Multilevel Monte Carlo simulations of composite structures with uncertain manufacturing defects
Multilevel Monte Carlo simulations of composite structures with uncertain manufacturing defects
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DOI：
10.1016/j.probengmech.2020.103116
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发表时间：
2021-01-07
影响因子：
2.6
通讯作者：
Scheichl, R.
中科院分区：
文献类型：
--
作者：
Dodwell, T. J.;Kynaston, S.;Scheichl, R.
通过采用多层蒙特卡罗(MLMC)框架，本文表明，只需要少量昂贵的精细计算就可以准确地估计复合材料结构的失效统计，而经典的蒙特卡罗分析通常需要数千次。本文介绍了MLMC方法，并提出了一种具有选择性精化的MLMC扩展方法，以有效地计算结构的失效概率。给出了易于实现的自适应算法，结果表明，对于复合材料性能分析中的两个新的实际问题：(I)纤维波纹度对复合材料抗压强度的影响和(Ii)具有随机铺层方向的复合材料面板的不确定屈曲性能，计算结果显示出巨大的计算收益。对于最具挑战性的估计复合材料板屈曲失效概率为1/150的测试案例，结果显示比经典蒙特卡罗加速系数>；1000。就绝对值而言，计算时间从218个CPU天减少到仅4.4个CPU小时，使得原本不可想象的随机模拟成为可能。
By adopting a Multilevel Monte Carlo (MLMC) framework, this paper shows that only a handful of costly fine scale computations are needed to accurately estimate statistics of the failure of a composite structure, as opposed to the many thousands typically needed in classical Monte Carlo analyses. The paper introduces the MLMC method and provides an extension called MLMC with selective refinement to efficiently calculated structural failure probabilities. Simple-to-implement, self-adaptive algorithms are given, and the results demonstrate huge computational gains for two novel, real world example problems in composites performance analysis: (i) the effects of fibre waviness on the compressive strength of a composite material and (ii) the uncertain buckling performance of a composite panel with random ply orientations. For the most challenging test case of estimating a 1/150 probability of buckling failure of a composite panel the results demonstrate a speed-up factor of > 1000 over classical Monte Carlo. In absolute terms, the computational time was reduced from 218 CPU days to just 4.4 CPU hours, making stochastic simulations that would otherwise be unthinkable now possible.