Generalized Conforming Thick Plate Element

Abstract

This chapter introduces how to use the generalized conforming theory to develop the plate element models for the analysis of both thick and thin plates. In Sect. 8.1 and 8.2, a review of the Reissner-Mindlin (thick) plate theory is firstly given, and then, a comparison between this theory and the Kirchhoff (thin) plate theory is presented. In the subsequent sections, the construction methods for the thick/thin plate elements are firstly summarized; especially, the shear locking difficulty caused by the traditional scheme (assuming deflection and rotation fields) is analyzed. Then, three new schemes which are proposed by the authors and can eliminate shear locking from the outset are introduced in detail, including the schemes of assuming rotation and shear strain fields, assuming deflection and shear strain fields, and introducing the shear strain field into the thin plate elements. The formulations of four triangular and rectangular element models are also presented. Numerical examples show that the proposed models exhibit excellent performance for both thick and thin plates, and no shear locking happens.