Papers by Author: Xiao Wei Gao

Abstract: This paper presents an elastostatic crack analysis in three-dimensional (3D), isotropic, functionally graded and linear elastic solids. A boundary element method (BEM) based on boundary-domain integral equations is applied. A multi-domain technique and discontinuous elements at the crack-front are adopted. To show the effects of the materials gradients on the crackopening- displacements (CODs) and the stress intensity factors (SIFs), numerical results for a pennyshaped crack are presented and discussed.

Abstract: In this paper, an isotropic elastic damage analysis is presented by using a meshless boundary element method (BEM) without internal cells. First, nonlinear boundary-domain integral equations are derived by using the fundamental solutions for undamaged, homogeneous, isotropic and linear elastic solids and the concept of normalized displacements, which results in boundary-domain integral equations without an involvement of the displacement gradients in the domain-integral. Then, the arising domain-integral due to the damage effects is converted into a boundary integral by approximating the normalized displacements in the domain-integral by a series of prescribed radial basis functions (RBF) and using the radial integration method (RIM). The damage variable used in the paper is the ratio of the damaged area to the total area of the material, and an exponential evolution equation for the damage variable is adopted. A numerical example is given to demonstrate the efficiency of the present meshless BEM.

Abstract: This paper presents a fracture mechanics analysis in continuously non-homogeneous, isotropic, linear elastic and functionally graded materials (FGMs). A meshless boundary element method (BEM) is developed for this purpose. Young’s modulus of the FGMs is assumed to have an exponential variation, while Poisson’s ratio is taken as constant. Since no simple fundamental solutions are available for general FGMs, fundamental solutions for homogeneous, isotropic and linear elastic solids are used in the present BEM, which contains a domain-integral due to the material non-homogeneity. Normalized displacements are introduced to avoid displacement gradients in the domain-integral. The domain-integral is transformed into a boundary integral along the global boundary by using the radial integration method (RIM). To approximate the normalized displacements arising in the domain-integral, basis functions consisting of radial basis functions and polynomials in terms of global coordinates are applied. Numerical results are presented and discussed to show the accuracy and the efficiency of the present meshless BEM.