Non-linear coupled multi-field mechanics and finite element for active multi-stable thermal piezoelectric shells

In this paper, a coupled multi-field mechanics framework is presented for analyzing the non-linear response of shallow doubly curved adaptive laminated piezoelectric shells undergoing large displacements and rotations in thermal environments. The mechanics incorporate coupling between mechanical, electric and thermal fields and encompass geometric non-linearity effects due to large displacements and rotations. The governing equations are formulated explicitly in orthogonal curvilinear coordinates and are combined with the kinematic assumptions of a mixed-field shear-layerwise shell laminate theory. A finite element methodology and an eight-node coupled non-linear shell element are developed. The discrete coupled non-linear equations of motion are linearized and solved, using an extended cylindrical arc-length method together with a Newton–Raphson technique, to enable robust numerical predictions of non-linear active shells transitioning between multiple stable equilibrium paths. Validation and evaluation cases on laminated cylindrical strips and cylindrical panels demonstrate the accuracy of the method and its robust capability to predict non-linear response under thermal and piezoelectric actuator loads. Moreover, the results illustrate the capability of the method to model piezoelectric shells undergoing large shape changes by actively jumping between stable equilibrium states and quantify the strong relationship between shell curvature, applied electric potential, applied temperature differential and induced shape change. Copyright © 2008 John Wiley & Sons, Ltd.