Solution of three basic problems of elasticity for half-plane

Abstract

Solution of elastic problem for half-plane is of the highest concern in almost every field of engineering. However, there are no relations binding the values of all components of the stress-strain state at the half-plane boundary This paper shows that arbitrary formulation of the boundary conditions considerably simplifies integral equations and transfers them to the class of Fredholm’s first kind equations. Considering symmetry, the problem for half-plane with mathematical cut is reduced to the problem on half-plane boundary. Regardless of the method, any solution is reduced to ill-posed problem.