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Spectral stochastic isogeometric analysis of linear elasticity

机译：线弹性谱随机等几何分析

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The stochastic isogeometric analysis of linear elasticity problem is investigated in this study. The spectral stochastic analysis is introduced into isogeometric analysis (IGA), and a novel, yet robust, stochastic analysis framework, namely the spectral stochastic isogeometric analysis (SSIGA), is freshly proposed. Unlike traditional numerical solutions of the Karhunen-Loeve (K-L) expansion, the non-uniform rational B-spline (NURBS) and T-spline basis functions are employed within the proposed framework of SSIGA, so the random fields acting on a continuous physical medium with complex geometry can be handled in an appropriate, physically feasible and efficient fashion. The polynomials chaos expansion (PCE) is implemented to represent the stochastic structural response (e.g., displacement, strain and stress), such that all corresponding statistical characteristics (e.g., mean and standard deviation) can be robustly acquired. Furthermore, by utilizing the nonparametric statistical analysis, both probability density functions (PDFs) and cumulative distribution functions (CDFs) of concerned structural displacements and stresses can be effectively established. Within the framework of IGA, by meticulously implementing the concept of the higher-order k-refinement, the proposed SSIGA provides a more legitimate and efficient stochastic computational approach for modern engineering structures which are complicated by both spatially dependent uncertainties and complex geometries (C) 2017 Elsevier B.V. All rights reserved.
机译：本研究研究了线性弹性问题的随机等几何分析。将光谱随机分析引入等几何分析（IGA），并提出了一种新颖而又健壮的随机分析框架，即光谱随机等几何分析（SSIGA）。与Karhunen-Loeve（KL）展开式的传统数值解决方案不同，在建议的SSIGA框架内采用了非均匀有理B样条（NURBS）和T样条基函数，因此随机场作用于连续物理介质可以以适当，物理上可行和有效的方式处理几何形状复杂的物体。实现多项式混沌扩展（PCE）以表示随机结构响应（例如位移，应变和应力），从而可以稳健地获取所有相应的统计特征（例如均值和标准差）。此外，通过利用非参数统计分析，可以有效地建立有关结构位移和应力的概率密度函数（PDF）和累积分布函数（CDF）。在IGA的框架内，通过精心实施高阶k精炼的概念，拟议的SSIGA为现代工程结构提供了一种更加合法有效的随机计算方法，该方法由于空间相关的不确定性和复杂的几何形状而变得复杂（C） 2017 Elsevier BV保留所有权利。

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