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

Authors : Armağan Karamanlı

Pages : 164-178

Doi:10.21541/apjes.357539

View : 12 | Download : 8

Publication Date : 2018-08-03

Article Type : Research Paper

Abstract :This paper is dedicated to present a Ritz-type analytical solution for buckling behavior of two directional functionally graded beams insert ignore into journalissuearticles values(2D-FGBs); subjected to various sets of boundary conditions by employing a third order shear deformation theory. The material properties of the beam vary in both axial and thickness directions according to the power-law distribution. The axial, transverse deflections and rotation of the cross sections are expressed in polynomial forms to obtain the buckling load. The auixiliary functions are added to displacement functions to satisfy the boundary conditions. Simply supported – Simply supported insert ignore into journalissuearticles values(SS);, Clamped-Simply supported insert ignore into journalissuearticles values(CS);, Clamped – clamped insert ignore into journalissuearticles values(CC); and Clamped-free insert ignore into journalissuearticles values(CF); boundary conditions are considered. Computed results are compared with earlier works for the verification and convergence studies. The effects of the different gradient indexes, various aspect ratios and boundary conditions on the buckling responses of the two directional functionally graded beams are investigated.
Keywords : Two Directional Functionally Graded Beam, Buckling Behavior, Third Order Shear Deformation Theory, Ritz Method