Stresses and displacements of a transversely isotropic elastic halfspace due to rectangular loadings

Analytical solutions in exact closed-forms are obtained for stresses and displacements in an solid due to rectangular loading. The stresses and displacements are induced in the solid due to the vertical and horizontal loadings uniformly distributed on a rectangular area. The rectangular area is horizontally embedded in or on the solid. The solid occupies a space of semi-infinite extent and has a linear elastic property with transverse isotropy. The classical integral transforms are used in the solution formulation. The solutions are systematically presented in matrix forms and in terms of elementary harmonic functions. The solutions are easily implemented for numerical calculations and applied to problems encountered in engineering. Comparisons of the present solution with existing similar solutions are presented for the stresses and displacements induced by the vertical load. In addition, the numerical results of the stresses and displacements in the solid induced by the horizontal and vertical loads are also presented. These results illustrate the effect of different elastic constants of transversely isotropic solids on the stress and displacement fields.