半解析有限元法分析环向加劲圆柱壳外压稳定性

采用一般有限元法分析环向加劲圆柱壳外压稳定性需要用确定的单元结点位移描述待定的各种失稳波形的变化,从而造成单元划分较多,基函数复杂,所需计算机内存大,往往使稳定性分析难于实现。本文利用半解析有限元法来分析圆柱壳的稳定性,可以利用解析的成果代替一般有限元法的离散化处理,有效地解决了用一般有限元法要遇到的难题。半解析有限元法的特点是:在位移模式中,周向引入圆环板和圆柱壳的解析函数,轴向和径向采用了离散型的内插多项式函数。由于采用了解析函数与离散函数相结合的位移模式,所以不但减少了自由度,并提高了计算精度,而且也能方便地处理各种复杂的结构及其不同的连接方式。本研究采用了几何非线性大挠度理论,据此,推导了单元的弹性刚度矩阵和几何刚度矩阵。在稳定性计算中,把求解失稳荷载和失稳变形形态的问题,转化为数学上求实矩阵的最大特征根及其特征向量的问题。本文最后给出了计算实例,计算结果与理论解吻合较好,说明此法是切实可行的,并且具有广泛的使用范围。

AN ANALYSIS OF THE SEMI-ANALYTICAL FINITE ELEMENT METHOD FOR STABILITY OF CIRCULAR STIFFENED CYLINDRICAL SHELLS UNDER EXTERNAL PRESSURES

If the standard finite element method is used to analyze stability of stiffened circular cylindrical shells under external pressures, one must adopt nodal displacements determined of elements to describe variation of various buckling wave shapes undetermined, which certainly increases the element number, complicacy of base functions, and needs a major inner memory capacity of the computer, so that it is very difficult to analyte stability. In this paper, the semi-analytical finite element method is used to analyze stability of cylindrical shells, thus analytical achievements are substituted for discretization of the standard finite element method, therefore the difficult problem encountered by the standard finite element method is solved effectively. Characteristics of the semi-analytical finite element method are that in the displacement models, analytical functions of the cylindrical shell and the round ring plate are introduced in the circumferential direction, and discrete interpolating polynomial functions are adopted in the axial and radial directions. Because the combined displacement models of the analytical and discrete functions are adopted, the freedom number is reduced, calculating accuracy is improved, and various complicated structures as well as their different joint forms can be treated conveniently. In the paper, we adopt the geometrical nonlinear large-deflection theory, and derive the elastic and geometrical stiffness matrixes of the element from it. In stability calculation, solution of the buckling load and the buckling deformation shape is converted into so iution of the maximum characteristic root and its characteristic vector of the real matrix on math. Finally, some calculating examples are given, and the calculating results are better agreement with the analytical solution, which demonstrates the method in the paper is practical and able to find wide use.