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工程力学  2014 

非线性动力方程的精细时空有限元方法

DOI: 10.6052/j.issn.1000-4750.2012.09.0664, PP. 23-28

Keywords: 非线性动力方程,Hamilton变作用定律,时空有限元,精细方法,传递矩阵

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Abstract:

根据Hamilton变作用定律构造了时空有限元矩阵;并根据传递矩阵原理,利用时间的一维性将时空有限元矩阵变换为时间方向的传递矩阵,将初值问题转化为一般矩阵相乘问题以方便求解。为了保证计算的稳定性,参考了精细积分的思想提出精细时空有限元方法,并给出线性问题在时间级数荷载作用下的计算式。数值分析结果证明该方法在线性问题分析上非常准确并可以推广到非线性动力方程的求解;只需将非线性解看作初始解和增量解的叠加,通过精细时空有限元线性求解方法计算增量解,逐步修正后即可得到非线性解。结果表明该方法是一个有效的求解非线性动力方程的方法。

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