Axisymmetric problem of a nonhomogeneous elastic layer

Summary The paper deals with a theoretical treatment of elastic behavior for a medium with nonhomogeneous materials property, which is defined by the relation , i.e., shear modulus of elasticity G varies with the dimensionless axial coordinate by the power product form, arbitrarily. Fundamental differential equation for such nonhomogeneous medium has been already proposed in 5]. It is given by a second-order partial differential equation. However, it was found that the fundamental equation is not sufficient in general to solve several kinds of boundary-value problems. On the other hand, it is shown in the present paper making use of the fundamental equations system for a nonhomogeneous medium, which has been proposed in our previous paper 7], it is possible to solve axisymmetric problems for a thick plate (layer) subjected to an arbitrarily distributed load or a concentrated load on its surfaces. Numerical calculations are carried out for several cases, taking into account the variation of the nonhomogeneous parameter m. The numerical results for displacements stress and components are shown in graphical form. Accepted for publication 25 March 1997