Study On General Solution On Elastic Dynamics With Porous Media

Porous media is a new type model of composite material. The body is a skeleton structure made of solid matter. And there are a lot of small pore structures in the solid skeleton. The pores are generally filled by liquid phase(saturated) or gas-liquid two phase(non saturated). Porous materials throughout our lives. The rock and soil in the nature, foam in the industrial, the filter in the filtering equipment, the ceramic, brick and tile and wood in the building materials are all considered to be the form of porous materials. As porous media material is a mixture of many materials, the structure is more complicated than the single medium material. Therefore, the study of porous media is often accompanied by the multi field coupling phenomenon, and the study of fluid solid coupling is the common of them. In accordance with the research idea for solving general solution in mathematical elastic mechanics we get the elastic dynamic solution, steady-state solution for the isotropic porous and the general solution of thermo elastic porous media by using the displacement method.On the study of the general solution of elasticity, it is often associated with the process about simplify the form of the general solution. So we often use some decomposition theory to decomposition the complex operator for getting a simple form of general solution. In the beginning of the paper, a way of decomposition is presented. It can make the decomposition a wider applicability. And it makes the operator on the general solution about the elastic dynamics in this paper can be resolved into more simple form, so we can get a more simple form about the solution.For the research on isotropic porous medium materials, we come with the constitutive equation of the porous materials, and combined with the momentum conservation equation and equation of the flow field. By the variation of the equation, we use the theory of operator for getting the expanding solution. And then we bring the solution into the initial equation to get the complete general solution. About the general solution of statics, we simplify the general solution on dynamics directly, remove the item about time to get the solution. Then we get more simple general solution form using the theory of decomposition.For the thermo poroelastic porous medium, we still begin with the constitutive equation, and combine with the equation of motion and flow field. We get the general solution in domain of y-convex by using Lur’e method and Almansi theory.