基于能量原理的双稳态各向同性柱壳力学特性研究  

Study on mechanical behavior of bi-stable isotropic cylindrical shell based on the principle of minimum strain energy

作　　者：吴耀鹏[1] 

机构地区：[1]西安建筑科技大学,西安710055

出　　处：《应用力学学报》2011年第3期243-248,325,共6页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(50978216);陕西省教育厅自然专项基金(2010JK634)

摘　　要：双稳态结构可以在伸展和卷拢两种状态下均保持稳定,作为一种新型可展开空间结构,其在航空航天等领域具有广阔的应用前景。选取各向同性材料作为研究对象,并假定该材料为理想弹塑性材料。建立柱壳的力学计算模型,推导结构变形时应变能的解析表达式,基于能量原理导出柱壳在两个稳定状态下的卷曲半径。结果表明,基于全量理论和增量理论的模型均能反映结构的双稳态特性,但后者能更准确地预测两个稳态对应的卷曲半径的大小。对于文中给定的柱壳,全量理论导出的卷曲半径R3x相对于增量理论结果误差为5.2%~11.6%,R5y相对误差为29.8%~41.3%。另外,应用有限元软件ABAQUS对各向同性柱壳结构的双稳态过程进行数值模拟,数值结果与增量理论结果的相对误差为0.9%~13.2%,二者吻合较好。Bi-stable structure can be stable in both the extended and rolled-up configurations.As a novel deployable structure,it shows a wide application prospect in the field of aeronautics and astronautics,etc.Isotropic material that assumed to be elastic-perfectly plastic is taken as the research object.By building the mechanical model for the cylindrical shells,the analytical expressions of strain energy can be derived when a cylindrical shell deforms.Based on the principle of minimum strain energy,the rolled-up radii of bi-stable shells are obtained finally.It is shown that applications of both total theory and incremental theory can predict the bi-stable behavior of the shells.The latter is proved to be a more suitable theory in accurate prediction of two rolled-up radii for the two stable states.For given cylindrical shells in this paper,the rolled-up radii from total theory compared with the incremental theoretical results,relative error of R3x is 5.2%~11.6% and relative error of R5y is 29.8%~41.3%.In addition,finite element analysis of the process of rolling up of a bi-stable cylindrical shell is performed using the ABAQUS package.Comparing with incremental theoretical results,relative error of numerical results is 0.9%~13.2%.It can be seen that numerical and theoretical results coincide very well.

关 键 词：双稳态 柱壳 理想塑性 应变能 数值模拟 

分 类 号：O344.3[理学—固体力学]