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Structural Engineering and Mechanics Volume 36, Number 5, November30 2010 , pages 545-560 DOI: https://doi.org/10.12989/sem.2010.36.5.545 |
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Thermal post-buckling analysis of uniform slender functionally graded material beams |
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K. Sanjay Anandrao, R.K. Gupta, P. Ramchandran and G. Venkateswara Rao
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| Abstract | ||
| Two or more distinct materials are combined into a single functionally graded material (FGM) where the microstructural composition and properties change gradually. Thermal post-buckling behavior of uniform slender FGM beams is investigated independently using the classical Rayleigh-Ritz (RR) formulation and the versatile Finite Element Analysis (FEA) formulation developed in this paper. The von-Karman strain-displacement relations are used to account for moderately large deflections of FGM beams. Bending-extension coupling arising due to heterogeneity of material through the thickness is included. Simply supported and clamped beams with axially immovable ends are considered in the present study. Post-buckling load versus deflection curves and buckled mode shapes obtained from both the RR and FEA formulations for different volume fraction exponents show an excellent agreement with the available literature results for simply supported ends. Response of the FGM beam with clamped ends is studied for the first time and the results from both the RR and FEA formulations show a very good agreement. Though the response of the FGM beam could have been studied more accurately by FEA formulation alone, the authors aim to apply the RR formulation is to find an approximate closed form post-buckling solutions for the FGM beams. Further, the use of the RR formulation clearly demonstrates the effect of bending-extension coupling on the post-buckling response of the FGM beams. | ||
| Key Words | ||
| Rayleigh-Ritz; finite element analysis; post-buckling; functionally graded materials; loaddeflection curves; geometric non-linearity; closed form solution. | ||
| Address | ||
| K. Sanjay Anandrao: Advanced Systems Laboratory, Kanchanbagh, Hyderabad - 500 058, India R.K. Gupta1a: Advanced Systems Laboratory, Kanchanbagh, Hyderabad - 500 058, India P. Ramchandran: Defense Research and Development Laboratory, Kanchanbagh, Hyderabad - 500 058, India G. Venkateswara Rao: School of Mechanical Engineering, Sreenidhi Institute of Science and Technology, Hyderabad - 501 301, India | ||