柔性梁大变形计算的一种新方法

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。

A consistent element for calculating large deformation of flexible beams

The large deformation problems of flexible Euler beams are studied. In large deformation analysis, existing total Lagrangian beam elements generally employ field-inconsistent interpolations, which result in degradation of element performances. In this paper, field-consistent interpolation functions are developed after the consistent equation of displacement variants is obtained, and the nonlinear control equations are derived based on the virtual work principle. Numerical examples are performed, which show the validity and efficiency of the presented method.