Fully parallel level set method for large-scale structural topology optimization

• Published in: Computers & structures 2019-09, Vol.221, p.13-27
• Main Authors: Liu, Hui, Tian, Ye, Zong, Hongming, Ma, Qingping, Wang, Michael Yu, Zhang, Liang
• Format: Article
• Language: English
• Subjects: Compactly supported radial basis function; Computational efficiency; Computing time; Design optimization; Design parameters; Equations of state; Finite element method; Large-scale structural topology optimization; Level set method; Mathematical analysis; Mesh generation; Nonuniformity; Parallel computing; Parallel processing; Parameterization; Radial basis function; Sensitivity analysis; Stiffness matrix; Topology optimization; Uniform and non-uniform structured meshes
• ISSN: 0045-7949; 1879-2243
• DOI: 10.1016/j.compstruc.2019.05.010

•A fully parallel parameterized level set method was developed for structural topology optimization.•High resolution structures were designed on both the uniform and non-uniform structured meshes.•The parameterization process of the level set function was carried out in parallel. To realize large-scale or high-resolution structural topology optimization design, a fully parallel parameterized level set method with compactly supported radial basis functions (CSRBFs) is developed based on both the uniform and non-uniform structured meshes. In this work, the whole computation process is parallelized, including mesh generation, sensitivity analysis, calculation and assembly of the element stiffness matrices, solving of the structural state equation, parameterization and updating of the level set function, and output of the computational results during the optimization iterations. In addition, some typical numerical examples, in which the calculation scale is up to 7 million 8-node hexahedral elements, are carried out for verifying the effectiveness of the proposed method. Finally, the computing time is also analyzed in detail. It is found that: (1) In the optimized structures, the thin sheet-like components gradually replace the truss-like ones when refining the mesh, (2) the parameterization process of the level set function will become fast as long as the non-uniformity of mesh is not very high and the supported radius of CSRBF is small enough, and (3) more than 80% of the total computing time is always consumed for solving the structural state equation during the finite element analysis (FEA).