Analysis of Bi-Stable Behavior of Isotropic Cylindrical Shell Structures Attached by Piezoelectric Layers

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.