状态空间法分析厚薄圆柱壳弯曲的多变量场

根据圆柱壳的控制方程及其混合变分原理 ,引入对偶变量即应力与位移作为状态变量 ,导出圆柱壳的状态方程 ,研究其解法。对于轴对称问题 ,应用分离变量法建立指数矩阵 ,将问题分解为两个一维问题。根据开莱 -哈密顿算法或直接展形法来计算指数矩阵 ,再根据应力与位移的边界条件 ,得到问题的定解方程 ,从而求得厚薄圆柱壳的两类场变量的统一解 ,即全部应力与位移量

The state space method for analysis of multivariable field problem of bending cylindrical shells

In this paper, based on control equation of cylindrical shell and its mixed variational principle. the state equation of cylindrical shell has been derived by introducing the couple variable of stresses and displacements as state vectors, and the solutions of the equation are studied. For symmetrical cylindrical shell, the operator of exponential matrix is established,and the problem can be decomposed into two one dimensional problems by the method of separation of variable, and the exponential matrix can be computed by direct expanding scheme or Kely Hamilton method. By introduing the boundary conditions of stresses and displacements, the definite equations can be obtained and the equations are solved, and the two kinds of field variables including all the stresses and displacements of the cylindrical shell can be calculated.