Abstract
In this paper, the bending problem of rectangular thin plates with free edges laid on tensionless Winkler foundation has been solved by employing Fourier series with supplementary terms. By assuming proper form of series for deflection, the basic differential equation with given boundary conditions can be transformed into a set of infinite algebraic equations. Because the boundary of contact region cannot be determined in advance, these equations are weak nonlinear ones. They can be solved by using iterative procedures.
Similar content being viewed by others
References
Tolstov, G.P.,Fourier Series, Gostechizdat (1960). (in Russian)
Yan Zong-da,Fourier Series Solutions in Structural Mechanics, Tianjin University Publishing House. (in Chinese), (to be published)
Zhang Fu-van and Huang Xiao-mei, A free rectangular plate on the elastic foundation,Applied Mathematics and Mechanics,5, 3 (1984), 1317–1324.
Darevskii, V.M., Bending of a rectangular plate with free edges that lies on an elastic foundation,Mechanics of Solid,12, 1 (1977), 75–85.
Selvadurai, A.P.S.,Elastic Analysis of Soil-Foundation Interaction, Elsevier, New York (1979).
Zhang Shi-zheng, Solution of beams on tensionless Winkler foundation by Fourier series and method of successive substitution,Journal of Tianjin University, 3 (1982). (in Chinese)
Author information
Authors and Affiliations
Additional information
Communicated by Long Yu-qui
Doctor candidate in Civil Engineering Department of Qinghua University at present.
Rights and permissions
About this article
Cite this article
Xiao-ming, B., Zong-da, Y. Bending of rectangular thin plates with free edges laid on tensionless Winkler foundation. Appl Math Mech 10, 435–442 (1989). https://doi.org/10.1007/BF02019233
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02019233