A family of quadrilateral hybrid-Trefftz p-elements for thick plate analysis

This paper presents a family of quadrilateral hybrid-Trefftz (HT) p-elements based on Reissner-Mindlin theory of moderately thick plates. As compared with existing higher-order HT thick plate elements (J. Petrolito), which make use of an incomplete set of polynomial homogeneous solutions for the internal displacement and rotation fields and of an auxiliary conforming frame field involving independently interpolated boundary distributions of displacements and rotations, the new elements differ essentially with respect to the following two points: (1) A T-complete set of homogeneous solutions including polynomial and nonpolynomial functions has been derived and used to represent the intraelement displacement and rotations fields. (2) The displacement component of the auxiliary frame field has been linked with the tangential component of the rotation so as to satisfy a particular constraint derived from equilibrium considerations. The practical efficiency of these modifications has been assessed through a series of numerical examples which have shown that the new p-elements are robust, more accurate in terms of the number of unknowns and of the computational effort, and that they do not lock in the thin limit. © 1995.