摘要
Euler- Cauchy法、Euler一次迭代法和 Euler- Newton法是非线性有限元中常用的非线性方程组求解方法 .讨论了这 3种方法在几何非线性有限元中的求解步骤 ,通过实例 ,分析了 3种方法的计算效率和计算精度 .研究表明 ,Euler- Cauchy法计算效率最高 ,但计算精度较差 ,与Euler- Cauchy法相比较 ,Euler一次迭代法的计算效率稍有降低 ,计算精度却显著提高 ,但该方法对于强非线性问题 ,当载荷增量步长较大时稳定性很差 ;Euler- Newtor法是最稳定可靠的方法 ,它适用于不同程度的非线性问题 ,但计算效率较低 .
In non linear Finite Element Method, Euler Newton method, Euler Cauchy method and Euler Once iteration method are always used to solve non linear equations.For a typical geometrically non linear problem, the processes of the three methods are presented in detail.Comparing the efficiency and accuracy of the three methods, the following conclusions can be drawn.Euler Cauchy method has the highest efficiency and lowest accuracy in the three methods.Although the efficiency of Euler Once iteration method is lower than that of Euler Cauchy method,the accuracy is higher remarkable.It should be noted that Euler Once iteraton method is unstable, when large load increment step is used to analyze a strong non linear problem.Euler Newton method is more stable and reliable than others, and it is robust for many kinds of non linear problems.But ,its efficiency is low.
出处
《西北建筑工程学院学报（自然科学版）》
CAS
2001年第2期5-8,共4页
Journal of Northwestern Institute of Architectural Engineering
基金
国家自然科学基金资助项目 (597750 2 3)
西安交通大学博士学位论文基金资助项目(DFXJU1 999- 6)
关键词
非线性方程组
有限元法
计算效率
non linear equations
finite element method
computation efficiency
computation accuracy
