DYNAMIC STRESS AND DEFORMATION OF MULTI-LAYERED POROELASTIC SHELLS OF REVOLUTION SATURATED IN VISCOUS FLUID

摘要

This paper describes an analytical formulation and a numerical solution of the dynamic problems of multi-layered porous shells of revolution saturated in viscous fluid. Each layer has different porosity and void radius. The equations of motion and the relations between the strains and displacements are derived by extending the Sanders elastic shell theory. As the constitutive relations, the consolidation theory of Biot for models of fluid-solid mixtures is employed. The flow of viscous fluid through a porous elastic solid is governed by Darcy's law. On the boundary surface of each layer, it is assumed that there is no flow resistance and the fluid pressure and the fluid flow are continuous. The fluid flow equations and deformation equations of shells are numerically solved using the finite difference method. As a numerical example, the simply supported three-layered truncated conical shell under a semi-sinusoidal internal load with respect to time is analyzed. Numerical computations are carried out by changing porosity and mean void radius of each layer, and the variations of pore pressure, displacements and internal forces with time are discussed.