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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。
Based on the traditional solving method of axisymmetric bending of cylindrical shell, state variable is introduced and the governing differential equation is transformed into first order differential equation. State space equation of axisymmetric bending of cylindrical shell is established. Its system matrix has the characteristics of a symplectic matrix, which can be solved by the precision integral method for high-precision numerical solution of the problem. The method can also conveniently promote the axisymmetric bending problem of the cylindrical shell used in the elastic foundation and the axisymmetric bending problem of the cylindrical shell with varying thickness. The calculation method has the advantages of simplicity and unity, and has certain application value.