解析层元法求解层状横观各向同性地基轴对称问题

Analytical layer-element method for axisymmetric problem of transversely isotropic multi-layered soils

提出了一个求解横观各向同性层状地基轴对称问题的解析层元方法。从弹性力学基本方程出发并利用Hankel变换,得到横观各向同性单层地基的传递矩阵解,进而推导出单层地基的解析层元刚度矩阵。利用有限元方法组装总体刚度矩阵,通过求解总体刚度矩阵,并采用Hankel逆变换的数值积分方法,可求出层状横观各向同性弹性体轴对称问题在物理域内的精确解。刚度矩阵元素中不存在正指数并具有对称的特点,不仅使计算过程简化,还提高了计算精度。最后文中给出了算例来证明推导结果的准确性。

An analytical layer-element method is proposed to solve the axisymmetric problem of transversely isotropic multi-layered soils.From the basic equations of elasticity and by using the Hankel transform,the transfer matrix of a single soil layer is obtained.Based on the transfer matrix,a precise stiffness matrix of a single soil layer is deduced.By employing the finite element method,we can further get the total stiffness matrix of multi-layered soils.A numerical inversion technique of the Hankel transform is adopted to obtain the exact solutions of axisymmetric problems of transversely isotropic multi-layered soils in the physical domain.Because of no existence of positive functions and the symmetry of the matrix,we can not only simplify the calculation but also improve its accuracy.Finally,a numerical example is given to prove the accuracy of the present results.