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http://dx.doi.org/10.12989/aas.2018.5.6.671

An inverse hyperbolic theory for FG beams resting on Winkler-Pasternak elastic foundation  

Sayyad, Atteshamuddin S. (Department of Civil Engineering, SRES's Sanjivani College of Engineering, Savitribai Phule Pune University)
Ghugal, Yuwaraj M. (Department of Applied Mechanics, Government Engineering College)
Publication Information
Advances in aircraft and spacecraft science / v.5, no.6, 2018 , pp. 671-689 More about this Journal
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.
Keywords
inverse hyperbolic beam theory; FG beam; displacements; stresses; critical buckling load; frequencies; Winkler-Pasternak elastic foundation;
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Times Cited By KSCI : 2  (Citation Analysis)
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