组合旋转壳体的安定上限分析

Shakedown Analysis of Combined Rotational Shells

对旋转组合壳体的各个子区的位移场进行双三次Ｂ样条插值，同时对子区交界处的广义力向量以单三次Ｂ样条展开，推导出以广义向量表示的组合壳体的平衡方程，然后从Ｂｅｔｉ互换定理和虚功原理出发推导出离散的壳体结构中可能的塑性应变率循环，从而给出了组合壳体安定上限分析的有限元列式，把组合壳体的安定上限分析归结为求解一个数学规划问题。

In this paper, the double 3 B spline functions are used to interpolate the sub region generalized displacement field of general combined rotational shells, and the generalized stress vectors of sub region interface are also interpolated with B spline function, equilibrium equations of combined rotational shell is then deduced. Kinematically admissible plastic strain rate cycles of discrete structures are obtained by proceeding derived from Bettis reciprocal theorem and the principle of virtual work. The FEM formulation of kinematic shakedown analysis of combined shells is then given. The problem studied is boiled down to solve a mathematical program.