Static analysis of shear actuated piezo-electric beams via hierarchical FEM theories
Y. Koutsawa, G. Giunta, H. Nasser, and S. Belouettar
Mechanics of Advanced Materials and Structures, vol. 22, no. 1-2, pp. 3-18, 2015
Several one-dimensional finite elements for the static analysis of shear actuated piezo-electric three-dimensional beams are presented. A generic expression of stiffness and mass matrices is obtained through a Unified Formulation. The derivation is general regardless of the approximation order of the displacements and the electric potential over the cross-section and the number of nodes along the axial direction. A Lagranges polynomials based layer-wise approximation is used. Several mechanical boundary conditions and sensor and actuator configurations are investigated. Results are assessed towards three-dimensional finite element solutions. It is demonstrated that the proposed class of finite elements is able to yield very accurate results.