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Advances in Aircraft and Spacecraft Science
  Volume 5, Number 6, November 2018, pages 671-689
DOI: https://doi.org/10.12989/aas.2018.5.6.671
 
open access

An inverse hyperbolic theory for FG beams resting on Winkler-Pasternak elastic foundation
Atteshamuddin S. Sayyad and Yuwaraj M. Ghugal

 
Abstract
    Bending, buckling and free vibration responses of functionally graded (FG) higher-order beams resting on two parameter (Winkler-Pasternak) elastic foundation are studied using a new inverse hyperbolic beam theory. The material properties of the beam are graded along the thickness direction according to the power-law distribution. In the present theory, the axial displacement accounts for an inverse hyperbolic distribution, and the transverse shear stress satisfies the traction-free boundary conditions on the top and bottom surfaces of the beams. Hamilton\'s principle is employed to derive the governing equations of motion. Navier type analytical solutions are obtained for the bending, bucking and vibration problems. Numerical results are obtained to investigate the effects of power-law index, length-to-thickness ratio and foundation parameter on the displacements, stresses, critical buckling loads and frequencies. Numerical results by using parabolic beam theory of Reddy and first-order beam theory of Timoshenko are specially generated for comparison of present results and found in excellent agreement with each other.
 
Key Words
    inverse hyperbolic beam theory; FG beam; displacements; stresses; critical buckling load; frequencies, Winkler-Pasternak elastic foundation
 
Address
Atteshamuddin S. Sayyad: Department of Civil Engineering, SRES\'s Sanjivani College of Engineering, Savitribai Phule Pune University,
Kopargaon-423601, Maharashtra, India
Yuwaraj M. Ghugal: Department of Applied Mechanics, Government Engineering College, Karad-415124, Maharashtra, India
 

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