三维直角坐标系下分层地基的传递矩阵解

Transfer Matrix Solutions for Multi-layered Soils in Rectangular Coordinate System

从直角坐标系下三维弹性力学问题的控制方程出发,构造出一组解耦变换,推导出非耦合的状态方程;利用二维Fourier变换以及Cayley-Hamilton定理得到了单层地基的传递矩阵;然后根据边界条件和层间结合条件利用矩阵传递技术,得出了多层地基在任意荷载作用下的传递矩阵解。编制了相应的程序,并将数值计算结果进行了比较和分析。计算结果表明:对弹性半无限体地基模型而言,结果与前人的结果是吻合的;而且土的分层性对土中位移有比较显著的影响。

Starting with the governing equations of three-dimensional elasticity problems in rectangular coordinate system,constructing a decoupled transform and getting the uncoupled state equations;the transfer matrix of a single soil layer is obtained by employing the double Fourier transform and Cayley-Hamilton theorem;after that,the transfer matrix method is applied to obtain the solutions of multi-layered elastic soils under arbitrary loads by use of the boundary conditions and the continuity conditions between ...