大变形薄板多体系统的动力学建模

Dynamic formulation for thin plate system with large deformation

基于非线性弹性理论,考虑剪切应变和横向应变,用绝对节点坐标法建立了大变形矩形薄板的动力学变分方程;为了提高非线性刚度阵的计算效率,根据非线性刚度阵与广义坐标阵的函数关系式,在非线性刚度阵中分离出广义坐标阵,从而避免了每个时间步长的单元刚度阵的积分运算。在此基础上,引入运动学约束关系,建立了大变形薄板系统第一类拉格朗日方程,对重力作用下大变形二连板进行数值仿真。计算结果表明:随着薄板的柔度增大,低频的弯曲变形与高频拉伸变形的耦合愈加显著;此外,系统机械能守恒验证了该模型正确性。

Based on nonlinear elastic theory,absolute nodal coordinate formulation for a rectangular plate with large deformation is established,in which both shear strain and transverse normal strain are taken into account.In order to improve the computational efficiency,by utilizing the function relationship between nonlinear stiffness matrices and generalized coordinate matrices,the generalized coordinate matrices are separated from the stiffness matrices to avoid the integral calculus for calculating element stiffness matrix in each time step.On this basis,the Lagrange equations of the first kind of the rectangular plate with large deformation are established by introduction of the kinematic constraint equations.The results of the simulation example of two rectangular plate with large deformation shows that with the increase of the flexibility of the thin plate,the coupling of the longitudinal deformation in low frequency and the transverse deformation in high frequency is more significant.Conservation of total energy verifies the correctness of the formulation in this paper.