A NEW 12-DOF QUADRILATERAL ELEMENT FOR ANALYSIS OF THICK AND THIN PLATES

This paper presents a simple quadrilateral 12 DOF plate bending elemen t based on a modified version of the hybrid-Trefftz approach. This ele ment makes use of two independent fields of generalized displacements: (i) a non-conforming field (11 Trefftz terms for transverse displacem ent w and the corresponding rotations Theta(x), Theta(y)) satisfying t he governing differential equations of Reissner-Mindlin theory; (ii) a n auxiliary conforming field with displacemnts w ($) over tilde linked to rotations Theta(x), Theta(y) by the requirement of constant bounda ry distribution of the corresponding tangential component ($) over til de S-t, of the transverse shear. This allows quadratic ($) over tilde w and linear Theta(x), Theta(y) at the element boundary to be obtained with only 3 DOF at the corner nodes. The resulting dement, denoted by ($) over tilde Q21-11, is robust and free of shear locking in the thi n limit. The numerical assessment involves comparison with several rec ently 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 ($) over tilde w and Theta(x), T heta(y).