Elastic Analysis of the Mode III Crack Problem

모드III 탄성 균열문제 해석에 대한 연구

An efficient method based on analytic solutions is applied to solve anti-plane Mode III crack problems. The analytic technique developed earlier by the present authors for Laplace's equation in a simply-connected region is now extended to general Mode III crack problems. Unlike typical numerical methods which require fine meshing near crack tips, the present method divides the cracked bodies, typically non-convex or multiply-connected, into only a few super elements. In each super element, an element stiffness matrix, relating the series coefficients of the traction and displacement, is first formed. Then an assembly algorithm similar to that used in the finite elements, is first formed. Then an assembly algorithm similar to that used in the finite elements, is developed. A big advantage of the present method is that only the boundary conditions are to be satisfied in the solution procedure due to the use of analytic solutions. Several numerical results demonstrate the efficiency and accuracy of the present method.