J. Jirousek et al., A NEW 12-DOF QUADRILATERAL ELEMENT FOR ANALYSIS OF THICK AND THIN PLATES, International journal for numerical methods in engineering, 38(15), 1995, pp. 2619-2638
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).