Open Access

ARTICLE

An Improved Graphics Processing Unit Acceleration Approach for Three-Dimensional Structural Topology Optimization Using the Element-Free Galerkin Method

Haishan Lu, Shuguang Gong^*, Jianping Zhang, Guilan Xie, Shuohui Yin

School of Mechanical Engineering, Xiangtan University, Xiangtan, 411105, China

* Corresponding Author: Shuguang Gong. Email:

(This article belongs to the Special Issue: Novel Methods of Topology Optimization and Engineering Applications)

Computer Modeling in Engineering & Sciences 2021, 128(3), 1151-1178. https://doi.org/10.32604/cmes.2021.016165

Received 13 February 2021; Accepted 16 April 2021; Issue published 11 August 2021

Abstract

We proposed an improved graphics processing unit (GPU) acceleration approach for three-dimensional structural topology optimization using the element-free Galerkin (EFG) method. This method can effectively eliminate the race condition under parallelization. We established a structural topology optimization model by combining the EFG method and the solid isotropic microstructures with penalization model. We explored the GPU parallel algorithm of assembling stiffness matrix, solving discrete equation, analyzing sensitivity, and updating design variables in detail. We also proposed a node pair-wise method for assembling the stiffness matrix and a node-wise method for sensitivity analysis to eliminate race conditions during the parallelization. Furthermore, we investigated the effects of the thread block size, the number of degrees of freedom, and the convergence error of preconditioned conjugate gradient (PCG) on GPU computing performance. Finally, the results of the three numerical examples demonstrated the validity of the proposed approach and showed the significant acceleration of structural topology optimization. To save the cost of optimization calculation, we proposed the appropriate thread block size and the convergence error of the PCG method.

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