Abstract
In this paper, we wish to use complex potential methods to solve the fundamental complete plane strain (CPS) problems of a three-dimensional nonhomogeneous elastic body with a doubly-periodic set of cracks in the x1, x2 plane. We resolve the complete plane strain state, which is a special three-dimensional elastic system, into two linearly independent two-dimensional (plane) elastic systems by the superposition principle of force. Based on a suitable modification of Cauchy-type integrals, which is defined by the replacement of the Cauchy kernel 1/(t — z) by the Weierstrass zeta function ζ(t — z), the general representation for the solution is constructed, under some general restrictions the boundary value problem is reduced to a normal type singular integral equation with a Weierstrass zeta kernel, and the existence of an essentially unique solution is proved.
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