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A perturbation method for stochastic meshless analysis in elastostatics
Author(s) -
Rahman S.,
Rao B. N.
Publication year - 2001
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.106
Subject(s) - regularized meshless method , singular boundary method , meshfree methods , mathematics , finite element method , mathematical optimization , boundary value problem , random field , computer science , mathematical analysis , boundary element method , physics , statistics , thermodynamics
A stochastic meshless method is presented for solving boundary‐value problems in linear elasticity that involves random material properties. The material property was modelled as a homogeneous random field. A meshless formulation was developed to predict stochastic structural response. Unlike the finite element method, the meshless method requires no structured mesh, since only a scattered set of nodal points is required in the domain of interest. There is no need for fixed connectivities between nodes. In conjunction with the meshless equations, classical perturbation expansions were derived to predict second‐moment characteristics of response. Numerical examples based on one‐ and two‐dimensional problems 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 Monte Carlo simulation. Since mesh generation of complex structures can be a far more time‐consuming and costly effort than the solution of a discrete set of equations, the meshless method provides an attractive alternative to finite element method for solving stochastic mechanics problems. Copyright © 2001 John Wiley & Sons, Ltd.