Electromechanical coupling analysis of geometrically exact functionally graded piezoelectric shells based on weak form quadrature element method

In this study, a numerical model for electro-mechanical coupling analysis of geometrically nonlinear functionally graded piezoelectric shell is developed based on the weak form quadrature element method. Both piezoelectric and flexoelectric effects are introduced to establish the geometrically exact shell model with its constituent BaTiO₃ and PZT-5H graded through the thickness. The electric potentials are assumed quadratic along the shell thickness to introduce the electric field for numerical implementation, while four different closed- or open-circuit conditions are considered. Four typical examples are presented to demonstrate the effectiveness of the present model and illustrate the influences of electro-mechanical couplings and functional graded materials on the responses of shells undergoing large displacements and rotations. This model is a feasible scheme for studying complex nonlinear behaviors of piezoelectric shells that might be helpful in devising piezoelectric shell-based nanoelectronics.