Bending Analysis of Thick Plates on a Multi-Layered Elastic Foundation by Boundary Element Method
Article Sidebar
Main Article Content
Abstract
In this paper, an analysis of the Mindlin plate on a multi- layered elastic foundation by Boundary Element Method (BEM) is presented. This analysis employed the principle of the analog equation. According to this concept, the governing differential equations of the original problem are replaced by Poisson’ s equations with fictitious sources under the same boundary conditions. Then the boundary element technique is applied to the established integral equations of solution. The radial basis function series is applied to approximate the fictitious sources. In this work, Thin Plate Splines (TPS) as the radial basis function are chosen. Domain integrals are converted to boundary integrals by employing boundary element technique. Consequently, the solutions of the problem are obtained by boundary integral equation in which the boundary of the problem is only discretized into elements. From this study, the results can be summarized as follows: 1) The results of the plate analyzed by the boundary element method compared with analytical solutions are excellent in terms of accuracy. 2) The boundary conditions directly affect behaviors of the plate structures. 3 ) A number of foundation layers have an influence on numerical results of structural responses. 4) In the analysis of plates with complex shapes, the results from the proposed method are in good agreement with those obtained from the finite element method.
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
The articles published are the opinion of the author only. The author is responsible for any legal consequences. That may arise from that article.
References
R. D. Mindlin, “Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates,” Journal of Applied Mechanics, vol. 18, no. 1, pp. 31–38, 1951.
E. Reissner, “The effect of transverse shear deformation on the bending of elastic plates,” ASME Journal of Applied Mechanics, vol. 12, no. 2, pp. 69–77, 1945.
E. Reissner, “On bending of elastic plates,” Quarterly of Applied Mathematics, vol. 5, no. 1, pp. 55–68, 1947.
E. Winkler, “Die Lehre von der Elasticitaet und Festigkeit,” Dominicus, Prague, 1867.
A. D. Kerr, “On the formal development of elastic foundation models,” Archive of Applied Mechanics, vol. 54, no. 6, pp. 455–464, 1984.
B. Chinnaboon, S. Chucheepsakul, and J. T. Katsikadelis, “A BEM-based domain meshless method for the analysis of Mindlin plates with general boundary conditions,” Computer Methods in Applied Mechanics and Engineering, vol. 200, no. 13–16, pp. 1379–1388, 2011.
Y. F. Rashed, M. H. Aliabadi, and C. A. Brebbia, “Hypersingular boundary element formulation for Reissner plates,” International Journal of Solids and Structures, vol. 35, no.18, pp. 2229–2249, 1998.
J. T. Katsikadelis and A. J. Yotis, “A new boundary element solution of thick plates modelled by Reissner's theory,” Engineering Analysis with Boundary Elements, vol. 12, no.1, pp. 65–74, 1993.
J. T. Katsikadelis, and A. E. Armenakas, “Plates on Elastic Foundation by BIE Method,” Journal of Engineering Mechanics, vol. 110, no.7, pp. 1086–1105, 1984.
J. Balaš, V. Sládek, and J. Sládek, “The boundary integral equation method for plates resting on a two-parameter foundation,” ZAMM - Journal of Applied Mathematics and Mechanics/ Zeitschrift für Angewandte Mathematik und Mechanik, vol. 64, no. 3, pp. 137–146, 1984.
J. A. Costa and C. A. Brebbia, “The boundary element method applied to plates on elastic foundations,” Engineering Analysis, vol. 2, no. 4, pp. 174–183, 1985.
J. Puttonen and P. Varpasuo, “Boundary element analysis of a plate on elastic foundations,” International Journal for Numerical Methods in Engineering, vol. 23, no. 2, pp. 287–303, 1985.
G. Bezine, “A new boundary element method for bending of plates on elastic foundations,” International Journal of Solids and Structures, vol. 24, no. 6, pp. 557–565, 1988.
N. Kamiya and Y. Sawaki, “The plate bending analysis by the dual reciprocity boundary elements,” Engineering Analysis, vol. 5, no.1, pp. 36–40, 1988.
W. Jianguo, W. Xiuxi, and H. Maokuang, “A boundary integral equation formulation for thick plates on a Winkler foundation,” Computers & Structures, vol. 49, no. 1, pp. 179–185, 1993.
Y. F. Rashed, M. H. Aliabadi, and C. A. Brebbia, “The boundary element method for thick plates on a Winkler foundation,” International Journal for Numerical Methods in Engineering, vol. 41, no. 8, pp. 1435–1462, 1998.
M. Altoé, N. S. Ribeiro, and V. J. Karam, “Analysis of simply supported and clamped Reissner ׳s plates on Pasternak-type foundation by the Boundary Element Method,” Engineering Analysis with Boundary Elements, vol. 52, pp. 64–70, 2015.
J. T. Katsikadelis, “Analysis of simply supported and clamped Reissner ׳s plates on Pasternaktype foundation by the Boundary Element Method,” Engineering Analysis with Boundary Elements, no. 27, pp. 13–38, 2002.
G. Bosson, “The flexure of an infinite elastic strip on an elastic foundation,” The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, vol. 27, no.180, pp. 37–50, 1939.
C. M. Wang, J. N. Reddy, and K. H. Lee, Shear Deformable Beams and Plates: Relationships with Classical Solutions, Elsevier Science Ltd, Kidlington, Oxford, 2000
H. Kobayashi and K. Sonoda, “Rectangular Mindlin plates on elastic foundations,” International Journal of Mechanical Sciences, vol. 31, no. 9, pp. 679–692, 1989.