Construction of optimal 3-node plate bending triangles by templates

Abstract

A finite element template is a parametrized algebraic form that reduces to specific finite elements by setting numerical values to the free parameters. The present study concerns Kirchhoff Plate-Bending Triangles (KPT) with 3 nodes and 9 degrees of freedom. A 37-parameter template is constructed using the Assumed Natural Deviatoric Strain (ANDES). Specialization of this template includes well known elements such as DKT and HCT. The question addressed here is: can these parameters be selected to produce high performance elements? The study is carried out by staged application of constraints on the free parameters. The first stage produces element families satisfying invariance and aspect ratio insensitivity conditions. Application of energy balance constraints produces specific elements. The performance of such elements in benchmark tests is presently under study.