Elastic field for eccentrically loaded rigid plate on multilayered solids

Abstract

This paper presents an analytical investigation of the contact problem of a multilayered elastic solid subjected to the eccentric indentation of a rigid circular plate in the framework of classical elasticity. The total number of the dissimilar layers is an arbitrary integer n. These elastic layers can rest either on a dissimilar elastic halfspace or on a rigid rock base. The rigid circular plate is in smooth contact with the multilayered elastic solid. The classical theory of Fourier integral transforms is employed to solve the partial differential equations governing the behaviour of the multilayered elastic solid subjected to surface loading. Systems of standard Fredholm integral equations of the second-kind are then developed to govern the interaction between the rigid plate and the multilayered elastic solid. Explicit solution expression is further presented for the elastic field in the multilayered solid due to the eccentric indentation of the rigid plate. Closed-form results are respectively obtained for the singular stress field at the rigid plate edge in the multilayered elastic solid and for the elastic field in a homogeneous elastic halfspace induced by the eccentric indentation of the rigid plate. In particular, an asymptotic technique is utilized to overcome the difficulty associated with the convergence and singularity of the solution near or at the surface of the multilayered solid. Numerical results are presented to verify the techniques adopted in the paper and to illustrate the effect of layering material non-homogeneity on the elastic field induced by the eccentrically loaded rigid plate. The solution can be applied to the interpretation of non-destructive testing of layered materials such as highway and airport pavements.