求解动荷载作用下多层粘弹性半空间轴对称问题的精确刚度矩阵法

利用Laplace—Hankel联合积分变换，推导出了单层粘弹性半空间轴对称问题在动荷载作用下，层间完全接触情况的刚度矩阵，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就可解出动荷载作用下多层粘弹性半空间轴对称问题的矩阵。由于刚度矩阵的元素中只含有负指数项，计算时不会出现溢出的现象。本文还成功地应用了Durbin的Laplace逆变换的数值方法，求解出了多层粘弹性体的时域解。最后，文中还给出了路面动弯沉的计算结果与实测结果的对比来证明推导结果的准确性。

Explicit solution for dynamic response of axisymmetrical problems in multilayered viscoelastic half space by exact stiffness matrix method

A stiffness matrix for single layer is derived firstly based on the fundamental visco-elasticity equations and Hankel Laplace combing integral transformation. And then a global stiffness matrix is established for multiplayer viscoelastic half space by using the finite element concepts considering the layers contact. Finally, an explicit solution for axisymmetrical problems in multiplayer viscoelastic half space can be obtained by inverse Hankel Laplace combing integral transformation. Because the stiffend matrix of the element is not included the positive exponential function, the calculation is not overflowed. Thus, the shortages of transfer matrix method are overcome. The concept of method is clear, and the corresponding formulas given are not only simple but also convenient for application. In addition, the method can be also used to solve the other problems for multiplayer viscoelastic half space, such as thermo field and dynamics. As an example, the road surface dynamic deflection is calculated. Compared its numerical results with testing results show correction.