Nonlinear Topology Optimization of Continuum Structures Based on HCA Algorithm

doi:10.3969/j.issn.1004-132X.2020.18.003

Abstract

Abstract: A HCA algorithm without gradient was used. The topology optimization was realized by coupling the CA rules with the LS-DYNA solver, the non-convergence problems such as numerical oscillation and catastrophe in the iteration processes were solved under the conditions of small deformation with material nonlinearity. By introducing volume constraint function and constantly updating the target values of strain energy density, the masses of the optimized structure might converge to the target masses accurately, the purposes of topology optimization results to the size optimization of structures were realized. The research results show that nonlinear analysis is very important for structural optimization design in practical engineering. The HCA topological ptimization algorithm combined with LS-DYNA solver is efficient and reliable for solving nonlinear problems, which may effectively overcome the singular solutions and the checkerboard problem. The HCA method has a practical value for engineering applications.

Key words: hybrid cellular automata(HCA), nonlinear, topology optimization, numerical simulation

摘要： 采用一种无梯度的混合元胞自动机 (HCA) 算法，通过将元胞自动机(CA)规则与LS-DYNA求解器耦合来实现拓扑优化，解决了材料非线性小变形工况在迭代过程中的振荡不收敛及突变现象。通过引入体积约束函数并不断更新应变能密度目标值，使优化结构的质量能够精确收敛于目标质量，实现了拓扑优化结果对结构尺寸优化的目的。研究结果表明，非线性分析对实际工程中的结构优化设计非常重要，结合LS-DYNA求解器的HCA拓扑优化算法对求解非线性问题高效可靠，能够有效减少奇异解并消除棋盘格现象，具有良好的工程应用价值。

关键词: 混合元胞自动机, 非线性的, 拓扑优化, 数值仿真

CLC Number:

TP391.41

WANG Guan1；ZHANG Qian2；KOU Linyuan1；LIU Zhiwen3；LI Shikang3. Nonlinear Topology Optimization of Continuum Structures Based on HCA Algorithm[J]. China Mechanical Engineering, DOI: 10.3969/j.issn.1004-132X.2020.18.003.

王冠1；张骞2；寇琳媛1；刘志文3；李世康3. 基于混合元胞自动机算法的连续体结构非线性拓扑优化[J]. 中国机械工程, DOI: 10.3969/j.issn.1004-132X.2020.18.003.

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