THE ANTI-PLANE PROBLEM OF THE COMPOSITES WITH MULTIPLE ELLIPTICAL RIGID INCLUSIONS

The model of composite consisting of a continuous matrix with multiple elliptical rigid inclusions is considered. The problem on interfacial maximum stress varying with shape of inclusions is solved. By using the conformal mapping technique together with the Laurent expansion method and coordinate transformation, the complex stress functions, which represent the interaction of elliptical rigid inclusions arbitrarily distributed in the isotropic elastic matrix, are constructed. The boundary condition of every inclusion is satisfied. By circulatory integral, the boundary equations are transformed into linear algebraic equations. Under the uniform load of anti-plane shear at infinity, the interfacial stress formula, the numerical results and the graph, which show that interfacial stresses maximum vary with the shape of inclusions(from circular rigid inclusions to linear rigid inclusions), have been obtained. A comparison is made with other numerical results to demonstrate the superiority of the proposed model and the accuracy of the solutions.