ANALYSIS OF PLATE BENDING BY THE BOUNDARY ELEMENT METHOD CONSIDERING PASTERNAK-TYPE FOUNDATION

ANALYSIS OF PLATE BENDING BY THE BOUNDARY ELEMENT METHOD CONSIDERING PASTERNAK-TYPE FOUNDATION

Karam, V. J.; Altoé, M.; Ribeiro, N. S.

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The Boundary Element Method (BEM) is used in this work to the analysis of plates resting on Pasternak-type foundations, considering Reissner´s theory. The used approach considers the fundamental solution already employed in the analysis of plates by the BEM. Integral equations that are used to solve the problem are presented, in which domain integrals related to soil reactions are included. The region situated over the foundation is discretized into constant internal cells and the integrals related to the cells are transformed into integrals over the boundary of these cells. Since the soil reactions are also unknowns to the problem and these forces are written in terms of transverse displacements and their derivatives, additional equations written for domain points situated in the cells are considered. In order to define additional equations to the original system, integral equations for transverse displacements at internal points and integral equations for the second derivatives of these transverse displacements are added to the system and these displacements and respective derivatives are also considered as unknowns to the resulting system. Continuous and discontinuous quadratic boundary elements are used in the numerical implementation. Some numerical examples are presented and results are compared with those obtained by other authors with different approaches.

The Boundary Element Method (BEM) is used in this work to the analysis of plates resting on Pasternak-type foundations, considering Reissner´s theory. The used approach considers the fundamental solution already employed in the analysis of plates by the BEM. Integral equations that are used to solve the problem are presented, in which domain integrals related to soil reactions are included. The region situated over the foundation is discretized into constant internal cells and the integrals related to the cells are transformed into integrals over the boundary of these cells. Since the soil reactions are also unknowns to the problem and these forces are written in terms of transverse displacements and their derivatives, additional equations written for domain points situated in the cells are considered. In order to define additional equations to the original system, integral equations for transverse displacements at internal points and integral equations for the second derivatives of these transverse displacements are added to the system and these displacements and respective derivatives are also considered as unknowns to the resulting system. Continuous and discontinuous quadratic boundary elements are used in the numerical implementation. Some numerical examples are presented and results are compared with those obtained by other authors with different approaches.

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DOI: 10.5151/meceng-wccm2012-19878

Referências bibliográficas

• [1] Altoé, M., Karam, V. J., “Análise de placas apoiadas sobre base elástica utilizando o Método dos Elementos de Contorno com o modelo de fundação de Pasternak”. XXX Cilamce: Iberian Latin American Congress on Computational Methods in Engineering, 2009.
• [2] Jianguo, W., Xiuxi, W., Maokuang, H., “Fundamental Solutions and Boundary Integral Equations for Reissner’s Plates on Two Parameter Foundations”. International Journal of Solids and Structures, 29, 1233-1239, 1992.
• [3] Karam, V. J., Telles, J. C. F., “On Boundary Elements for Reissner’s Plate Theory”. Engineering Analysis, 5(1), 21-27, 1988.
• [4] Paiva, J. B., “Aplicação do Método dos Elementos de Contorno à análise de placas apoiadas em base elástica”. X Congresso Ibero-Latino-Americano sobre Métodos Computacionais em Engenharia, Portugal, A47 – A59, 1989.
• [5] Rashed, Y. F., Aliabadi, M. H., Brebbia, C. A., “The Boundary Element Method for Thick Plates on a Winkler Foundation”. International Journal for Numerical Methods in Engineering, 41, 1435-1462, 1998.
• [6] Rashed, Y. F., Aliabadi, M. H., Brebbia, C. A., “A Boundary Element Formulation for a Reissner Plate on a Pasternak Foundation”. Computers and Structures, 70, 515-532, 1999.
• [7] Reissner, E., “The Effect of Transverse Shear Deformation on the Bending of Elastic Plates”. Journal of Applied Mechanics. 12, A69-A77, 1945.
• [8] Ribeiro, N. S., Karam, V. J., “Análise de placas apoiadas sobre base elástica pelo Método dos Elementos de Contorno com o modelo de fundação de Winkler”. XXX Cilamce: Iberian Latin American Congress on Computational Methods in Engineering, 2009.
• [9] Van der Weeën, F., “Application of the Direct Boundary Element Method to Reissner’s Plate Model”. Boundary Elements in Engineering, 487-499, 1982.
• [10] Yu, Y. Y., “Axisymmetric bending of circular plates under simultaneous action of lateral load, Force in the Middle Plane and Elastic Foundation”. Journal of Applied Mechanics, 24,141-143, 1957.

Como citar:

Karam, V. J.; Altoé, M.; Ribeiro, N. S.; "ANALYSIS OF PLATE BENDING BY THE BOUNDARY ELEMENT METHOD CONSIDERING PASTERNAK-TYPE FOUNDATION", p-4414-4426. 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-wccm2012-19878