Mémoire de Maîtrise
DOI
https://doi.org/10.11606/D.18.2019.tde-13052019-111946
Document
Auteur
Nom complet
Henrique Barbosa Soares
Unité de l'USP
Domain de Connaissance
Date de Soutenance
Editeur
São Carlos, 2019
Directeur
Jury
Paccola, Rodrigo Ribeiro (Président)
Baságlia, Cilmar Donizeti
Souza, Alex Sander Clemente de
Titre en portugais
Formulação e implementação numérica para análise de estabilidade de perfis de parede fina via MEF posicional
Mots-clés en portugais
Análise não-linear
Elemento finito posicional
Perfis de parede fina
Resumé en portugais
Titre en anglais
Formulation and numerical implementation for stability analysis of thin-walled members by positional MEF
Mots-clés en anglais
Geometric non-linearity
Non-linear analysis
Positional finite element
Structural instability
Thin-walled members
Resumé en anglais
In the present work, a computational program is developed to perform instability analysis in thin-walled profiles employing the finite element method (FEM), using shell elements. For this purpose, a non-linear geometric formulation of FEM is adopted, with Total Lagrangean description of the equilibrium, having nodal positions and unconstrained vectors as fundamental variables of the formulation, instead of displacements and rotations, making possible the adoption of complete three-dimensional constitutive law. Given the adoption of generalized vectors instead of rotations, the problem arises of the vectors' non-uniqueness in the regions of connection between non-coplanar shell elements. To overcome this problem, some coupling strategies are developed that are efficient and do not result in ill conditioning of the resulting system of equilibrium equations. Then, a strategy based on buckling analysis is considered in the program, which consists of obtaining eigenvalues and eigenvectors related, respectively, to critical loads and instability modes. An extension of this strategy is developed to consider the nonlinear analysis of instability, making possible to determine critical points along the equilibrium path of a point in the structure. A graphical interface is also developed for the program, for which algorithms are implemented for triangular and quadrilateral finite elements mesh generations and easy boundary conditions assignments. Finally, some examples are presented to validate the developments and to explore the potentialities of the computational tool obtained in the work. From the results, it is possible to conclude that the program works properly, offering as main advantage volumetric responses, in general, free of locking when compared to results using the conventional FEM formulation, as found in the literature.

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Date de Publication
2019-06-11

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