Avec l'avancé des méthodes numériques, de nouvelles méthodes dites « sans maillage » sont apparues pour remédier à certaines limitations de la méthode des éléments finis. Ces méthodes ont la particularité de n’employer aucun maillage prédéfini : elles utilisent un ensemble de nœuds dispersés dans le domaine considéré et sur ses frontières. L’objectif de cette étude est de montrer l’intérêt de l’application des méthodes sans maillage basées sur les fonctions de base radiale pour la simulation des procédés de mise en forme en général et de poinçonnage rapide en particulier. Une attention particulière sera portée sur la méthode RPIM qui offre l’avantage de proposer une interpolation nodale. La démarche proposée dans ce document consiste: à rappeler succinctement les principes essentiels des méthodes sans maillage en précisant leurs avantages par rapport aux méthodes classiques, à présenter et à mettre en œuvre la technique numérique de la méthode sans maillage RPIM avec un calibrage des paramètres caractéristiques, et enfin, à traiter des exemples numériques de procédés de mise en forme avec amorçage et propagation de fissure qui confirmeront ces avantages. / In recent years, new methods named Meshfree methods have been developed to surmount limitations of the finite element method. The main characteristic of these methods is to not employ any pre-defined mesh: they use a set of nodes scattered within the problem domain as well as sets of nodes scattered on the boundaries of the domain. A particular attention is paid to the RPIM method, which proposes a nodal interpolation. The followed steps are: a presentation of « Meshfree methods » and their advantages compared to the traditional methods, an introduction to the meshfree RPIM method with a calibration of its associated parameters, and finally, a discussion on results obtained with the RPIM in forming processes exhibiting initiation and propagation of a crack showing the interest of the approach.

Submitted by Edisangela Bastos (edisangela@ufpa.br) on 2013-05-03T22:23:10Z No. of bitstreams: 2 license_rdf: 23898 bytes, checksum: e363e809996cf46ada20da1accfcd9c7 (MD5) Dissertacao_MetodologiaDiscretizacaoEspacial.pdf: 10601472 bytes, checksum: b4354bb62056e69310170ea2834e0ead (MD5) / Approved for entry into archive by Ana Rosa Silva(arosa@ufpa.br) on 2013-05-06T15:13:55Z (GMT) No. of bitstreams: 2 license_rdf: 23898 bytes, checksum: e363e809996cf46ada20da1accfcd9c7 (MD5) Dissertacao_MetodologiaDiscretizacaoEspacial.pdf: 10601472 bytes, checksum: b4354bb62056e69310170ea2834e0ead (MD5) / Made available in DSpace on 2013-05-06T15:13:55Z (GMT). No. of bitstreams: 2 license_rdf: 23898 bytes, checksum: e363e809996cf46ada20da1accfcd9c7 (MD5) Dissertacao_MetodologiaDiscretizacaoEspacial.pdf: 10601472 bytes, checksum: b4354bb62056e69310170ea2834e0ead (MD5) Previous issue date: 2013 / Neste trabalho, foi desenvolvido e implementado um método de discretização espacial baseado na lei de Coulomb para geração de pontos que possam ser usados em métodos meshless para solução das equações de Maxwell. Tal método aplica a lei de Coulomb para gerar o equilíbrio espacial necessário para gerar alta qualidade de discretização espacial para um domínio de análise. Este método é denominado aqui de CLDM (Coulomb Law Discretization Method ) e é aplicado a problemas bidimensionais. Utiliza-se o método RPIM (Radial Point Interpolation Method) com truncagem por UPML (Uniaxial Perfectlly Matched Layers) para solução das equações de Maxwell no domínio do tempo (modo TMz). / In this work, a new method, based on Coulomb's Law, has been developed and computationally implemented for performing spatial discretization for meshless methods. The new methodology, named Coulomb Law Discretization Method (CLDM), employs an adapted version of the Coulomb's vector force equation for obtaining a balanced distribution of nodes in space, in such way to achieve high discretization quality for the node set. The Radial Point Interpolation Method (RPIM) and the Uniaxial Perfectly Matched Layers (UPML) are used for solving Maxwell's Equations in time domain for 2D problems (TMz mode).