加肋轴对称旋转壳非线性稳定性分析

Nonlinear Stability Analysis of Ring-stiffened Axial Symmetrical Shell of Revolution

应用Total Lagrange描述、弹塑性本构关系及非线性壳体理论,建立加肋轴对称旋转壳的非线性稳定性分析的控制方程。将所求得的控制方程应用于截锥壳单元,推导出截锥壳单元的非线性稳定性分析的有限元列式,用截锥壳单元离散和逼近加肋轴对称旋转壳,构成有限元分析模型,从而建立了分析加肋轴对称旋转壳稳定性分析的有限元模型。应用所获得的有限元列式,由平衡路径追踪,求出结构的弹性极值点载荷和弹塑性极值点载荷,将所求得的极值点载荷适当地划分成多个载荷步,求出相应的位移增量,在每一个增量步作特征值分析,由特征值分析求出非线性失稳临界载荷。文中分别将本方法与材料的弹性本构关系和弹塑性本构关系相结合,采用Crisfield圆弧加载法对某精车模型进行平衡路径追踪,得出了该模型的弹性极值点载荷、弹塑性极值点载荷和弹塑性失稳临界载荷。所求得的弹塑性极值点载荷和弹塑性失稳临界载荷与模型实验测试值均吻合较好,其中弹塑性失稳临界载荷值与实验值更为接近。从而证明:本文方法可直接求出加肋轴对称旋转壳的弹塑性失稳临界载荷,而勿须使用Cg、Cs系数进行修正。

Using Total Lagrange method and elastic-plastic constitutive equation and non-linear theory of thin shell, the basic formulas for the ring-stiffened axial symmetric shell of revolution have been introduced in this paper. Combining the basic formulas obtained with the cone shell element, the finite element equation of the cone shell element for non-linear stability analysis has been derived. By making a finite element analysis model of ring-stiffened axial symmetric shell of revolution with the cone shell element, the finite element method of stability analysis for the ring-stiffened axial symmetric shell of revolution have been introduced accordingly in this paper. Using element analysis formulas derived out in this paper, and tracking the equilibrium behavior of structure, an elastic extremum load and an elastic-plastic extremum load are obtained. The extremum loads obtained are divided further into several load steps properly, then the correspondence displacement increments have been solved. The eigenvalue analysis has been done at every load step, and the non-linear instablity critical loads can be obtained through the eigenvalue analysis. Combining the method introduced in this paper respectively with elastic material constitutive relation and with the elastic-plastic material constitutive relation, and using Crisfield Arc-Length method, the numerical calculations for equilibrium behavior of a finish machining model of ring-stiffened shell of revolution have been done, and the elastic extremum load and the elastic-plastic extremum load and an elastic-plastic bulking critical load have been obtained by non-linear stability analysis. The caculation results of the elastic-plastic extremum load and the elastic-plastic bulking load obtained by this method are agreed with the experiment value of the collapsed load, but the calculation results of the elastic-plastic bulking load are more closed to the experiment value. It has been shown that instablity critical load of the ring-stiffened axial symmetric shell of revolution can be directly determined by this way without using the parameters of Cg ,Cs for correcting the theoretical result obtained by linear theory.