A new method for derivation of locking‐free plate bending finite elements via mixed/hybrid formulation

Abstract

The shear‐locking phenomenon in discrete bending analysis of Mindlin/Reissner plates is investigated. Mixed/hybrid variational principles are introduced which, unlike the rigorous displacement model, allow systematic derivation of locking‐free finite elements. This is achieved by satisfaction of an auxiliary condition, having the clear physical interpretation of shear‐force elimination on account of equilibrium. An example, using competitive techniques, demonstrates the applicability of the idea.

An efficient hybrid / mixed element for geometrically nonlinear analysis of plate and shell structures

“…However, the use of reduced or selected integration technique may induce the appearance of spurious singular modes or zero-energy deformation modes and gives erratic results. In order to overcome these shortcomings and accurately describe structural behavior, various methods such as hybrid/mixed formulations (Bathe and Dvorkin 1985;Gellert 1988;Lee and Pian 1978), enhanced strain method (Simo and Rifai 1990;Simo and Armero 1992) and mode decomposition projection element (Belytschko et al 1986 and were suggested. Moreover, recent researches have demonstrated that loading patterns, geometric characteristics and boundary constraints subjected on the analyzed structures may lead to locking phenomena as well (Bathe et al 2000(Bathe et al , 2003Chapelle and Bathe 1998;Chapelle and Bathe 2000).…”