摘要
本文提出了一种建立在常规有限元模型上的超单元分析方法,对复杂结构的振动分析进行降阶简化处理。这种方法是把结构重新以超单元形式划分,在超单元内部采用了简化的动减缩方法;边界上则采用局部位移场重新插值方法,或采用局部刚化的方法。由超单元组装得到的总体矩阵仍具有对称、稀疏等性质,得到的动力学方程仍具有常规形式。这种超单元分析方法不但大大降低了求解模型的阶次,扩大了求解能力,而且易于编程,求解方便。文中还通过摄动分析讨论了内部模态截取准则,以保证求解的有效性和可靠性。数值算例表明,本文方法是很有效的,且具有较高的求解精度。
In this paper, a superelement analysis method based on the common finite element modeling is developed to reduce the Degrees of Freedom (DOF) for the vibration systems of the large complex structures. A simplified dynamic reduction is used in the internal domains of the superelements, and a locai displacement field reassumption is introduced on the boundary areas. This method greatly reduces the order of DOF. expands the ability of solution, and is simple to program and convenient to calculate. A reduction criterion of internal DOF is suggested through the perturbation analysis. Some numerical examples verify that the method is very effective and has high calculation precision.
关键词
结构振动
有限元
摄动法
structural vibration, finite element analysis, perturbation method, superelement method, dvnamic reduction
