双稳态薄壳结构的边界效应研究.pdf

第30 卷第2 期 Vol.30 No.2 工 程 力 学 2013 年 2 月 Feb. 2013 ENGINEERING MECHANICS 266 文章编号：1000-4750(2013)02-0266-06 双稳态薄壳结构的边界效应研究 吴耀鹏 (西安建筑科技大学土木工程学院，西安 710055) 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。 关键词：薄壳结构；双稳态；边界效应；应变能；卷曲半径 中图分类号：O343 文献标志码：A doi: 10.6052/j.issn.1000-4750.2011.08.0538 STUDY ON BOUNDARY EFFECTS ON BI-STABLE THIN SHELL STRUCTURES WU Yao-peng (School of Civil Engineering, Xi’an University of Architecture and Technology, Xi’an 710055, China) Abstract: 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