中空轴对称域多孔介质力学问题的解析解

ANALYTIC SOLUTION TO PORO MECHANICAL PROBLEMS IN A HOLLOW AXISYMMETRIC DOMAIN

给出在有界中空轴对称域多孔介质中渗流－力学耦合问题解析解。根据Ｂｉｏｔ理论推导了在弹性多孔介质中渗流－力学耦合问题的方程，并指出在轴对称问题中渗流方程可以化为解耦形式。在无界域中，解耦的渗流方程是齐次的，只有扩散系数的改变。在有界域中，解耦的渗流方程是非齐次的。这时，它是一个线性微分－积分方程，在时间域用分离变量法求解。

An analytic solution of coupled poro mechanical problem in a finite hollow axisymmetric elastic medium is given. According to Biot theory, the coupled elastic poro mechanical equations are derived rigorously and it is demonstrated that in the axisymmetric problems the diffusion equation can be uncoupled. In the problem of infinite domain the uncoupled diffusion equation is homogeneous and only the diffusion coefficient is changed. In the problem of finite domain the uncoupled equation is nonhomogeneous. In fact, it is a linear differential integral equation and can be solved by variables separation method in time domain.