ON THE TRANSFORM METHOD OF SOLUTION OF THE PROBLEM OF A GRIFFITH CRACK AT THE INTERFACE OF AN ELASTIC HALF-PLANE AND A RIGID FOUNDATION

Abstract

The stress and displacement fields are determined in a semi-infinite elastic media bounded to a rigid foundation, containing a crack at the interface. The elastic medium is assumed to be under shear. The problem has been solved in closed form within the linear theory of elasticity, assuming plain strain conditions to hold good. The well-known Fourier Transform method has been applied to reduce the mixed boundary value problem to a simultaneous set of dual integral equations  involving trignometric kernels. The set of dual equations have been solved by the usual technique of solving such equations and the displacement and stress field have been calculated from the present solution of these dual equations. It is observed, as usual, that the solution yeilds an oscillatory phenomenon near the ends of the crack and thus the present method of solution of the simultaneous set of dual equations gives a right answer to the question of Validity of the Transform method of solving such crack problems. The technique of solving the set of simultaneous dual equations is general and can be applied even to the set that arises while solving the same crack problem when the crack is opened by a equal and opposite pressure.