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

TL;DR

This paper introduces a multilevel method for large-scale topology optimization with buckling constraints, significantly reducing computational costs while improving design robustness through coarse mode approximation and iterative solvers.

Contribution

The novel multilevel approach efficiently incorporates buckling constraints into large-scale topology optimization using coarse discretization and preconditioned iterative solvers.

Findings

Drastic reduction in eigenvalue analysis costs.

Improved buckling resistance in optimized designs.

Effective handling of large 2D and 3D structures.

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 are solved in Matlab 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.