3D static Analysis of a Transversely Isotropic Half-Space

In this paper an exact analytical solution is presented for displacement and stresses of a three – dimensional linear Green elastic transversely isotropic half-space subjected to an arbitrary , finite , surface , static force, The equations of equilibrium in terms of displacements are uncoupled by using a set of two potential functions introduced in [1], which is the static case of the potential functions given in [3] . The boundary value problems for the potential functions are solved by applying Fourier expansion and Hnkel integral transforms with respect to angular and radial coordinates, respectively. The development includes a set of transformed stress-potential and displacement- potential relations which are useful in a variety of elastostatic problems. To verify the accuracy of the numerical evaluation of the present solutions comparisons with existing solutions for an isotropic material are given. Selected numerical results for displacements and stresses and stresses are also included to demonstrate the influence of the degree of the material anisotropy on the response. The solutions for transversely isotropic material are also degenerated for the isotropic material response analytically.

Keywords:

Potential function , transversely isotropic , Hankel transform