求解多层弹性半空间轴对称问题的精确刚度矩阵法  

Explicit Solution for Axisymmetrical Multilayered Elastic Half Space Problems by Exact Stiffness Matrix Method

作　　者：钟阳[1] 张永山[1] 

机构地区：[1]广州大学土木学院,广州510405

出　　处：《力学季刊》2003年第3期395-400,共6页Chinese Quarterly of Mechanics

摘　　要：本文首先从弹性力学的基本方程出发,利用Hankel积分变换等数学手段,推导出了单层弹性半空间轴对称问题的刚度矩阵,然后按传统的有限元方法组成总体刚度矩阵。通过求解由总体刚度矩阵所构成的代数方程和Hankel积分逆变换就可解出静荷载作用下多层弹性半空间轴对称问题的精确解。由于刚度矩阵的元素中不含有正指数项,计算时不会出现溢出的现象,从而克服了传递矩阵法的缺点。由于在推导过程中摒弃了应力函数的选择,使得问题的求解更加理论化和合理化,同时也为进一步研究这类问题如温度场,动力学等方向奠定了理论基础。最后,文中还给出了计算实例来证明推导结果的准确性。In the paper, the stiffness matrix for a layer was derived firstly based on the fundamental elasticity equations and some mathematic methods such as Hankel integral transformation. And then the global stiffness matrix was established for multilayered elastic half space by using the finite element concepts in which the layers are completely contacted. Finally, the explicit solution for axisymmetrical problems in multilayered elastic half space was obtained from the solution of the algebra equation formed by global stiffness matrix and the inverse Hankel integral transformation. Because the element of matrix is not included positive exponential function,the calculation is not overflowed. Therefore,the shortages of transfer matrix method are overcome. This method is clear in concept,and the corresponding formulas given in the paper are not only simple but also convenient for application. More important thing is that the method can be used to solve the other problems for multilayered elastic half space such as thermo field and dynamics. An example of road surface deflection was presented to prove the calculated results correction.

关 键 词：多层弹性体半空间 刚度矩阵 积分变换 

分 类 号：TU311[建筑科学—结构工程]