任意荷载作用下层状横观各向同性弹性地基的直角坐标解

首次建立了在直角坐标系下层状地基力学问题的通用解法,改变了过去仅能在柱坐标系下进行求解此类的状况。首先将坐标系的原点选在荷载影响范围以外足够远处,从直角坐标系下的横观各向同性弹性问题的基本方程出发,利用Laplace变换及其微分性质,建立了单层横观各向同性弹性地基的状态控制方程,并利用状态空间理论给出了单层地基的解答。然后再利用传递矩阵技术,给出了任意荷载作用下的层状横观各向同性弹性地基的解析解。用提供的方法求解层状横观各向同性地基的非轴对称问题比在极坐标下求解简单、快捷。

ANALYTICAL SOLUTION OF TRANSVERSELY ISOTROPIC ELASTIC MULTILAYERED SUBGRADE UNDER ARBITRARY LOADING IN RECTANGULAR COORDINATES

A general method for solving mechanical problems of multilayered subgrade is performed in a rectangular coordinate system, whereas solutions only existed in cylindrical coordinates before. First, the origin of the rectangular coordinate system is placed at a point out of the influential extention of the loading. Starting from the essential equations of transversely isotropic elastic mechanics, the state-controlling equations of one transversely isotropic elastic layer is derived by using Laplace transform and its differential properties, and the answer for one-layer subgrade is given with the theory of the state space. Then the analytical solution is obtained for transversely isotropic multi-layered elastic subgrade under arbitrary loadings by means of transferring matrix method. The new method is much more simple and expedient, especially for solving the non-axisymmetrical problems of multilayered subgrade, than the previous method base on cylindrical coordinate system.