Displacement and stress predictions from field- and line-consistent versions of the eight-node mindlin plate element

Abstract

The eight-node isoparametric Mindlin plate bending element based on the serendipity shape functions has a long history of investigation behind it, and has seen various devices to improve it—mixed methods, enforcing of constraints, tensorial transformations, etc. Only very recently have successful versions free of locking in general quadrilateral form and without kinematic modes emerged. In this paper, we shall examine two of the most successful displacement method procedures (a field-consistency approach and a line-consistency approach) and proceeding from these, design three very accurate versions—one based on a variationally correct field-consistency paradigm alone, and two versions derived from the need to ensure consistency of tangential shear strains along principal reference lines so that the usual patch tests are exactly passed. The latter two have shear strain definitions that leave the element free of all problems (locking and kinematic modes) for all boundary suppressions and element distortions whereas the former has two kinematic modes. These line-consistent elements, however, introduce spurious quadratic shear stress oscillations as they have not been derived in a variationally correct sense. The recovery of accurate transverse shear stress resultants must therefore be performed very carefully, and a filtering technique is implemented for this.