Stress-constrained topology optimization of geometrically nonlinear continuum structures by using parallel computing strategy

Stress-constrained topology optimization under geometrical nonlinear conditions is still an open topic as it often encounter difficulties such as mesh distortion, inaccurate stress evaluation and low computational efficiency. For this purpose, this paper develops a novel parallel-computing based topology optimization methodology for geometrically nonlinear continuum structures with stress constraints. To alleviate the mesh distortions in the low-density regions, a smooth material interpolation scheme from with different penalization for the elastic and nonlinear stiffness is proposed. Moreover, a new hybrid stress finite element formulation is included into the geometrically nonlinear topology optimization to capture a more accurate stress distribution that is less sensitive to mesh distortions. Then, to improve the computational efficiency of geometrically nonlinear and sensitivity analysis, a parallel computing framework based on the assembly free iterative solution is established. Meanwhile, an efficient sparse matrix-vector multiplication strategy, which is applicable to solve the geometrically nonlinear problems, is proposed to exploit the computing power of GPU effectively. Finally, several numerical examples are given to illustrate the efficiency and feasibility of the proposed method.