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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。
The shell structure mechanics model is improved, and the analytical expression of structural strain energy is derived theoretically when the boundary effect is considered. Based on the energy principle, the bistable characteristics of the thin shell structure are studied and the curvature and curl radius of the thin shell structure are derived. For the initial stress thin shell structure, its strain energy in the curled state has a minimum, there is the second steady state, the bistable structure. The numerical results show that the curl radius of the second stable state of the shell structure becomes larger and the corresponding strain energy is smaller than that without considering the boundary effect, considering the boundary effect. In addition, the boundary effect of the shell structure decreases with the increase of the initial central angle of the structure, and the displacement caused by the boundary effect is a small order of high order with respect to the radius of curl. The results agree well with the theoretical and finite element results, and the validity of the model is verified.