基于绝对节点坐标法的弹性线方法研究

相比于浮动坐标系法, 绝对节点坐标法(absolute nodal coordinateformulation, ANCF)在处理柔性体非线性大变形问题上具有显著优势,ANCF将单元节点坐标定义在全局坐标系下,采用斜率矢量代替节点转角坐标, 具有常数质量阵,不存在科氏离心力等优点, 然而弹性力阵为非线性项,其求解将比较耗时且占用资源. 据此, 在弹性力求解方法中,引入弹性线方法(elastic line method, ELM),该方法将格林--拉格朗日应变张量定义在中心线上,采用曲率公式来定义弯曲应变, 转角公式来定义扭转应变.同时采用有限元法对三维柔性梁位移场进行离散,求解梁单元常数质量阵、广义刚度阵、广义力阵,进而得到单元的动力学方程, 通过转换矩阵得到三维梁的动力学方程.接着从理论上指出连续介质力学方法(continuum mechanics method,CMM)和弹性线方法在求解弹性力上的不同点, 并编制动力学仿真软件.最后分别采用连续介质力学方法和弹性线方法对柔性单摆以及履带式车辆的动力学问题进行仿真分析,结果表明:弹性线方法能在保证精度的前提下有效提高计算效率. 

RESEARCH ON ELASTIC LINE METHOD BASED ON ABSOLUTE NODAL COORDINATE METHOD1)

Compared with the floating frame of reference formulation, the absolute nodal coordinate formulation (ANCF) has significant advantages in dealing with the nonlinear large deformation problem of flexible bodies. ANCF defines the nodal co-ordinates in a global co-ordinate system, uses the global slopes instead of angles to define the orientation of the elements, has a constant mass matrix, and does not have the Coriolis centrifugal force. However,the elastic force matrix is a nonlinear term, and the solution will be time consuming and occupied resources. According to this,the elastic line method is introduced for solving the elastic force, the Green-Lagrangian strain tensor is defined on the centerline, the curvature formula is used to define the bending strain, and the torsion angle formula is used to define the torsional strain. At the same time, the finite element method is used to describe the displacement field of the three-dimensional flexible beam, and the constant mass matrix, the generalized stiffness matrix and the generalized force matrix of the beam element are solved, and then the dynamic equations of the element are obtained. The dynamic equations of the three-dimensional beam are obtained by the transformation matrix. Then the differences between the continuum mechanics method and the elastic line method are pointed out theoretically, and the dynamic simulation software is compiled. Finally, the dynamics behaviors of a flexible pendulum and a tracked vehicle are numerical investigated with the continuum mechanics method and the elastic line method. The results show that the elastic line method can effectively improve the calculation efficiency under the premise of ensuring accuracy.