横观各向同性弹性力学空间轴对称问题的复变函数解法

The method of solving transversely isotropic axisymmetric problem in elastic space by complex function

从横观各向同性体的Lekhnitskii通解出发 ,证明了Lehnitskii应力函数可用适当选择的复变量解析函数表示 ,并导出了应力分量、位移分量以及边界条件的复变函数表达式 .

This paper proves that Lekhnitskii's stress function of space axisymmetric problem can be represented by choosing two generalized analytic functions of complex variable reasonably, and deduces the expression of the components of stress,displacement and boundary condition in complex function. In the end, the stresses in a transversely isotropic elastic space with a spherical cavity is solved by using the formulae founded.