Body-fitted bi-directional evolutionary structural optimization using nonlinear diffusion regularization

The bi-directional evolutionary structural optimization (BESO) method effectively uses basic strategies of removing and adding material based on element sensitivity. However, challenges remain in generating smooth boundaries to improve the finite element analysis accuracy and achieve structural aesthetics. This work develops a body-fitted triangular/tetrahedral mesh generation algorithm to yield smooth boundaries in the BESO method. The optimization problem is regularized by adding a diffusion term in the objective function. We found that the first has the best regularization effect of Lorentzian, Tikhonov, Perona–Malik, Huber, and Tukey functions. The void elements are excluded from spatial optimization to save computation costs and computer memory. Numerical examples show that the proposed method converges quickly, only taking dozens of iterations to converge. Also, the smooth boundaries of the optimized structures in 2D/3D scenarios are naturally obtained from the proposed method, not from smoothing post-processing. Compared with the optimization toolbox in Abaqus, the example of the automotive control arm demonstrates smoother boundaries and lower average mean compliance.