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.

翻译：优化后的轻质结构（如浅穹顶和细长塔架）易发生突然屈曲失效，因为几何不确定性/缺陷可能导致其屈曲荷载急剧下降。本文提出了一种考虑几何非线性和随机几何缺陷的屈曲荷载鲁棒优化框架。通过随机缺陷的蒙特卡洛采样并对每个样本执行非线性有限元计算，估计屈曲荷载的均值与标准差。采用扩展系统法直接计算屈曲荷载，避免了耗时的路径跟踪过程。此外，通过实施基于Sobol序列的拟蒙特卡洛采样生成更均匀分布的样本，显著减少了有限元计算次数。采用贝叶斯优化对由屈曲荷载均值与标准差加权和构成的目标函数进行优化。通过对多个几何非线性桁架算例进行鲁棒尺寸优化，验证了所提框架的准确性与效率。