Stress-constrained topology optimization using approximate reanalysis with on-the-fly reduced order modeling

Abstract

Most of the methods used today for handling local stress constraints in topology optimization, fail to directly address the non-self-adjointness of the stress-constrained topology optimization problem. This in turn could drastically raise the computational cost for an already large-scale problem. These problems involve both the equilibrium equations resulting from finite element analysis (FEA) in each iteration, as well as the adjoint equations from the sensitivity analysis of the stress constraints. In this work, we present a paradigm for large-scale stress-constrained topology optimization problems, where we build a multi-grid approach using an on-the-fly Reduced Order Model (ROM) and the p-norm aggregation function, in which the discrete reduced-order basis functions (modes) are adaptively constructed for adjoint problems. In addition to reducing the computational savings due to the ROM, we also address the computational cost of the ROM learning and updating phases. Both reduced-order bases are enriched according to the residual threshold of the corresponding linear systems, and the grid resolution is adaptively selected based on the relative error in approximating the objective function and constraint values during the iteration. The tests on 2D and 3D benchmark problems demonstrate improved performance with acceptable objective and constraint violation errors. Finally, we thoroughly investigate the influence of relevant stress constraint parameters such as the p norm factor, stress penalty factor, and the allowable stress value.

Minimization of the stress concentration in Formed Parts through Non-Parametric Optimization

“…Topology optimization involves using mathematical methods to determine how to distribute materials within a fixed geometric domain while adhering to certain constraints, in order to optimize the mechanical performance of a structure [19,20].…”

Torsional strength analysis of universal joint’s ZP-11A due to yokes modification and materials

“…With acceptable goal and constraint violation errors, the tests on benchmark 2D and 3D show increased performance. The impact of important stress constraint factors, thus the allowable stress value, stress penalty factor, and pnorm factor, is carefully examined by Xiao et al [17].…”