中文摘要：

改进壳结构力学模型，理论推导考虑边界效应时结构应变能的解析表达式。基于能量原理研究薄壳结构的双稳态特性，并导出其在稳定状态下的曲率和卷曲半径。对于有初始应力薄壳结构，其在卷曲状态下的应变能有极小值，存在第2个稳定状态，为双稳态结构。数值计算结果表明：同不考虑边界效应相比，考虑边界效应时薄壳结构第2个稳定状态的卷曲半径将变大，且对应的应变能较不考虑边界效应时小。另外，薄壳结构边界效应随着结构初始圆心角的增大而减小，且边界效应引起的位移相对于卷曲半径而言为高阶小量。该文结果与已有理论结果和有限元结果吻合较好，验证了模型的有效性。

英文摘要：

An improved model is proposed to derive the analytical expressions of strain energy taking into account boundary effects on the thin shell structures. Based on the principle of energy, the two stable configurations of the thin shell structures can be obtained, and the corresponding curvatures and rolled-up radii are derived. It is shown that the potential energy of the thin shell structure with initial stress is minimal when the shell is in the coiled state. The shell has the second stable configuration. Thusly, it is a bi-stable structure. Compared with the thin shell structure without a boundary effect, the computation shows that the rolled-up radius for the second stable state of the shell including a boundary effect becomes larger and the corresponding strain energy becomes smaller. In addition, the larger initial central angle for the cross-section of the thin shell structure, the smaller influence of the boundary effects will be. Compared with the rolled-up radii, the deformation caused by boundary effects is a higher order trace value. The theoretical results of this paper agree well with the exiting theoretical results and numerical results, which proves the validity of the models.