High-Performance 4-Node Shell Element with Piezoelectric Coupling

The paper focuses on the topic of smart and adaptive structures using embedded piezoelectric sensors and actuators. A new high-performance degenerated continuum based solid piezoelectric shell element is developed herein. It is an isoparametric 4-noded quadrilateral layered element based on the Reissner-Mindlin theory of plates with piezoelectric coupling. It assumes linear elasticity and small displacements, rotations and strains theories. The element is free of both membrane and transverse shear locking effects, and it has fully ranked stiffness matrix. This is ensured by a carefully selected combination of the Enhanced Assumed Strain, Discrete Shear Gap, and Drilling Rotations approaches. The element was implemented into ANSYS 7.1 and named SHELL10X. The pure-mechanical and static behavior is tested, e.g., using the standard set of test problems - patch tests - proposed by Harder and MacNeal. Furthermore, an experimental measurement has been carried out on a steel beam with applied piezoelectric patches. The harmonic response of the beam was studied to test the piezoelectric behavior and to show the reliability of the element. Good agreement between the measured and calculated data was achieved.