Boundary-based finite element method for two-dimensional anisotropic elastic solids with multiple holes and cracks

Abstract

A special boundary element for the two-dimensional anisotropic elastic solids containing a single elliptical hole or crack is applied. The main feature of this special boundary element is that no meshes are needed along the hole or crack boundary. Take this special boundary element as a base, in this paper a new method called boundary-based finite element method is developed to deal with the problems of two-dimensional anisotropic elastic solids containing multiple holes and cracks. This method is established by using the relation between nodal force of finite element and surface traction of boundary element. With the aid of this relation, a combination of boundary elements can be transformed into a single finite element. By purposely arranging each subregion with a single hole or crack and assembling the entire region according to the rule of finite element method, the problems with multiple holes and cracks can be solved. Furthermore, simple formulae to evaluate the stress concentration factor of hole and the stress intensity factors of crack are derived, by which these factors can be evaluated by using only the remote boundary displacements and tractions. Accuracy and efficiency are illustrated by comparison with analytical solutions, conventional boundary element, and finite element method.