Coupled mechanics and finite element for non-linear laminated piezoelectric shallow shells undergoing large displacements and rotations

A theoretical framework is presented for analysing the coupled non-linear response of shallow doubly curved adaptive laminated piezoelectric shells undergoing large displacements and rotations. The formulated mechanics incorporate coupling between in-plane and flexural stiffness terms due to geometric curvature, coupling between mechanical and electric fields, and encompass geometric non-linearity effects due to large displacements and rotations. The governing equations are formulated explicitly in orthogonal curvilinear co-ordinates and are combined with the kinematic assumptions of a mixed-field shear-layerwise shell laminate theory. Based on the above formulation, a finite element methodology together with an incremental-iterative technique, based on Newton–Raphson method is formulated. An eight-node coupled non-linear shell element is also developed. Various evaluation cases on laminated curved beams and cylindrical panels illustrate the capability of the shell finite element to predict the complex non-linear behaviour of active shell structures including buckling, which is not captured by linear shell models. The numerical results also show the inherent capability of piezoelectric shell structures to actively induce large displacements through piezoelectric actuators, by jumping between multiple equilibrium states