Towards solving large-scale topology optimization problems with buckling constraints at the cost of linear analyses

Abstract

This work presents a multilevel approach to large-scale topology optimization accounting for linearized buckling criteria. The method relies on the use of preconditioned iterative solvers for all the systems involved in the linear buckling and sensitivity analyses and on the approximation of buckling modes from a coarse discretization. The strategy shows three main benefits: first, the computational cost for the eigenvalue analyses is drastically cut. Second, artifacts due to local stress concentrations are alleviated when computing modes on the coarse scale. Third, the ability to select a reduced set of important global modes and filter out less important local ones. As a result, designs with improved buckling resistance can be generated with a computational cost little more than that of a corresponding compliance minimization problem solved for multiple loading cases. Examples of 2D and 3D structures, discretized by up to some millions of degrees of freedom in Matlab, are presented to show the effectiveness of the proposed method. Finally, a post-processing procedure is suggested in order to reinforce the optimized design against local buckling.

Efficient stress‐constrained topology optimization using inexact design sensitivities

“…One approach is to utilize multiple resolutions. This includes grid refinement as the optimization progresses; 11‐13 utilizing fine grids to represent the design together with the coarsest possible grids to solve the state problem; 14‐17 and sophisticated use of coarse grids to avoid solving a costly state problem on the fine scale 18 . Another approach is to develop scalable computational procedures that are compatible with high performance parallel hardware.…”

Topology optimization for stability problems of submerged structures using the TOBS method

“…35 and 37, respectively. Recent works have discussed and improved the efficiency to compute buckling sensitivities [15,28], but this analysis (see Eq. 38) still presents a non-trivial computational routine and potential challenges inherent to the nature of the problem.…”

“…This simplified approach, however, is still complicated, and explains the notable gap between compliance-only based optimization problems and those considering stability parameters [14][15][16].…”

Topology Optimisation in Structural Steel Design for Additive Manufacturing

“…Recent advances already allow accounting for buckling in TO endeavours in a computationally feasible manner [438][439][440][441][442], mitigating some of the aforementioned problems. Though, those methods rely on linearized buckling, which is generally regarded as an inadequate simplification for many engineering problems [137,443,444] and therefore, face significant opposition from many researchers.…”