ANALYSIS OF EULER-BERNOULLI AND TIMOSHENKO BEAMS BY THE BOUNDARY ELEMENT METHOD

ANALYSIS OF EULER-BERNOULLI AND TIMOSHENKO BEAMS BY THE BOUNDARY ELEMENT METHOD

Carrer, J. A. M.; Mansur, W. J.; Scuciato, R. F.; Fleischfresser, S. A.

Full Article:

Boundary element formulations for the static analysis of Euler-Bernoulli and Timoshenko beams are presented in this work. As the problems are stated in one dimension, the boundary is constituted only by the extreme nodes of the beam. The four usual types of beams, i.e. pinned-pinned, fixed-fixed, fixed-pinned and fixed-free are solved for a loading uniformly distributed along the length of the beam. The potentialities of the proposed formulations are assessed by comparing the numerical results with the analytical ones.

Boundary element formulations for the static analysis of Euler-Bernoulli and Timoshenko beams are presented in this work. As the problems are stated in one dimension, the boundary is constituted only by the extreme nodes of the beam. The four usual types of beams, i.e. pinned-pinned, fixed-fixed, fixed-pinned and fixed-free are solved for a loading uniformly distributed along the length of the beam. The potentialities of the proposed formulations are assessed by comparing the numerical results with the analytical ones.

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DOI: 10.5151/meceng-wccm2012-18818

Referências bibliográficas

• [1] Antes H., “Fundamental Solution and Integral Equations for Timoshenko Beams”. Computers and Structures 81, 383-396, 2003.
• [2] Borges M. S. S., “Análise do Efeito da Deformabilidade por Cisalhamento na Flexão de Vigas – Formulação Geral do Problema e Determinação do Coeficiente de Cisalhamento”. Seminário para Qualificação ao Doutorado, COPPE/UFRJ, Rio de Janeiro, RJ, Brasil, 1996.
• [3] Brebbia C. A., Telles J. C. F., Wrobel L. C., “Boundary Element Techniques: Theory and Applications in Engineering”. Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1984.
• [4] Cowper G. R., “The Shear Coefficient in Timoshenko’s Beam Theory”. Journal of Applied Mechanics 33, 335-340, 1966.
• [5] Fleischfresser S. A., “Análise do Efeito da Deformabilidade por Cisalhamento na Flexão de Vigas: uma Formulação do Método dos Elementos de Contorno para Vigas de Timoshenko”. Seminário para Qualificação ao Doutorado, PPGMNE/UFPR, Curitiba, PR, Brasil, 2012.
• [6] Graff K. F., “Wave Motion in Elastic Solids”. Dover Publications, New York, 1991.
• [7] Rao S. S., “Mechanical Vibrations”. Addison-Wesley Publishing Company, 3rd Edition, 1995.
• [8] Timoshenko S. P., “On the Correction for Shear of the Differential Equation for Transverse Vibrations of Prismatic Bars”. Philosophical Magazine 41, 744-746, 1921.

Como citar:

Carrer, J. A. M.; Mansur, W. J.; Scuciato, R. F.; Fleischfresser, S. A.; "ANALYSIS OF EULER-BERNOULLI AND TIMOSHENKO BEAMS BY THE BOUNDARY ELEMENT METHOD", p-2333-2349. In: In Proceedings of the 10th World Congress on Computational Mechanics [= Blucher Mechanical Engineering Proceedings, v. 1, n. 1]. São Paulo: Blucher, 2014.
ISSN 23580828, DOI 10.5151/meceng-wccm2012-18818