Journal article
A Meshless Method for Computational Stochastic Mechanics
International journal of computational methods in engineering science and mechanics, Vol.6(1), pp.41-58
01/01/2005
DOI: 10.1080/15502280590888649
Abstract
This paper presents a stochastic meshless method for probabilistic analysis of linear-elastic structures with spatially varying random material properties. Using Karhunen-Loève (K-L) expansion, the homogeneous random field representing material properties was discretized by a set of orthonormal eigenfunctions and uncorrelated random variables. Two numerical methods were developed for solving the integral eigenvalue problem associated with K-L expansion. In the first method, the eigenfunctions were approximated as linear sums of wavelets and the integral eigenvalue problem was converted to a finite-dimensional matrix eigenvalue problem that can be easily solved. In the second method, a Galerkin-based approach in conjunction with meshless discretization was developed in which the integral eigenvalue problem was also converted to a matrix eigenvalue problem. The second method is more general than the first, and can solve problems involving a multi-dimensional random field with arbitrary covariance functions. In conjunction with meshless discretization, the classical Neumann expansion method was applied to predict second-moment characteristics of the structural response. Several numerical examples are presented to examine the accuracy and convergence of the stochastic meshless method. A good agreement is obtained between the results of the proposed method and the Monte Carlo simulation. Since mesh generation of complex structures can be far more time-consuming and costly than the solution of a discrete set of equations, the meshless method provides an attractive alternative to the finite element method for solving stochastic-mechanics problems.
Details
- Title: Subtitle
- A Meshless Method for Computational Stochastic Mechanics
- Creators
- S Rahman - Department of Mechanical Engineering, The University of IowaH Xu - Department of Mechanical Engineering, The University of Iowa
- Resource Type
- Journal article
- Publication Details
- International journal of computational methods in engineering science and mechanics, Vol.6(1), pp.41-58
- Publisher
- Taylor & Francis Group
- DOI
- 10.1080/15502280590888649
- ISSN
- 1550-2287
- eISSN
- 1550-2295
- Language
- English
- Date published
- 01/01/2005
- Academic Unit
- Mechanical Engineering
- Record Identifier
- 9984064229702771
Metrics
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