The nonlinear mechanics for piezoelectric laminates and plates is presented, including nonlinear effects due to large displacements and rotations. The mechanics is incorporated into the piezoelectric mixed-field laminate theory. Using this mechanics, a nonlinear finite-element method and an incremental solution are formulated for the nonlinear analysis of adaptive plate structures. An eight-node-plate finite element is developed. The mechanics is applied to predict the buckling of piezoelectric plates induced by combined electromechanical loading. Application cases quantify the mechanical buckling of composite beams and plates with piezoelectric sensors, the piezoelectric buckling of active beams and plates, and the feasibility of active buckling compensation.

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SUMMARYA 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.

SUMMARYIn 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.