HIERARCHICAL STOCHASTIC FINITE ELEMENT METHOD FOR STRUCTURAL ANALYSIS

• Published in: Acta mechanica solida Sinica 2013-04, Vol.26 (2), p.189-196
• Main Authors: Yang, Lufeng, Zhou, Yue'e, Zhou, Jingjing, Wang, Meilan
• Format: Article
• Language: English
• Subjects: Classical Mechanics; Computer simulation; Engineering; Finite element method; hierarchical stochastic finite element method; Karhunen-Loève series; Mathematical analysis; Mathematical models; Modulus of elasticity; Monte Carlo methods; random field; Stochasticity; Surfaces and Interfaces; Theoretical and Applied Mechanics; Thin Films; variational principle; Vectors (mathematics); 位移矢量; 扩展技术; 级数表示; 结构分析; 蒙特卡罗模拟; 随机变分原理; 随机有限元方法; 随机有限元法
• ISSN: 0894-9166; 1860-2134
• DOI: 10.1016/S0894-9166(13)60018-X

In this paper, the hierarchical approach is adopted for series representation of the stochastic nodal displacement vector using the hierarchical basis vectors, while the Karhunen- Loire series expansion technique is employed to discretize the random field into a set of random variables. A set of hierarchical basis vectors are defined to approximate the stochastic response quantities. The stochastic variational principle instead of the projection scheme is adopted to develop a hierarchical stochastic finite element method （HSFEM） for stochastic structures under stochastic loads. Simplified expressions of coefficients of governing equations and the first two statistical moments of the response quantities in the schemes of the HSFEM are developed, so that the time consumed for computation can be greatly reduced. Investigation in this paper suggests that the HSFEM yields a series of stiffness equations with similar dimensionality as the perturbation stochastic finite element method （PSFEM）. Two examples are presented for numerical study on the performance of the HSFEM in elastic structural problems with stochastic Young＇s Modulus and external loads. Results show that the proposed method can achieve higher accuracy than the PSFEM for cases with large coefficients of variation, and yield results agreeing well with those obtained by the Monte Carlo simulation （MCS）.