Extended Finite Element Method

Appendix A

Westergaard Stress Function Method

One of the analytical methods for finding the stress intensity factor was introduced in section 2.2, the Westergaard stress function method. It is one of the simplest methods for dealing with stress intensity factors. Before the main content is introduced, the essential concepts of elastic mechanics and complex variable functions are briefly reviewed and some practical formulae are provided.

A.1. Plane Problem and Antiplane Shear Problem in Linear Elastic Mechanics

A.1.1. Definition of Plane Problem

As shown in Figure A.1, the z-axis is the thickness direction of a plate. If the plate is very thick, it is not easily deformed along the z direction, so εz=γxz=γyz=0, which is the plane strain condition. Now, ...