Analytical Approximations to Large Hygrothermal Buckling Deformation of a Beam
Publication: Journal of Structural Engineering
Volume 134, Issue 4
Abstract
This paper presents analytical approximate solutions for the geometrically nonlinear, large deformation postbuckling of a linear-elastic and hygrothermal beam with axially nonmovable pinned-pinned ends and subjected to a significant increase in swelling. The solution for the limiting case of a string is also obtained. Analytical approximations to large deformation of the beam are established by combining the Newton’s method with the method of harmonic balance. In contrast to the classical method of harmonic balance, the linearization is performed prior to proceeding with harmonic balancing, thus resulting in a set of linear algebraic equations instead of one of nonlinear algebraic equations. We are hence able to establish analytical approximate solutions. These approximate solutions show excellent agreement with the referenced solution obtained by the shooting method, and are valid for a small as well as a large angle of rotation at the end of the beam.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The work described in this paper was supported by Research Grants Council of the Hong Kong Special Administrative Region (Project No. UNSPECIFIED9041145) and the Program for New Century Excellent Talents in University, PRC (985 Program of Jilin University).
References
Ascher, U. M., Mattheij, R. M. M., and Russell, R. D. (1988). Numerical solution of boundary value problems for ordinary differential equations, Prentice-Hall, Englewood Cliffs, N.J.
Boley, B. A., and Weiner, J. H. (1997). Theory of thermal stresses, Dover, New York.
Cisternas, J., and Holmes, P. (2002). “Buckling of extensible thermoelastic rods.” Math. Comput. Modell., 36, 233–243.
Coffin, D. W., and Bloom, F. (1999). “Elastica solution for the hygrothermal buckling of a beam.” Int. J. Non-Linear Mech., 34, 935–947.
El Naschie, M. S. (1976). “Thermal initial postbuckling of the extensional elastica.” Int. J. Mech. Sci., 18, 321–324.
Jekot, T. (1996). “Nonlinear problems of thermal buckling of a beam.” J. Therm. Stresses, 19(4), 359–367.
Li, S. R., and Cheng, C. J. (2000). “Analysis of thermal post-buckling of heated elastic rods.” Appl. Math. Mech., 21, 133–140.
Nowinski, J. L. (1978). Theory of thermoelasticity with applications, Sijthoff and Noordhoff, Alphen a/d Rijn.
Vaz, M. A., and Solano, R. F. (2003). “Post-buckling analysis of slender elastic rods subjected to uniform thermal loads.” J. Therm. Stresses, 26, 847–860.
Wu, B. S., Lim, C. W., and Sun, W. P. (2006a). “Improved harmonic balance approach to periodic solutions of non-linear jerk equations.” Phys. Lett. A, 354, 95–100.
Wu, B. S., Sun, W. P., and Lim, C. W. (2006b). “An analytical approximate technique for a class of strong non-linear oscillators.” Int. J. Non-Linear Mech., 41, 766–774.
Wu, B. S., Yu, Y. P., and Li, Z. G. (2007). “Analytical approximations to large post-buckling deformation of elastic rings under uniform hydrostatic pressure.” Int. J. Mech. Sci., 49, 661–668.
Ziegler, F., and Rammerstorfer, F. G. (1989). “Thermoelastic stability.” Temperature stresses III, R. B. Hetnarski, ed., Ch. 2., Elsevier, Amsterdam, The Netherlands, 108–113.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 134 • Issue 4 • April 2008
Pages: 602 - 607
Copyright
© 2008 ASCE.
History
Received: Apr 10, 2007
Accepted: Oct 8, 2007
Published online: Apr 1, 2008
Published in print: Apr 2008
Notes
Note. Associate Editor: M. Asghar Bhatti
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.