Analytical Solution for Contact and Crack Problem in Homogeneous Half Plane

Abstract In this study, the contact and crack problem of an elastic homogeneous half-infinite plane is investigated according to the elasticity theory. There are two rigid blocks on the half-endless plane and the P and Q loads are transferred to the half-infinite plane by these blocks. The effect of the mass forces is not included, the stress and displacement expressions to be used for the contact problem are obtained by using Navier equations and Fourier integral transformation technique, and the boundary conditions determined for the problem are applied. The equations to be used for the crack problem are specified and the boundary conditions for the crack are applied to these equations. The problem is reduced to an integral equation system consisting of four singular integral equations where contact stresses and crack displacements are unknown. Numerical solution of the integral equation system has been realized by using Jacobi polynomials. Numerical results on sub-block stress distributions and stress intensity factors were obtained for different loading conditions, geometric sizes and presented by graphics.