Multi-scale modelling for bending analysis of heterogeneous plates by coupling BEM and FEM. (February 2015)

• Record Type: Journal Article
• Authors: Fernandes, G.R.; Pituba, J.J.C.; de Souza Neto, E.A
• Is Part Of: Engineering analysis with boundary elements. Volume 51(2015:Feb.)
• Page Start: 1
• Page End: 13
• Publication Date: 2015-02
• Subjects: Multi-scale modeling -- Homogenization -- Boundary elements -- Plate bending; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2014.10.005
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: A multi-scale modelling for analyzing the bending problem of plates composed of heterogeneous materials is presented. The macro-continuum is modelled by a non-linear formulation of the boundary element method (BEM) taking into account the consistent tangent operator (CTO). The micro-scale is represented by the RVE (representative volume element) being its equilibrium problem solved by a finite element formulation that takes into account the Hill-Mandel Principle of Macro-Homogeneity while the volume averaging hypothesis of the strain and stress tensors is used to make the micro-to-macro transition. Three different boundary conditions are imposed over the RVE: (i) linear displacements, (ii) periodic displacement fluctuation and (iii) uniform boundary tractions. The material behaviour is governed by the Von Mises elasto-plastic criterion although the proposed multi-scale model can be used with any other non-linear model. Numerical examples are presented to illustrate the main features and scope of the proposed formulation.