The action of a concentrated force inside an elastic half-plane with a step

A solution of the plane problem in the theory of elasticity of the stressed state of a half-plane with a step, at an arbitrary internal point of which a concentrated force is applied, is presented. The solution is constructed by the method of Cauchy-type integrals, developed by Muskhelishvili. A Koppenfels function is used for the conformal mapping of the half-plane with a step into a half-plane. Graphs of the distribution of the maximum shear stresses in the neighbourhood of the point of application of the force and the trajectories of the principal tensile stresses are presented. Being exact and expressed in terms of elementary functions, the solution presented can be used as a test problem to debug numerical solutions as well as a-component part of software packages for computer aided calculations and the optimization of constructive solutions of supports, sunk into inclines. (C) 2003 Elsevier Science Ltd. All rights reserved.