Bayesian buckling load optimisation for structures with geometric uncertainties

TL;DR

This paper presents a Bayesian optimisation framework for enhancing the buckling load robustness of lightweight structures with geometric uncertainties, using advanced sampling and finite element techniques for efficient and accurate results.

Contribution

It introduces a novel combination of Monte Carlo, quasi-Monte Carlo, and Bayesian optimisation for robust buckling load design considering geometric imperfections.

Findings

Reduced number of finite element computations with Sobol sampling

Effective robust optimisation of nonlinear truss structures

Demonstrated accuracy and efficiency of the framework

Abstract

Optimised lightweight structures, such as shallow domes and slender towers, are prone to sudden buckling failure because geometric uncertainties/imperfections can lead to a drastic reduction in their buckling loads. We introduce a framework for the robust optimisation of buckling loads, considering geometric nonlinearities and random geometric imperfections. The mean and standard deviation of buckling loads are estimated by Monte Carlo sampling of random imperfections and performing a nonlinear finite element computation for each sample. The extended system method is employed to compute the buckling load directly, avoiding costly path-following procedures. Furthermore, the quasi-Monte Carlo sampling using the Sobol sequence is implemented to generate more uniformly distributed samples, which significantly reduces the number of finite element computations. The objective function consisting of the weighted sum of the mean and standard deviation of the buckling load is optimised using Bayesian optimisation. The accuracy and efficiency of the proposed framework are demonstrated through robust sizing optimisation of several geometrically nonlinear truss examples.