Bi-stable states of initially stressed elastic cylindrical shell structures with two piezoelectric surface layers

A theoretical model is proposed in this paper to predict the bi-stable states of initially stressed cylindrical shell structures attached by surface anisotropic piezoelectric layers. The condition for existence of bi-stability of the shell structural system is presented and analytical expressions for corresponding rolled-up radii of the stable shell are given based on the principle of minimum strain energy. The resulting solution indicates that the shell system may have two stable configurations besides its initial state under a combined action of the actuating electric field and initial stresses characterized by the bending moment. If the piezoelectric layer materials act as only sensor materials without the actuating electric field, initial stresses may produce the bi-stable states, but one corresponding to its initial state. For the shell without initial stresses, the magnitude in the actuating electric field determines the number of the stable states, one or two stable configurations besides the initial state. The theoretical prediction for the bi-stable states is verified by finite element method (FEM) simulation by using the ABAQUS code.