealing with the issues of derivative calculation difficulties when directly considering fatigue constraints in existing topology optimization methods, this study establishes a mathematical formulation suitable for structural topology optimization of hub central components by combining modified structural safety fatigue limits based on iso-life curves. Then the sensitivity analysis of design variables is derived, and More >

Tianyuan Qi¹, Junpeng Zhao^1,2,*, Chunjie Wang^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.145, No.1, pp. 127-151, 2025, DOI:10.32604/cmes.2025.070769 - 30 October 2025

Abstract A major bottleneck in large-scale eigenfrequency topology optimization is the repeated solution of the generalized eigenvalue problem. This work presents an efficient graphics processing unit (GPU) solver for three-dimensional (3D) topology optimization that maximizes the fundamental eigenfrequency. The Successive Iteration of Analysis and Design (SIAD) framework is employed to avoid solving a full eigenproblem at every iteration. The sequential approximation of the eigenpairs is solved by the GPU-accelerated multigrid-preconditioned conjugate gradient (MGPCG) method to efficiently improve the eigenvectors along with the topological evolution. The cluster-mean approach is adopted to address the non-differentiability issue caused by… More > Graphic Abstract

Minjie Shao, Tielin Shi, Qi Xia^*, Shiyuan Liu^*

CMES-Computer Modeling in Engineering & Sciences, Vol.144, No.3, pp. 2685-2703, 2025, DOI:10.32604/cmes.2025.068078 - 30 September 2025

Abstract A data-driven model of multiple variable cutting (M-VCUT) level set-based substructure is proposed for the topology optimization of lattice structures. The M-VCUT level set method is used to represent substructures, enriching their diversity of configuration while ensuring connectivity. To construct the data-driven model of substructure, a database is prepared by sampling the space of substructures spanned by several substructure prototypes. Then, for each substructure in this database, the stiffness matrix is condensed so that its degrees of freedom are reduced. Thereafter, the data-driven model of substructures is constructed through interpolation with compactly supported radial basis More >

Hang Zhou^*, Xiaojun Ding, Song Chen, Qijun Zhang

CMES-Computer Modeling in Engineering & Sciences, Vol.144, No.2, pp. 1907-1933, 2025, DOI:10.32604/cmes.2025.069198 - 31 August 2025

Abstract Structural Reliability-Based Topology Optimization (RBTO), as an efficient design methodology, serves as a crucial means to ensure the development of modern engineering structures towards high performance, long service life, and high reliability. However, in practical design processes, topology optimization must not only account for the static performance of structures but also consider the impacts of various responses and uncertainties under complex dynamic conditions, which traditional methods often struggle accommodate. Therefore, this study proposes an RBTO framework based on a Kriging-assisted level set function and a novel Dynamic Hybrid Particle Swarm Optimization (DHPSO) algorithm. By leveraging… More >

Jianchang Hou¹, Zhanpeng Jiang¹, Fenghe Wu¹, Hui Lian¹, Zhaohua Wang², Zijian Liu³, Weicheng Li^1,*

CMES-Computer Modeling in Engineering & Sciences, Vol.144, No.2, pp. 1545-1572, 2025, DOI:10.32604/cmes.2025.068482 - 31 August 2025

Abstract In this paper, a topology optimization method for coordinated stiffness and strength design is proposed under mass constraints, utilizing the Solid Isotropic Material with Penalization approach. Element densities are regulated through sensitivity filtering to mitigate numerical instabilities associated with stress concentrations. A p-norm aggregation function is employed to globalize local stress constraints, and a normalization technique linearly weights strain energy and stress, transforming the multi-objective problem into a single-objective formulation. The sensitivity of the objective function with respect to design variables is rigorously derived. Three numerical examples are presented, comparing the optimized structures in terms More >

Xuefei Yang, Ying Zhou, Liang Gao, Hao Li^*

CMC-Computers, Materials & Continua, Vol.85, No.1, pp. 613-635, 2025, DOI:10.32604/cmc.2025.068756 - 29 August 2025

Abstract Inspired by natural biomimetic structures exemplified by femoral bones, the shell-infill composite design has emerged as a research focus in structural optimization. However, existing studies predominantly focus on uniform-thickness shell designs and lack robust methodologies for generating high-resolution porous infill configurations. To address these challenges, a novel topology optimization framework for full-scale shell-filled composite structures is developed in this paper. First, a physics-driven, non-uniform partial differential equation (PDE) filter is developed, enabling precise control of variable-thickness shells by establishing explicit mapping relationships between shell thickness and filter radii. Second, this study addresses the convergence inefficiency… More >