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Nonconforming generalized H-R mixed element for static and dynamic analysis of piezoelectric composite laminated plates

Chenchen Li, Yanhong Liu and Yuhang Wang

Vol. 18 (2023), No. 3, 405–425
Abstract

A nonconforming generalized H-R mixed finite element is developed for static and dynamic analysis of piezoelectric composite laminated plates. The overall structure is solved discretely using 8-node hexahedral nonconforming solid elements, discarding many of the artificial assumptions in the plate and shell theories. The displacement and stress can be obtained directly through linear equations, including potential and electric displacement. The C0-continuous polynomial shape function commonly for the displacement methods is used to represent the displacement variables and stress variables, and the nonconforming term is introduced into the interior of the elements, which allows it to show better numerical performance than the similar conforming elements. The displacement and stress boundary conditions are introduced simultaneously so that the actual out-of-plane stress results are obtained at the free boundary. The free-vibrational characteristic equations for piezoelectric laminated plates are derived by combining the nonconforming generalized H-R mixed variational principle with Hamiltonian principle. The accuracy of the present method is verified by analyzing several representative numerical examples of laminated plates.

Keywords
nonconforming generalized mixed element, piezoelectric laminated plates, composite material, static and dynamic analysis
Milestones
Received: 1 November 2022
Revised: 15 December 2022
Accepted: 3 January 2023
Published: 5 May 2023
Authors
Chenchen Li
College of Aeronautical Engineering
Civil Aviation University of China
Tianjin
China
Yanhong Liu
College of Aeronautical Engineering
Civil Aviation University of China
Tianjin
China
Yuhang Wang
College of Aeronautical Engineering
Civil Aviation University of China
Tianjin
China