Abstract

In this work, a combination of the spectral stochastic finite element method (SSFEM) and the time-domain spectral element method (TSEM), referred to as the stochastic time domain spectral element method (STSEM), is presented to compute the stochasticity of strain and stress of a higher-order sandwich composite beam with spatial variability in the material properties. The method proposed in this work employs the efficiencies of both SSFEM and TSEM for the uncertainty analysis of a sandwich beam. The material properties of face sheets and core are considered as Gaussian random fields, which are discretized using the Karhunen-Loéve expansion, and polynomial chaos expansion is used to represent the response quantity. A numerical example is considered for which, first, a sensitivity analysis is performed to identify the most sensitive material properties. Then, the proposed STSEM is used to demonstrate the computational efficiency and numerical accuracy in comparison with Monte-Carlo simulation. Moreover, the effect of core depth on strain and stress variability is also examined.

摘要

在这项工作中，提出了一种将谱随机有限元法（SSFEM）和时域谱元法（TSEM）相结合的方法，即随机时域谱元法（STSEM）来计算应变的随机性。高阶夹层复合梁的材料特性空间可变性和应力。本工作中提出的方法利用 SSFEM 和 TSEM 的效率对夹层梁进行不确定性分析。面板和芯材的材料属性被认为是高斯随机场，使用Karhunen-Loéve展开将其离散化，并使用多项式混沌展开来表示响应量。考虑一个数值例子，首先，执行敏感性分析以确定最敏感的材料特性。然后，与蒙特卡罗模拟相比，所提出的 STSEM 用于证明计算效率和数值精度。此外，还检查了核心深度对应变和应力变化的影响。