Two-dimensional deformation of an elastic layer subjected to surface loads

The two-dimensional deformation of a uniform, elastically isotropic layer of a finite thickness (FT) over a rough-rigid base caused by surface loads has been solved analytically. The stresses and the displacements for an isotropic layer are obtained in the integral form by applying the Airy’s stress function approach. Using the appropriate boundary conditions, the problem of surface loads is discussed in detail. The integrals cannot be evaluated analytically due to the complicated expression of denominator. The linear combination of exponential terms occurring in the denominator is expanded by a finite sum of exponential terms (FSET) using the method of least squares and then the integrals are evaluated analytically. The analytical displacements are obtained for normal strip loading, normal line loading and shear line loading. The displacements have been plotted numerically for normal strip loading to find the effect of layer thickness for a Poissonian layer and compared with the half-space.