半无限大层状均匀各向同性介质的基本解

从三维弹性力学最基本的平衡方程和本构关系出发，推导出状态传递微分方程，在求解状态传递微分方程时，对指数矩阵进行分解，避免了直接解法导致状态变量的发散，引入了半无限体的无究边界条件，推导出半无限层表面的位移与应力关系式，根据状态传递方程，可得出层状介质任意点的应力和位移的值，此结果可直接退化到半无限域经典的Mindlin解。

A Fundamental Solution for Semi-infinite Layered Media

A transfer matrix differential equation is derived from the three-dimensional equilibrium equations and constitutive equations of a homogeneous, isotropic linear elastic body. The exponential matrix is discomposed in order to avoid non-convergence in solving directly the transfer matrix differential equations. The relations between the displacements and the stresses on the surface of semi-infinite body are obtained by introducing the infinite boundary conditions. The displacements and stresses in an arbitrary point of the semi-infinite body are easily deduced by use of the transfer matrix equation. The results derived here can be degenerated to the classic Mindline's solution in a semi-infinite body.