摘要
分析了上下表面含有压电层材料的各向同性壳体结构的双稳态特性.通过分析壳体结构内力与中面应变和柱壳曲率增量之间的关系,建立了含有压电材料的各向同性弹性柱壳的力学模型,推导给出了结构系统的弹性应变能的数学表达式.根据最小势能原理推导出实现圆柱壳双稳态的条件方程.结果表明,柱壳双稳态特性与结构系统初始曲率及电场作用形式有关.当满足一定条件时,柱壳具有双稳态,其对应于第二个平衡状态,即柱壳的第二个(卷曲)稳定状态.同时,建立了含有压电材料各向同性壳体结构的有限元模型,对其卷曲过程进行了数值模拟,获得了结构系统稳态卷曲半径和应力分布.理论与数值模拟结果的比较验证了理论模型的正确性.
The bi-stable behavior of isotropic cylindrical shell structures attached by piezoelectric layers was presented in this paper. Based on the relation between the internal forces and strains with variance of curvatures in the shell, a theoretical model was proposed to characterize the deployable stability of the shell. The expression of strain energy for the structural system was formulated. The condition for bi-stability of the system was derived using the principle of minimum potential energy. The results indicate that occurrence of bi-stability depends on the initial curvature and how external electric fields act on the system. The predicted bi-stable state corresponds to the second equilibrium state of the system. Meanwhile, A FEM model was constructed to simulate the process of rolled-up. The numerical results for stress distribution in the structure and rolled-up radius were obtained. The theoretical evaluation for the rolled-up radius was compared with the numerical simulation. The results show the validity of the theoretical model.
出处
《力学季刊》
CSCD
北大核心
2014年第1期10-21,共12页
Chinese Quarterly of Mechanics
关键词
双稳态
各向同性
圆柱壳
压电
应变能
卷曲半径
有限元
bi-stable behavior
isotropic
cylindrical shell
piezoelectric
strain energy
rolled-up radius
finite element