Second order effects in an elastic half-space acted upon by a non-uniform shear load

Abstract

A closed form solution to the second order elasticity problem, when an isotropic compressible elastic half-space undergoes a deformation owing to a non-uniformly distributed shear load, is presented. The method of integral transform is employed to determine the solutions. An example is discussed in detail to illustrate the second order effects. Numerical calculations for the second order elastic material for thez-direction displacement and the stresst rz are carried out. It is found that the second order effect is to reduce thez-direction displacement and to dereaset rz inside the circle but to increase its value outside the circle.