Two Problems for a Strip with a Transverse Crack: Exact Solutions

Abstract

Abstract In this paper for the first time we have constructed the exact solutions of two boundary value problems of the theory of elasticity for an infinite strip with a central transverse crack on which a constant normal stress is given (even-symmetric deformation). In the first problem the sides of the strip are free, while in the second they are rigidly clamped. The solution is represented in the form of series in Papkovich–Fadle eigenfunctions. The expansion coefficients (Lagrange coefficients) have the form of simple Fourier integrals. The final formulas are simple and can easily be used in engineering.