Issue 50

K. Meftah et alii, Frattura ed Integrità Strutturale, 50 (2019) 276-285; DOI: 10.3221/IGF-ESIS.50.23 276 A nonlinear elasto-plastic analysis of Reissner-Mindlin plates by finite element method Meftah Kamel University of Biskra, Laboratoire de Génie Energétique et Matériaux, LGEM, Faculty of Sciences and Technology, Biskra, 07000, Algeria k.meftah@univ-biskra.dz , http://orcid.org/0000-0002-5671-602X Sedira Lakhdar University of Biskra, Laboratoire de Génie Mécanique, LGM, Faculty of Sciences and Technology, Biskra, 07000, Algeria l.sedira@univ-biskra.dz, http://orcid.org/0000-0003-1735-2195 A BSTRACT . In this paper, a finite element simulation of nonlinear elasto- plastic deformations of Reissner-Mindlin bending plates is described. The previously proposed four-node Q4  element with transverse energy of shearing for thick bending plates is extended to account for isotropic material nonlinearities. An incremental finite element procedure has been used for the elasto-plastic analysis of the thick bending plate. Modified Newton-Raphson method has been used to solve the nonlinear equations. Von-Mises yield criteria have been applied for yielding of the materials along with the associated flow rule. To verify the present element, simple tests are demonstrated and various elasto-plastic problems in which the development of the plastic zone are solved. K EYWORDS . Plate element; Reissner-Mindlin plates; Elasto-plasticity; Nonlinear analysis. Citation: Meftah, K., Sedira, L., A nonlinear elasto-plastic analysis of Reissner-Mindlin plates by finite element method, Frattura ed Integrità Strutturale, 50 (2019) 276-285. Received: 26.06.2019 Accepted: 16.08.2019 Published: 01.10.2019 Copyright: © 2019 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. I NTRODUCTION n recent years, considerable work has been devoted to the study of nonlinear elasto-plastic responses of Reissner- Mindlin bending plates, since plates are very important parts of engineering structures. The nonlinear elasto-plastic bending plates are analyzed by the finite element methods, the finite difference methods, the discrete element methods and the direct numerical methods. However, the finite element method is a suitable approach and has been successfully used in nonlinear elasto-plastic analysis of plates. For example, a finite element analysis of Reissner-Mindlin bending plates has been investigated by Owen and Hinton [1], Meftah [2], Rezaiee-Pajand and Sadeghi [3] and Kanber and Bozkurt [4]. The finite volume formulation is also adopted for the elasto-plastic analysis of Reissner-Mindlin plates by adapting the layered approach [5] and non-layered model [6]. The elasto-plastic analysis using the Element Free Galerkin I