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研究了柔性梁大变形问题。常规Lagrangian有限元格式在处理大变形问题时,由于其单元插值函数不满足位移场的协调性要求,从而需要划分较多的单元,才能得到较好的结果。本文首先推导了Lagrangian坐标描述下的位移场变量满足的协调关系式,利用此关系式给出了位移场协调的非线性单元插值函数。基于虚功原理导出了梁大变形问题的非线性控制方程,数值计算结果证明了本文方法的正确性和有效性。
The problem of large deformation of flexible beam is studied. Conventional Lagrangian Finite Element Method (FEM) can deal with large deformation problems, because its element interpolation function does not meet the coordination requirements of displacement field, so more cells need to be divided to get better results. In this paper, firstly, the coordination relation of displacement field variables under the Lagrangian coordinate description is deduced. By using this relation, the nonlinear element interpolation function coordinated by displacement field is given. Based on the principle of virtual work, the nonlinear governing equations of large deformation of beam are derived. The numerical results show the correctness and effectiveness of the proposed method.