2015 EJRNL PP Shirong Li 1.pdf?
Terbatas Irwan Sofiyan
» ITB
Terbatas Irwan Sofiyan
» ITB
The relationship between the critical buckling loads of functionally graded material
(FGM) Levinson beams (LBs) and those of the corresponding homogeneous Euler-Bernoulli beams
(HEBBs) is investigated. Properties of the beam are assumed to vary continuously in the depth
direction. The governing equations of the FGM beam are derived based on the Levinson beam
theory, in which a quadratic variation of the transverse shear strain through the depth is included.
By eliminating the axial displacement as well as the rotational angle in the governing equations,
an ordinary differential equation in terms of the deflection of the FGM LBs is derived, the form
of which is the same as that of HEBBs except for the definition of the load parameter. By solving
the eigenvalue problem of ordinary differential equations under different boundary conditions
clamped (C), simply-supported (S), roller (R) and free (F) edges combined, a uniform analytical
formulation of buckling loads of FGM LBs with S-S, C-C, C-F, C-R and S-R edges is presented
for those of HEBBs with the same boundary conditions. For the C-S beam the above-mentioned
equation does not hold. Instead, a transcendental equation is derived to find the critical buckling
load for the FGM LB which is similar to that for HEBB with the same ends. The significance of
this work lies in that the solution of the critical buckling load of a FGM LB can be reduced to
that of the HEBB and calculation of three constants whose values only depend upon the throughthe-
depth gradient of the material properties and the geometry of the beam. So, a homogeneous
and classical expression for the buckling solution of FGM LBs is accomplished.