Boundary contour method for plane problems in a dual formulation with quadratic shape functions

The present section is devoted to the boundary contour method for plane problems in the dual system of elasticity. In this system the governing equations are given in terms of stress functions of order one. After clarifying the conditions of single valuedness we construct the fundamental solution for the dual basic equations. Then the integral equations of the direct method have been established. It has been shown that the integrals on the right side of the corresponding boundary integral equations are divergence free in the dual system provided that the unknown functions satisfy the field equations. Consequently these integrals can be given in closed form if appropriate shape functions have been chosen to approximate the unknown functions on the contour. Numerical examples prove the efficiency of this technique.