Comparison of Post-Buckling Behaviors of a S-S FGM Beam under Conservative and Non-Conservative Distributed Forces

Abstract:

Based on the large deformation theory and considering the axial extension of the beam, the governing equations of post-buckling of a simply supported elastic FGM beam subjected to conservative and non-conservative distributed forces were established. In the analysis, it was assumed that the material properties of the beam vary continuously as a power function of the thickness coordinate. By using shooting method, the nonlinear boundary-value problem was solved numerically and the equilibrium paths as well as the post- buckling configurations of the deformed beam were presented. A comparison between the results of conservative system and that of non-conservative systems were given. The results shows that the features of the equilibrium paths of the the functionally graded beam under non-conservative are evidently different from those to a conservative one.

• Periodical: Advanced Materials Research (Volumes 250-253)
• Pages: 266-270
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.250-253.266
• Online since: May 2011
• Authors: Qing Lu Li, Shi Rong Li
• Keywords: Equilibrium Path, Functionally Graded Material Beam, Non-Conservative, Post-Buckling, Shooting Method

References

[1] Bolotin V.V. Non-conservative Problem of the Theory of Elastic Stability. (Pergamon Press, London 1963).

[2] B.S. Shvartaman. Journal of Sound and Vibration, 304 (2007), pp.969-973.

[3] H. Leipholz, stability of Elastic Systems, Sijthoff and Noordhoff, (The Netherlands, 1980).

[4] B.N. Rao G.V. Rao. Journal of Sound and Vibration, (1978) pp.459-460.

[5] S.-R. Li, Y.-H. Zhou. Mechanics Research Communication, 359-367(2005).

[6] Koizumi M. Functionally Gradient Materials,34.pp.3-10(1993).

[7] LI Shi-rong, ZHANG Jing-hua.Applied Mathematics and Mechanics, ,27(6):803-810(2007).

[8] Li S R , Zhou Y H, Zheng X J . J ournal of Thermal Stresses, 25 (1) pp.45-56(2002).