TECHNICAL PAPERS
Oct 1, 1987

Beams on Variable Two‐Parameter Elastic Foundation

Publication: Journal of Engineering Mechanics
Volume 113, Issue 10

Abstract

Two methods for the solution of beams on variable two‐parameter elastic foundation are presented. The first is based on using the exact shape functions for beams on variable two‐parameter foundation, in order to obtain the stiffness, consistent mass, and geometric stiffness matrices. The second is based on using the cubic shape functions of a regular beam element and adding the contribution of the foundation as element foundation stiffness matrices. The two solutions are compared in an example that includes static, buckling, and vibration frequency analyses.

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References

1.
Clastornik, J., Eisenberger, M., Yankelevsky, D. Z., and Adin, M. A. (1986). “Beams on variable Winkler elastic foundation.” J. Appl. Mech., ASME, 53(4), 925–928.
2.
Eisenberger, M., and Clastornik, J. (1987). “Vibrations and buckling of beams on variable Winkler elastic foundation,” to appear in Sound and Vibrations.
3.
Eisenberger, M., Yankelevsky, D. Z., and Clastornik, J. (1986). “Stability of beams on elastic foundations.” Computers and Structures, 24(1), 135–140.
4.
Filomenko‐Borodich, M. M. (1940). “Some approximate theories of the elastic foundation.” Uchenyei Zapiski Moskovoskogo Gosudarstuennogo Universiteta Mechanika, U.S.S.R., No. 46, 3–8 (in Russian).
5.
Kerr, A. D. (1964). “Elastic and viscoelastic foundation models.” J. Appl. Mech., ASME, 31, 491–498.
6.
Pasternak, P. L. (1954). “On a new method of analysis of an elastic foundation by means of two foundation constants.” Gosudarsvennoe Izdatelstvo Literaturi po Stroitelstvu i Arkhitekure, Moscow, U.S.S.R. (in Russian).
7.
Vlasov, V. Z., and Leontev, U. N. (1966). Beams, plates and shells on elastic foundations, (trans. from Russian), Israel program for scientific Translation, Jerusalem, Israel.
8.
Weaver, W., Jr., and Johnston, P. R. (1984). Finite elements for structural analysis, Prentice‐Hall, Englewood Cliffs, N.J.
9.
Zhaohua, F., and Cook, R. D. (1983). “Beam element on two‐parameter elastic foundations.” J. Engrg. Mech. Div., ASCE, 109(6), 1390–1402.

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Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 113Issue 10October 1987
Pages: 1454 - 1466

History

Published online: Oct 1, 1987
Published in print: Oct 1987

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Authors

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Moshe Eisenberger
Sr. Lect., Dept. of Civ. Engrg., Technion, Israel Inst. Tech., Haifa 32000, Israel
Jose Clastornik
Grad. Student, Dept. of Civ. Engrg., Technion, Israel Inst. Tech., Haifa 32000, Israel

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