Axisymmetric contact problems of the theory of elasticity for inhomogeneous layers

Abstract

AbstractAn approach for constructing semi‐analytical solutions in contact problems of the theory of elasticity for inhomogeneous layers is developed. The approach is efficient for the layer of arbitrary thickness which is either continuously inhomogeneous (functionally graded) or piecewise homogeneous (i.e. presented as a set of homogeneous layers with different elastic properties). The foundation is also assumed to be elastic, but much stiffer than the layer. The loads considered address the case of axisymmetric contact problems under torsion and indentation of a rigid circular punch with the flat base. The technique based on integral transforms is used to reduce the problems to the integral equations. Special approximations for the kernel transforms are used to obtain analytical solutions of the integral equations. The main results include computations of the profiles of contact stresses under the punch and the dependences of displacements with depth for different types of variation of elastic properties in the layer. The results are also compared with those obtained by other methods.