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Submitted
July 31, 2023
Published
July 31, 2023
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Abstract

Thermal postbuckling behavior of uniform, heated columns is presented, by using a novel linear Finite Element (FE) formulation. In this investigation, the general Green axial nonlinear strain- displacement relation is used, instead of the popularly used simpler von-Karman nonlinearity, which is a subset of Green nonlinearity. In the earlier complex nonlinear FE formulations, time consuming iterative or step-by-step methods are used to obtain the solution for thermal postbuckling. In the novel FE formulation, normally used FES , for performing linear buckling analysis, is proposed to obtain thermal postbuckling loads. The nodal degrees of freedom are deflection and its first derivative with respect to the axial coordinate. The geometric nonlinearity is incorporated through the tensile loads induced, with axially restrained ends of the column, due to large deflections. The effectiveness of the novel FE formulation is demonstrated, from the numerical results obtained, in terms of the ratio of thermal postbuckling to buckling loads, for specified reference deflection and slenderness ratios, of the columns with different boundary conditions. The numerical results reveal some interesting phenomena of thermal postbuckling behavior of columns.

Keywords

Thermal Loads, Thermal Buckling, Thermal Postbuckling, Novel Finite Element Formulation, Linear Eigenvalue Problem.

Article Details

How to Cite
Venkateswara Rao, G., Kartikeyan, T., Durga Rao, K., & Manzoor Hussain, M. (2023). Thermal Postbuckling of Heated Uniform Columns Considering Green Nonlinearity: A Novel Liner Finite Element Formulation. Journal of Aerospace Sciences and Technologies, 68(1), 37–46. https://doi.org/10.61653/joast.v68i1.2016.237
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References

  1. Thompson J.M.T. and Hunt, G.W., "A General Theory of Elastic Stability", John Wiley, London, 1973.
  2. Timoshenko, S.P. and Gere, J.M., "Theory of Elastic Stability", McGraw-Hill, New York, 1961.
  3. Ziegler, F. and Rammerstorfer, F.G., "Thermo Elastic Stability, Thermal Stress III, Ed. Hetnarski, R. B", Elsevier Amsterdam, 1989, pp. 107-189.
  4. Gunda, J.B., "Thermal Post-Buckling Analysis of Square Plates Resting on Elastic Foundation: Simple Closed-form Solutions", Applied Mathematical Modeling, doi.org/10.1016/j.apm.2012.09.031.
  5. Rao, G.V. and Raju, K. K., "Thermal Post-Buckling of Columns", AIAA Journal, Vol.22, 1984, pp.850-851.
  6. Raju, K.K. and Rao, G.V., "Finite Element Analysis of Thermal Post-Buckling of Tapered Columns", Computers and Structures, Vol.19, 1984, pp.617-620.
  7. Raju, K.K. and Rao, G.V., "Thermal Post-Buckling of a Square Plate Resting on an Elastic Foundation by Finite Element Method", Computers and Structures, Vol.28, 1988, pp.195-199.
  8. Dym, C.L., "Stability Theory and its Application to Structural Mechanics", Noordhoff International, Leyden, 1964.
  9. Przemieniecki, J.S., "Theory of Matrix Structural Analysis", McGraw-Hill, New York, 1968.
  10. Zienkiewicz, O.C., "The Finite Element Method", McGraw-Hill, London, 1977.
  11. Shames, I. H. and Pittarresi, J. M., "Introduction to Solid Mechanics", PHI, 2006.
  12. Reddy, J.N., "An Introduction to the Finite Element Method", McGraw-Hill, London, 2005.
  13. Rao, G.V. and Raju, K.K., "Thermal Post-Buckling of Uniform Columns: A Simple Intuitive Method", AIAA Journal, Vol.40, 2002, pp.2138-2140.
  14. Gupta, R.K., Anandrao, K.S., Jagadish, B., Janardhana, G.R. and Rao, G.V., "Comparative Study of Thermal Post-Buckling Analysis of Columns Using an Equilibrium Path Method and an Equivalent Eigenvalue Problem", IES Journal Part A : Civil and Structural Engineering, Vol.2, 2009, pp.296-303.
  15. Woinowsky-Krieger, S., "The Effect of an Axial Force on the Vibration of Hinged Bars", Journal of Applied Mechanics, Vol.7, 1950, pp.35-36.
  16. Rao, G.V., Ratnam, B. S. and Gunda, J. B., "Master Formula for Evaluating Vibration Frequencies of Structural Members Under Compressive Loads", The IES Journal Part A: Civil and Structural Engineering, Vol.4, 2011, pp.79-88.
  17. Shirong, L. and Changjun, C., "Analysis of Thermal Post-Buckling of Heated Elastic Rods", English Edition, Vol.21, 2000, pp.133-140.
  18. Rao, G. V., Ravi, B., and Gupta, A. V. S. S. K. S., "Prediction of Thermal Postbuckling Behavior of uniform Shear Flexible Column undergoing Large Lateral Deflections Through an Intuitive Formulation", Journal of Aerospace Sciences and Technologies", Vol.66, 2014, pp.12-20.