TECHNICAL NOTES
Apr 15, 2002

Solution Method for Beams on Nonuniform Elastic Foundations

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Publication: Journal of Engineering Mechanics
Volume 128, Issue 5

Abstract

This technical note presents an analytical method, accompanied by a numerical scheme, to evaluate the response of beams on nonuniform elastic foundations, namely, when the foundation modulus is k=k(x). The method employs a Green’s function formulation, which results in a system of nonsingular integral equations for the distributed reaction q(x). These equations can be discretized in a straightforward manner to yield a system of linear algebraic equations that can be solved by elementary numerical techniques.

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References

Gao, J., Selvarathinam, A., and Weitsman, Y. J., (1999). “Analysis of adhesively jointed composite beams.” J. Sandwich Struct. Mater., 1, 323–339.
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Guo, Y. J., and Weitsman, Y. J. (2001b). “A modified DCB specimen to determine mixed mode fracture toughness of adhesives.” Eng. Fract. Mech. (in press).
Hetenyi, M. (1946). Beams on elastic foundations, The Univ. of Michigan Press, Ann Arbor, Mich.
Selvadurai, A. P. S. (1979). Linear elastic analysis of soil foundation, Elsevier, New York.
Timoshenko, S., (1921). “On the correction for shear of the differential equation for transverse vibration of prismatic bars.” Philos. Mag., 41, 744.
Vlasov, V. Z., and Leont’ev, N. N. (1960). Beams, plates, and shells on elastic foundations, translated from Russian by Israel Program for Scientific Translations, NASA/NSF Publication, 1966.
Winkler, E. (1867). Die lehre von elastizitat und festigkeit (on elasticity and fixity), Prague, p. 182.
Yin, J.-H., (2000a). “Comparative modeling study on reinforced beam on elastic foundation.” J. Geotech. Geoenviron Eng., 126(3), 265–271.
Yin, J.-H., (2000b). “Closed-formed solution for reinforced Timoshenko beam on elastic foundation.” J. Eng. Mech., 126(8), 868–874.

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Published In

Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 128Issue 5May 2002
Pages: 592 - 594

History

Received: Feb 16, 2001
Accepted: Sep 13, 2001
Published online: Apr 15, 2002
Published in print: May 2002

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Authors

Affiliations

Ya-Jun Guo
Postdoctoral Research Associate, Dept. of Mechanical and Aerospace Engineering and Engineering Science, 307 Perkins Hall, The Univ. of Tennessee, Knoxville, TN 37996-2030.
Y. Jack Weitsman
Distinguished Scientist, Division of Engineering Technology, Mail Stop 8051, Oak Ridge National Laboratory, Oak Ridge, TN 37831-8051 (corresponding author).

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