Deformation of an orthotropic layer overlying a rough-rigid base due to surface loads

In the present paper, we have studied the two-dimensional deformation of an elastically orthotropic layer of finite thickness overlying a rough-rigid base due to surface loads. For a two-dimensional approximation, the governing equations are split into two cases: plane strain and anti-plane strain case. We consider plane strain case only. The Airy stress function approach is used to obtain the stresses and displacements in the integral form at any point of the layer. To solve the integrals analytically, the linear combination of exponential terms occurring in the denominator is expanded by binomial expression and then approximated by a finite sum of exponential terms using the least square method. Then, the integrals are evaluated using standard integral tables. The analytical expressions for the displacements are obtained for the normal line loading. Two orthotropic materials, such as Topaz and Barytes, have been considered and graphs showing the displacement field for Topaz, Barytes and the isotropic case have been plotted.