摘要
该文讨论了考虑几何非线性动力方程数值积分方法,对比了常用的平均加速度方法(AAM)与M.A.Crisfield提出的能量守恒方法离散等式的差别。基于共旋方法编写了非线性有限元程序,并采用单摆作为验证算例,计算结果与解析解一致,验证了程序的可靠性。然后对平面桁架模型和某实际工程中的空间正放四角锥网架进行动力计算。算例分析表明随着时间积分步长的加大,平均加速度方法的计算结果都会出现不稳定的情况,而能量守恒积分算法表现出良好的稳定性。建议在非线性动力计算中使用能量守恒积分算法。
This paper discusses numerical integration methods considering the geometric nonlinear equation of motion, and compares the difference between the average acceleration method(AAM) and the energy conserving method that presented by M.A.Crisfield. Based on co-rotational technologies, the nonlinear finite element program is written. The reliability of the program is verified by comparing the analytical and numerical solutions of a simple pendulum. The dynamic analysis of a planar truss structure and a commonly used space structure show that the energy of AAM is unbounded with a larger time interval, while the response of the energy conserving method is always stable with different time intervals. Therefore, we suggest that the energy conserving method should be more suitable for the dynamic computation with geometric nonlinearity.
出处
《工程力学》
EI
CSCD
北大核心
2014年第9期21-27,共7页
Engineering Mechanics
基金
国家自然科学基金项目(51161120360
91315301-09)
关键词
能量守恒
数值稳定
几何非线性
空间网架
有限单元法
energy conservation
numerical stability
geometric nonlinearity
truss structure
finite element method
