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- Sharif Rahman
- Math. Comput.
- 2014

Abstract. The main theme of this paper is error analysis for approximations derived from two variants of dimensional decomposition of a multivariate function: the referential dimensional decomposition (RDD) and analysisof-variance dimensional decomposition (ADD). New formulae are presented for the lower and upper bounds of the expected errors committed by… (More)

- Sharif Rahman
- 2000

The objective of this study was to evaluate the adequacy of current J-estimation models commonly used in probabilistic elastic±plastic analysis of ductile cracked structures. A newly developed probabilistic model based on elastic±plastic ®nite element method was used to evaluate the J-estimation model. In both models, the analyses involve elastic±plastic… (More)

- Sharif Rahman
- 2009

This paper presents an extended polynomial dimensional decomposition method for solving stochastic problems subject to independent random input following an arbitrary probability distribution. The method involves Fourier-polynomial expansions of component functions by orthogonal polynomial bases, the Stieltjes procedure for generating the recursion… (More)

- Sharif Rahman
- Rel. Eng. & Sys. Safety
- 2011

This paper presents a polynomial dimensional decomposition (PDD) method for global sensitivity analysis of stochastic systems subject to independent random input following arbitrary probability distributions. The method involves Fourier-polynomial expansions of lower-variate component functions of a stochastic response by measure-consistent orthonormal… (More)

This paper presents a Galerkin-based meshless method for calculating stress-intensity factors (SIFs) for a stationary crack in two-dimensional functionally graded materials of arbitrary geometry. The method involves an element-free Galerkin method (EFGM), where the material properties are smooth functions of spatial coordinates and two newly developed… (More)

- Robert Firmature, Sharif Rahman
- 2000

This paper presents new elastic and elastic±plastic ®nite element solutions of the J-integral for a pipe containing o-center through-wall cracks under pure bending. The analysis is based on a three-dimensional nonlinear ®nite element method and small-strain theory. One hundred and ®ve analyses were performed using the ABAQUS commercial code for a wide… (More)

- B. N. Rao, Sharif Rahman
- 2005

This paper presents a new continuum shape sensitivity method for calculating the mixed-mode stress-intensity factors of a stationary crack in two-dimensional, linear-elastic, orthotropic functionally graded materials with arbitrary geometry. The method involves the material derivative concept taken from continuum mechanics, the mutual potential energy… (More)

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 eld. A meshless formulation was developed to predict stochastic structural response. Unlike the nite element method, the meshless method requires no structured… (More)

- Sharif Rahman
- 2010

This technical note presents explicit formulas for calculating the response moments of stochastic systems by polynomial dimensional decomposition entailing independent random input with arbitrary probability measures. The numerical results indicate that the formulas provide accurate, convergent, and computationally efficient estimates of the second-moment… (More)

This paper examines two stochastic methods stemming from polynomial dimensional decomposition (PDD) and polynomial chaos expansion (PCE) for solving random eigenvalue problems commonly encountered in dynamics of mechanical systems. Although the infinite series from PCE and PDD are equivalent, their truncations endow contrasting dimensional structures,… (More)