基于CR理论的近似能量守恒算法在壳元中的应用

An Approximate Energy Conservation Algorithm for Shell Structure Based on Co-rotational (CR) Theory

研究了壳单元几何非线性下的结构动态响应高精度计算方法。基于CR理论,针对薄壁结构的几何非线性问题,将空间旋转矢量参数化,推导和简化了三维壳单元的切线刚度矩阵和单元内力的求解格式。针对结构非线性的动态响应分析,引入中间时间步的预估-校正的流程,发展了一种基于CR理论的近似能量守恒算法。通过一柱段静力分析验证了所推导公式的计算精度,通过非线性动态响应的算例仿真,与传统非线性Newmark方法相比在处理强非线性问题时稳定性和计算精度有了明显提高。

Aim.Starting from Ref.11 by Zhong and Crisfield,we develop an approximate energy conservation algorithm,which is explained in sections 1 and 2 of the full paper.The core of section 1 is that,using the CR theory,we derive and simplify the expression of tangent stiffness matrix and that of internal force of a three-node shell element of a geometrically nonlinear structure by parameterizing its spatial rotational vector.The core of section 2 is that,by introducing a predictor-corrector procedure with mid-point step,we develop an approximate energy conservation algorithm for nonlinear dynamic response analysis.Section 3 analyzes the static force of part of a cylinder to validate our expression of tangent stiffness matrix and that of internal force;it conducts the numerical simulation of our algorithm.The simulation results,given in Figs.6 and 7,and their analysis show preliminarily that our algorithm has a better stability and precision than the conventional nonlinear Newmark method.