Boundary integral equation method for periodic dissimilar elastic inclusions in an infinite plate

This paper provides a theoretical derivation and a numerical solution for an infinite plate with periodic dissimilar inclusions. The matrix and periodic inclusions have different elastic properties, and a remote loading is applied for the infinite matrix. The original problem is decomposed into two problems, one is the interior boundary value problem (BVP) and the other is the exterior BVP. Both BVPs are formulated in the form of complex variable boundary integral equation (CVBIE). In addition, both BIEs are solved numerically after discretization of the integral equations. For the exterior BVP with periodic notches, the remainder estimation technique (RET) is suggested to evaluate the influence to the central notch from many (from Nth to infinity) neighboring notches. This will significantly improve the efficiency of solution. Two numerical examples are provided. In the examples, the ratio of the two shear moduli of elasticity changes from near 0 (1.d - 6), 0.1, 0.5, 1, 2 to 10.