分数阶导数粘弹性模型的有限元法

摘要

在分析分数阶导数三元件模型理论的基础上，把分数阶导数三元件模型引入有限元模型中，推导出具有分数阶导数三元件本构关系的粘弹性结构动力学有限元格式。同时，应用分数阶导数型粘弹性结构动力学方程的数值算法求解了该有限元格式的数值解。并以二维沥青路面结构为例进行了路面动态粘弹性响应分析。算例分析表明，该方法能够正确有效地进行路面动态粘弹性分析。%The finite element scheme of viscoelastic structural dynamics with fractional derivative three el ements model constitutive relation was derived based on the analysis of the theory of the fractional deriv ative three elements model in this paper. And the numerical solution of the finite element equation was calculated using the numerical algorithm for the dynamics equation of the fractional derivative viscoelas ticity structure. Moreover, the efficiency of the finite element scheme was confirmed by the dynamic vis- coelastic response of two-dimensional asphalt pavement.