变厚度圆柱壳轴对称弯曲问题的状态空间法

State space method for axi-symmetric bending of variable thickness cylindrical shells

以圆柱壳轴对称弯曲问题传统的求解方法为基础,引进状态变量,将控制微分方程转化为一阶微分方程组,建立了圆柱壳轴对称弯曲问题的状态空间方程。其系统矩阵具有辛矩阵的特性,可用精细积分法求该问题的高精度数值解。该方法还可方便地推广应用于弹性地基中的圆柱壳的轴对称弯曲问题,以及变厚度圆柱壳的轴对称弯曲问题;计算方法具有简捷、统一的特点,具有一定的应用价值。

State vectors were introduced into the conventional method for analyzing the axi-symmetric bending of cylindrical shells. The control differential equations were then converted to first-order differential equations representing the state space equations for the axi symmetric bending of cylindrical shells. The system matrix is a symplectic matrix, so numerical results with higher accuracies can be obtained using a precise integration method. The simple method can be applied to axi-symmetric bending of cylindrical shells in elastic foundations or with variable thicknesses, which is uniform in calculation and convenient for application.