Three-dimensional elastic behavior of a nonhomogeneous layer

This paper deals with the theoretical treatment of a three-dimensional elas tic problem governed by a cylindrical coordinate system (r, theta, z) for a medium with nonhomogeneous material property. This property is defined by the relation G(z) = G(0)(1 + z/a)(m) where G(0), a and m are constants, i.e ., shear modulus of elasticity G varies arbitrarily with the axial coordina te z by the power product form. We propose a fundamental equation system fo r such nonhomogeneous medium by using three kinds of displacement functions and, as an illustrative example, we apply them to an nonhomogeneous thick plate (layer) subjected to an arbitrarily distributed load (not necessarily axisymmetric) on its surfaces. Numerical calculations are carried out for several cases, taking into account the variation of the nonhomogeneous para meter m. The numerical results for displacement and stress components are s hown graphically.