中文摘要：

建立各向同性柱壳的力学模型，分析初始应力对各向同性材料结构双稳态性能的影响．通过对柱壳变形应变能的分析，利用最小势能原理导出柱壳实现双稳态的条件．同时，采用ABAQUS建立壳单元模型，通过施加边界弯矩对柱壳的双稳态过程进行有限元数值模拟．结果表明，双稳态柱壳卷曲半径的数值结果与理论结果相吻合；无论是否存在初始应力，其变形过程中均有两个平衡点，且柱壳在任一平衡位置均无扭转变形；对于无初始应力的柱壳，第1个平衡点为稳定的平衡状态，第2个平衡点为不稳定的平衡状态；对于有初始应力的柱壳，在初始应力满足一定条件下，柱壳为双稳态结构，且两个稳定状态对应的曲率方向相反．这与反对称铺层复合材料层合壳的双稳态曲率方向相同的情况不同．

英文摘要：

A mechanical model for isotropic cylindrical shell is built to illustrate the effect of prestress on bi-stable behaviors of such structures. The conditions for bi-stability of isotropic cylindrical shell axe derived based on the principle of minimum strain energy. Meanwhile, using the shell element in ABAQUS, the numerical simulation on bi-stable process is carried out by imposing edge bending moment on the shell. The results show that the numerical results of rolled-up radius is in agreement with the predicted results. Furthermore, a deformed isotropic cylindrical shell without or with prestress has two equilibrium positions where there is no twisting deformation. For the cylindrical shell without prestress, the first equilibrium position is stable while the second one is unstable. However, a prestressed shell has its bi-stable states if the prestress satisfies some confined conditions, and it has two opposite curvatures corresponding to the two stable states. So it is different from the case for composite laminated shell with anti-symmetrical lay -up.