Coupled nonlinear mechanics for the electromechanical response of multi-stable piezoelectric shallow shells with piezoelectric films

Abstract

This paper considers the nonlinear electromechanical response of shallow piezoelectric laminated shells of arbitrary double curvature, undergoing to snap through buckling and eventually to elastic instability, under mechanical pressure loads. The computational framework is based on coupled nonlinear mechanics encompassing the electromechanical coupling field and geometric nonlinearity due to large displacements and rotations. The first shear deformation theory is combined with a linear layerwise theory for describing the elastic and electric state variables through the laminate thickness, respectively. The governing equations are expressed with respect to an orthogonal curvilinear coordinate system. Building upon the nonlinear multifield mechanics an eight-node shell finite element is developed to discretize the generalized coupled nonlinear equations, which are subsequently linearized and iteratively solved, using the Cylindrical Arc-Length method in combination with the Newton-Raphson iterative technique. Numerical results demonstrate the capability of the present model to predict the complex electromechanical response of shallow cylindrical shells that transit between two stable equilibrium states. The electromechanical (generated electric charge-energy) conversion is highly complex (depending on both nonlinear piezoelectric and stiffness matrices) and predicted along the stable and unstable paths of bi-stability. At the same time the feasibility to relate the sensory electric potential with the snap through buckling of smart shells is also quantified. The influence of shell thickness, curvature and laminate configuration on the electromechanical conversion, is finally investigated.