An efficient finite element model for static and dynamic analyses of functionally graded piezoelectric beams

This study deals with static, free vibration and dynamic response of functionally graded piezoelectric material (FGPM) beams using an efficient three-nodded beam element. This beam finite element is based on a refined sinus model. It does not require shear correction factor and ensures continuity conditions for displacements, transverse shear stresses as well as boundary conditions on the upper and lower surfaces of the FGPM beam. This conforming finite element does not suffer from shear locking. The number of the mechanical unknowns is independent of the number of layers. A high-order electrical potential field is considered through each graded piezoelectric layer. The proposed FE is validated through static, free vibration and dynamic tests for FGPM beams. For various electrical and mechanical boundary conditions, excellent agreement is found between the results obtained from the proposed formulation and reference results from open literature or 3D FEM.