TABLE OF CONTENTS SHARIF RAHMAN
Department of Mechanical and Industrial Engineering
The University of Iowa, Iowa City, IA 52245, USA
E- mail: rahman@engineering.uiowa.edu
This chapter provides an exposition of stochastic meshfree methods that involves deterministic meshfree formulation, spectral representation of random fields, multivariate function decomposition, statistical moment analysis, and reliability analysis. Numerical results indicate that stochastic meshfree methods, employed in conjunction with dimension-reduction and decomposition methods, yield accurate and computationally efficient estimates of statistical moments and reliability. Although significant strides have been made, breakthrough research on enhancing speed and robustness of meshfree methods is essential for their successful implementation into stochastic mechanics.
During the last decade, much attention has been focused on collocation1 , 2- or Galerkin-based 3 8 meshfree or meshless methods to solve computational mechanics problems without using a structured grid. Among these methods, the element-free Galerkin method (EFGM)4 is particularly appealing, due to its simplicity and use of a formulation that corresponds to the well-established finite element method (FEM). Similar to other meshfree methods, EFGM employs moving least-squares approximation9 that permits the resultant shape functions to be constructed entirely in terms of arbitrarily placed nodes. Since no element connectivity data are needed, burdensome meshing or remeshing required by FEM is avoided. This issue is particularly important for crack propagation in solids for which FEM may be ineffective in addressing substantial remeshing. 10 15 Hence, EFGM and other meshfree methods provide an attractive alternative to FEM in solving computational-mechanics problems.
However, most meshfree development...
