基于混合变量传递函数方法的圆柱壳屈曲分析

Buckling Analysis of Cylindrical Shell Based on Mixed Variables Transfer Function Method

提出了一种分析正交各向异性圆柱壳和阶梯圆柱壳稳定性问题的混合变量传递函数方法。首先在壳体环向利用三角级数对位移变量进行展开 ,利用Fl櫣ｇｇｅ薄壳理论和变分原理 ,建立圆柱壳的平衡方程 ,找出对偶力变量 ,将平衡方程写成混合变量形式 ;通过定义混合状态变量 ,建立了系统的状态空间方程 ;然后利用传递函数方法 ,得到了具有任何轴对称边界条件轴压圆柱壳屈曲问题的解析解 ;最后通过位移连续和力平衡条件 ,得到了阶梯圆柱壳屈曲问题的解。理论解推导过程表明此方法在引入边界条件和进行阶梯圆柱壳求解时非常方便。

A mixed variables transfer function is presented for analyzing the stability of orthotropic cylindrical shells and stepped cylindrical shells. First, displacement variables are expanded in trigonometric series of circumferential coordinate. Flügge thin shell theory and variational principle are adopted to obtain governing equations and find dual force variables. Consequently, governing equations are written in the form of mixed variables. State space equation of the system is established by defining mixed state variables. Then, by transfer function method, closed formed solutions for buckling problems of cylindrical shells under axial compression with arbitrary axisymmetric boundary conditions are obtained. Finally, solutions for buckling problems of stepped cylindrical shells are obtained by enforcing displacement continuity and force balance. Driving process of analytical solutions show that it is very convenient for introducing boundary conditions and solving the buckling problems of stepped cylindrical shells in this method. Numerical results validate this method.