Alternative displacement frame formulations in hybrid-Trefftz Kirchhoff plate p-elements

Abstract

The thin plate p-elements considered in this paper are based on assumed displacement field chosen so as to a priori satisfy the governing Lagrange equation within the element. The required C¹ conformity is then enforced in a weak sense trough an auxiliary displacement frame defined in terms of nodal and side mode parameters. While thus far the standard approach consisted in using three parameters (one displacement and two rotations) at corner nodes and an optional number of side mode parameters associated with midside nodes, other alternative formulations are also possible wherein the number of corner mode parameters is either inferior or superior to three. As compared to the standard frame, such alternative formulations may exhibit some advantages and some shortcomings with respect to accuracy, convergence rate, error distribution, computational efficiency and/or ease of use. The paper surveys and critically assesses some of such formulations and reports the results of extensive numerical studies involving regular and singular plate bending applications.