Static response of a multilayered medium under inclined surface loads

The general solutions to the problem of an inclined static load on a circular area of the surface of a multilayered medium are obtained. The inclined load is assumed to be a linear combination of a normal load and an asymmetrical shear load; each layer of the multilayered medium is assumed to be homogeneous and isotropic, and the interfaces of the layers are perfectly welded. Through the Thomson-Haskell matrix method, the generalized components of displacements and stresses, which are expressed in the integral form, have been obtained on the surface, at the interfaces, and at any point in the multilayered medium. They are reducible to an axisymmetrical or asymmetrical surface load on an n-layered medium, including a half-space. The present formulation has avoided the generally cumbersome nature of the problem and is adaptable to numerical evaluation. Through an elementary transformation, the general solutions for an inclined static load have been extended to evaluate the components of total displacements and total stresses due to a system of inclined loads of arbitrary orientation on the surface of a multilayered medium.