First-order topology optimization via inexact Finite Element Analysis. (April 2023) - Pan, Zherong; Gao, Xifeng; Wu, Kui
Abstract: Topology Optimization (TO) is an essential tool for optimizing the structural robustness of load-bearing mechanical parts. An ideal TO solver should be computationally efficient for designers to preview the results, while ultimately converge to locally optimal designs. However, existing TO solvers either incur a high iterative cost or fail to provide the convergence guarantee. Borrowing ideas from recent advances in first-order bilevel optimization, we propose a new TO solver combining the Projected Gradient Descent (PGD) algorithm and inexact Finite Element Analysis (FEA). We further show that our method is convergent to a first-order critical point. Our proposed First-Order Bilevel Topology Optimization (FBTO) can solve several, important problems in the robot design paradigm, including TO under self-weight and multiple external loads. Finally, we evaluate and compare FBTO with prior TO solvers on a row of 2D and 3D problems. Highlights: A new formulation of topology optimization (TO) via bilevel optimization. First-order TO algorithm class, FBTO, and convergence analysis. Numerical evaluation of FBTO on CPU/GPU.