关键词: integro-differential equations, Kuratowski measure of noncompactness, coupled lower and upper quasisolutions, monotone iterative method, elastic half-space, second order elasticity problem, integraltransform

Abstract: A closed form solution to the second order elasticity problem, when an isotropiccompressible elastic half-space undergoes a deformation owing to a non-uniformlydistributed normal load,is presented,The method of integral transform is employedand the case when loading is distributed,in accordance with Hertz’x law, is discussed.The limiting solution for incompressible isotropic elastic material is also derived.Numerical calculations for the second order elastic material for the displacement and the normal stress in the z-direction are carried out.It is found that,in comparison to the linear elastic case,the displacement increases and the normal stress decreases in the second order elastic material.

Key words: integro-differential equations, Kuratowski measure of noncompactness, coupled lower and upper quasisolutions, monotone iterative method, elastic half-space, second order elasticity problem, integraltransform