A new 12 DOF quadrilateral element for analysis of thick and thin plates

Abstract

Abstract This paper presents a simple quadrilateral 12 DOF plate bending element based on a modified version of the hybrid‐Trefftz approach. This element makes use of two independent fields of generalized displacements: a non‐conforming field (11 Trefftz terms for transverse displacement w and the corresponding rotations Θ x , Θ y ) satisfying the governing differential equations of Reissner‐Mindlin theory; an auxiliary conforming field with displacements w̃ linked to rotations \documentclass{article}\pagestyle{empty}\begin{document}$ \tilde \Theta _x,\tilde \Theta _y$\end{document} , by the requirement of constant boundary distribution of the corresponding tangential component S̃ t , of the transverse shear. This allows quadratic w̃ and linear \documentclass{article}\pagestyle{empty}\begin{document}$ \tilde \Theta _x,\tilde \Theta _y $\end{document} , at the element boundary to be obtained with only 3 DOF at the corner nodes. The resulting element, denoted by Q̃21–11, is robust and free of shear locking in the thin limit. The numerical assessment involves comparison with several recently presented 12 DOF thick plate quadrilaterals as well as with the standard 16 DOF hybrid‐Trefftz quadrilateral, Q21‐15S, with 15 Trefftz terms and independently interpolated w̃ and \documentclass{article}\pagestyle{empty}\begin{document}$ \tilde \Theta _x,\tilde \Theta _y $\end{document} .