具有几何不确定性的结构的贝叶斯屈曲载荷优化
Bayesian buckling load optimisation for structures with geometric uncertainties
AI总结：
针对几何不确定性导致的屈曲载荷下降问题，提出结合蒙特卡洛采样、扩展系统法和贝叶斯优化的鲁棒优化框架，在桁架示例中验证了准确性与效率。
摘要：
优化的轻质结构，如浅穹顶和细长塔，容易发生突然的屈曲破坏，因为几何不确定性/缺陷可能导致其屈曲载荷急剧降低。我们引入了一个用于屈曲载荷鲁棒优化的框架，考虑了几何非线性和随机几何缺陷。屈曲载荷的均值和标准差通过随机缺陷的蒙特卡洛采样并对每个样本进行非线性有限元计算来估计。采用扩展系统方法直接计算屈曲载荷，避免了昂贵的路径跟踪过程。此外，实现了使用Sobol序列的准蒙特卡洛采样，以生成更均匀分布的样本，这显著减少了有限元计算的数量。由屈曲载荷的均值和标准差加权和组成的目标函数使用贝叶斯优化进行优化。通过几个几何非线性桁架示例的鲁棒尺寸优化，证明了所提出框架的准确性和效率。
英文摘要：
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.
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