Fundamental solutions for a fluid‐saturated,transversely isotropic,poroelastic solid

The fundamental solutions were obtained for step‐like point forces acting in three orthogonal directions and an instantaneous fluid point source in a fluid‐saturated, porous, infinite solid of transversely isotropic elasticity and permeability. After expressing the governing equations in the form of matrix in the Laplace space, we employed Kupradze's method together with the triple Fourier transforms. This method reduces the simultaneous partial differential equations with respect to three displacement components and a pore fluid pressure to a differential equation in terms of only one potential scalar function, which can be operationally solved in the transformed space. After the Laplace inversion of the potential, the residue theorem was applied to its Fourier inverse transform with respect to one of the transformation variables. The Fourier transforms with respect to two other variables were rewritten into the Hankel transforms. Copyright © 2002 John Wiley & Sons, Ltd.