微分求积有限单元法求解杆单元体系的动力响应

Differential Quadrature Finite Element Method to Solve Dynamic Response of Rod Unit System

采用微分求积有限单元法DQFEM对基于Gurtin变分能量泛函的杆单元体系进行动力响应分析。通过DQFEM对Gurtin变分能量泛函进行离散,得到对应的应变能项、动能项、初始影响项及边界力项,从而形成相应的刚度矩阵、质量矩阵和初始影响项。由求得的刚度矩阵、质量矩阵和初始影响项推导出位移迭代方程,并分别编写Matlab程序,求出需要的相应位移值。通过对比解析解,验证微分求积有限元法研究杆单元体系动力响应的可行性及精确性。

In this paper,the differential quadrature finite element method （DQFEM） is used to analyze the dynamic response of the rod unit system based on the Gurtin variational energy functional. The Gurtin variational energy functional is discretized by DQFEM,and the corresponding strain energy terms, kinetic energy terms, initial influence terms and boundary force terms are obtained,thus the corresponding stiffness matrix, mass matrix and initial influence term are formed. The displacement iteration equation is derived from the stiffness matrix,the mass matrix and the initial influence. The corresponding displacement values are obtained by programming the Matlab program respectively. The feasibility and accuracy of differential quadrature finite element method for dynamic response of rod element system are verified by comparing analytical solutions.