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Doctoral Thesis
DOI
https://doi.org/10.11606/T.18.2018.tde-20042018-205254
Document
Author
Full name
Antonio Carlos Rigitano
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 1999
Supervisor
Committee
Laier, José Elias (President)
Brasil, Reyolando Manoel Lopes Rebello da Fonseca
Martinez, Miguel Angel Buelta
Souza, João Carlos Antunes de Oliveira e
Varoto, Paulo Sérgio
Title in Portuguese
Contribuição para a determinação de matrizes de rigidez e vetores de ações nodais equivalentes com o emprego da formulação Hermitiana livre
Keywords in Portuguese
Elementos finitos
Matriz de rigidez
Operadores de diferenças finitas hermitianos
Abstract in Portuguese
No presente trabalho empregam-se operadores de diferenças finitas hermitianos para formular matrizes de rigidez e vetores de ações nodais equivalentes, tendo como base as teorias de Euler-Bernoulli, Timoshenko e a de fundação sobre base elástica bi-paramétrica. Examina-se também o caso da torção de elementos estruturais através da teoria de Saint-Venant. Sabe-se que as formulações referentes a esses temas são bastante conhecidas e objeto de consideração por diversos autores, porém o objetivo desta pesquisa é o de desenvolver uma nova metodologia para a consideração dos denominados erros de truncamento. Para tanto, são utilizadas as técnicas de diferenças finitas hermitianas na geração de tais matrizes e vetores, tendo-se em mente que as expressões de erros locais resultantes, providenciam uma medida da magnitude relativa desses erros. São feitas comparações entre as soluções obtidas e as formuladas através do método dos elementos finitos.
Title in English
not available
Keywords in English
not available
Abstract in English
Hermitian finite difference operators are employed to formulate element stiffness matrix and load vectors, based on Euler-Bernoulli, Timoshenko beams bending theory and two-parametric elastic foundations. Elastic torsion of structural elements by Saint-Venant's theory is considered. It is well known that approaches has been presented by several authors to solve these kind of problems, so the aim of this research is to develop a special method in considering explicitly the truncation errors. Finite difference techniques are used to derive such elements matrix and vectors, having in mind that a local truncation error expression provides a measure of relative errors magnitudes. The solutions attained are compared with those given by the finite-element analysis.
 
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Publishing Date
2018-04-23
 
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