Modified Vlasov Model for Beams on Elastic Foundations
Publication: Journal of Geotechnical Engineering
Volume 117, Issue 6
Abstract
Realizing the inadequacy of the classical Winkler model to represent an elastic continuum, Vlasov and Leont'ev developed a two‐parameter model for a beam on an elastic foundation. The Vlasov model required an estimation of a parameter, 7, that controls the decay of stresses in the continuum. Vallabhan and Das developed a unique iterative technique to determine a consistent value of the y parameter. Their model is called a “modified” or “refined Vlasov” model. Here, the finite different technique is employed to solve the fourth‐order differential equations. The results of sample problems obtained by using the modified Vlasov model are compared with more sophisticated finite element solutions.
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References
1.
Jones, R., and Xenophontos, J. (1977). “The Vlasov foundation model.” Int. J. Mech. Sci., Pergamon Press, 19, 317–323.
2.
Kerr, A. D. (1964). “Elastic and viscoelastic foundation models.” J. Appl. Mech., 31(3), 491–498.
3.
Matlock, H., and Reese, L. C. (1960). “Generalized solutions of laterally loaded piles.” Proc, ASCE, 86(5).
4.
Nogami, T., and Lam, Y. C. (1987). “Two‐parameter layer model for analysis of slab on elastic foundation.” J. Engrg. Mech., ASCE, 113(9).
5.
Pasternak, P. L. (1954). “On a new method of analysis of an elastic foundation by means of two foundation constants.” Gos. Izd. Lit. po Strait i Arkh, Moscow, the Soviet Union (in Russian).
6.
Scott, R. F. (1981). Foundation analysis. Prentice Hall, Englewood Cliffs, N.J.
7.
Sim, J. H. (1987). “A critical study of Vlasov model for beams on elastic foundations,” thesis presented to Texas Tech Univ., Lubbock, Texas, in partial fulfillment of the requirements for the degree of Master of Science.
8.
Terzaghi, K. (1955). “Evaluation of coefficients of subgrade reaction.” Geotechnique, London, U.K., 5(4), 297–326.
9.
Vallabhan, C. V. G., and Sivakumar, J. (1985). “Application of boundary element methods for soil‐structure interaction problems.” Boundary Element VI, Proc., Sixth Int. Conf. on Board the Liner Queen Elizabeth II, July.
10.
Vallabhan, C. V. G., and Das, Y. C. (1987). “A parametric study of beams on elastic foundations.” J. Engrg. Mech., ASCE, 114(12).
11.
Vallabhan, C. V. G., and Das, Y. C. (1988). “An improved model for beams on elastic foundations,” Proc, 1988 ASME Pressure Vessel and Piping Conf., Pittsburgh, Pa., June.
12.
Vlasov, V. Z., and Leont'ev, N. N. (1966). Beams, plates and shells on elastic foundations. Israel Program for Scientific Translations, Jerusalem, Israel.
13.
Winkler, E. (1867). Theory of elasticity and strength, H. Dominicus, Prague, Czechoslovakia.
Information & Authors
Information
Published In
Journal of Geotechnical Engineering
Volume 117 • Issue 6 • June 1991
Pages: 956 - 966
Copyright
Copyright © 1991 ASCE.
History
Published online: Jun 1, 1991
Published in print: Jun 1991
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