Stress and displacement distributions in an elastic layer acted on by internal point forces

2D Green’s functions for an elastic layer on a rigid support loaded by an internal point force

“…Although the analytical solution for a half plane and a half space loaded by an interior point load was provided by Melan (1932) and Mindlin (1953), respectively (Melan, 1932;Mindlin, 1953), no closed form solution of the problem of an elastic layer of finite height loaded by an internal point force can be found in Literature. The latter problem is partially addressed in Shekhter and Prikhodchenko (1964) by representing the displacement field through the Marguerre solution. In that reference, the solution is sought as a sum of a particular solution, connected to the point load acting inside the layer, and a homogeneous solution, which allows satisfying the boundary conditions (BCs) at the boundaries.…”

A layerwise boundary integral equation model for layers and layered media

“…Kupradze [13] studied elastic bodies bounded by either one or two parallel planes, and sought the solution in the form of Fourier type integrals involving Kelvin's fundamental matrix. In the area of soil mechanics, Shekhter and Prikhodchenko [29,30] studied the response of a three-dimensional layer on a rigid base under a horizontal force by using Kelvin's solution and an auxiliary Galerkin's vector.…”