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Structural Engineering and Mechanics Volume 44, Number 3, November10 2012 , pages 339-361 DOI: https://doi.org/10.12989/sem.2012.44.3.339 |
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Non-linear free vibrations and post-buckling analysis of shear flexible functionally graded beams |
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K. Sanjay Anandrao, R.K. Gupta, P. Ramchandran and G. Venkateswara Rao
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| Abstract | ||
| Large amplitude free vibration and thermal post-buckling of shear flexible Functionally Graded Material (FGM) beams is studied using finite element formulation based on first order Timoshenko beam theory. Classical boundary conditions are considered. The ends are assumed to be axially immovable. The von-Karman type strain-displacement relations are used to account for geometric non-linearity. For all the boundary conditions considered, hardening type of non-linearity is observed. For large amplitude vibration of FGM beams, a comprehensive study has been carried out with various lengths to height ratios, maximum lateral amplitude to radius of gyration ratios, volume fraction exponents and boundary conditions. It is observed that, for FGM beams, the non-linear frequencies are dependent on the sign of the vibration amplitudes. For thermal post-buckling of FGM beams, the effect of shear flexibility on the structural response is discussed in detail for different volume fraction exponents, length to height ratios and boundary conditions. The effect of shear flexibility is observed to be predominant for clamped beam as compared to simply supported beam. | ||
| Key Words | ||
| functionally graded materials; large amplitude vibrations; post-buckling; finite element analysis; shear flexibility; von-Karman geometric non-linearity; Newton-Raphson method | ||
| Address | ||
| K. Sanjay Anandrao and R.K. Gupta: Advanced Systems Laboratory, Kanchanbagh, Hyderabad-500058, India P. Ramchandran: DRDL, Kanchanbagh, Hyderabad-500058, India G. Venkateswara Rao: Department of Mechanical Engineering, Vardhaman College of Engineering, Shamshabad, Hyderabad-501218, India | ||