Analytical Solutions for Buckling Behavior of Two Directional Functionally Graded Beams Using a Third Order Shear Deformable Beam Theory


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KARAMANLI A. F.

ACADEMIC PLATFORM-JOURNAL OF ENGINEERING AND SCIENCE, vol.6, no.2, pp.164-178, 2018 (Peer-Reviewed Journal) identifier

Abstract

This paper is dedicated to present a Ritz-type analytical solution for buckling behavior of two directionalfunctionally graded beams (2D-FGBs) subjected to various sets of boundary conditions by employing a thirdorder shear deformation theory. The material properties of the beam vary in both axial and thickness directionsaccording to the power-law distribution. The axial, transverse deflections and rotation of the cross sections areexpressed in polynomial forms to obtain the buckling load. The auixiliary functions are added to displacementfunctions to satisfy the boundary conditions. Simply supported – Simply supported (SS), Clamped-Simplysupported (CS), Clamped – clamped (CC) and Clamped-free (CF) boundary conditions are considered.Computed results are compared with earlier works for the verification and convergence studies. The effects ofthe different gradient indexes, various aspect ratios and boundary conditions on the buckling responses of thetwo directional functionally graded beams are investigated.