Finite element modeling and analysis of low symmetry piezoelectric shells for design of shear sensors

Abstract

This work presents the development of a novel non-polynomial electromechanical shell theory for analysis of composite piezoelectric shell structures. The 2D shell theory is utilized to explore novel shear sensors made of low symmetry materials with simple patch geometries. Specifically, three configurations of patch sensors are analyzed: (i) torsional sensor operating in 36 mode, i.e., exhibiting in-plane shear coupling with electric field, (ii) transverse shear sensor operating in 35 mode exhibiting transverse shear coupling with electric field, and (iii) flexural sensor operating in 31 mode exhibiting bending stress-electric field coupling. To model these sensors, the electric potential and displacement fields are assumed to be inverse-hyperbolic functions of the thickness coordinate. A new computationally efficient C0 continuous deep shell finite element framework is developed starting from the principle of minimum potential energy, and additional continuity requirements are imposed through the use of penalty parameter approach. The results are verified by comparing with 3D FEM results. It is also observed that the inverse-hyperbolic theory has higher accuracy compared to the third-order polynomial theory for the same number of degrees of freedom. Parametric studies are subsequently performed to analyze the effect of geometric parameters such as thickness, radius of curvature of the shell, boundary conditions, thickness of the piezoelectric layer etc., on the sensor response of piezoelectric shell structures. It is observed that the response of these sensors is highly dependent on the boundary conditions, placement and thickness of the piezoelectric layer.