横观各向同性地基空间问题的位移函数解法

Displacement function method of space problem for transversely isotropic foundation

从横观各向同性弹性体空间问题的基本方程出发,通过引入各向同性弹性体力学伽辽金(Galerkin)位移势函数的修正,采用位移函数解法,借助Hankel积分变换和Bessel函数理论,在象域内严格导出了横观各向同性地基空间问题的一般解。运用Hankel积分反演变换,针对横观各向同性地基材料特征根相等或不相等的两种情形,分别导出了横观各向同性地基空间问题的应力分量和位移分量的解析表达式,可用于多种边界条件下具体问题的求解。

A general three-dimensional solution for transversely isotropic foundation in the image field was strictly obtained by use of the displacement function method. The Galerkin＇s displacement function for isotropic elasticity was modified, and Hankel integration transform and Bessel function theory were employed in the solution. With the Hankel integration inversion shift theory, the fundamental expression of strain and stress in the transversely isotropic foundation was presented for different cases that the characteristic roots were equal or not. The solution included the axisymmetric problem and asymmetrical problem. The obtained general solution could be simplified to the general solution of axisymmetric problems of a transversely isotropic foundation through the coefficient transform. It could be used to solve some specific asymmetrical problems for semi-infinite space under different boundary conditions.