A buckling analysis of perfect and imperfect functionally graded columns

Abstract

Due to the asymmetry of the material properties about the middle plane, perfect columns made of functionally graded materials (FGMs) may not remain straight when a compressive axial point load is concentrically applied. This article analytically derives the displacement functions and the buckling load of both perfect and imperfect Euler–Bernoulli functionally graded columns. The method of derivation is based on the translation of the reference plane to the position at which the coupling between the axial and bending deformations is eliminated, i.e. the physical neutral surface position. Then, all the governing equations and their solutions turn out to have the same form as those of homogeneous columns subjected to an eccentric axial load. The effects of geometric imperfection are studied with the main purpose of finding imperfect shapes that make an imperfect column stronger than a perfect one. Further, the governing equations that are used to find those analytical solutions are expanded so that the equations can deal with large deformation and large strain analysis. These new governing equations are solved by finite element (FE) method based on linear exact shape functions. Then, the FE solutions are used to compare and validate the analytical solutions obtained earlier.

Keywords

buckling columns imperfection functionally graded materials physical neutral surface

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References

Feldman

Aboudi

Buckling analysis of functionally graded plates subjected to uniaxial loading. Compos. Struct, 1997, 38, 29–36.

Javaheri

Eslami

Buckling of functionally graded plates under in-plane compressive loading. ZAMM, 2002, 82(4), 277–283.

Najafizadeh

Eslami

Buckling analysis of circular plates of functionally graded materials under uniform radial compression. Int. J. Mech. Sci, 2002, 44, 2479–2493.

Chen

Liew

Buckling of rectangular functionally graded material plates subjected to nonlinearly distributed in-plane edge loads. Smart Mater. Struct, 2004, 13, 1430–1437.

Ganapathi

Prakash

Sundararajan

Influence of functionally graded material on buckling of skew plates under mechanical loads. J. Eng. Mech, 2006, 132, 902–905.

Shariat

BAS

Javaheri

Eslami

Buckling of imperfect functionally graded plates under in-plane compressive loading. Thin Walled Struct, 2005, 43, 1020–1036.

Aydogdu

Conditions for functionally graded plates to remain flat under in-plane loads by classical plate theory. Compos. Struct, 2008, 82, 155–157.

Prakash

Singha

Ganapathi

Influence of neutral surface position on the nonlinear stability behavior of functionally graded plates. Comput. Mech, 2009, 43, 341–350.

Elishakoff

Gentilint

Santoro

Some conventional and unconventional educational column stability problems. Int. J. Struct. Stab. Dyn, 2006, 6(1), 139–151.

10.

Singh

Buckling of functionally graded and elastically restrained non-uniform columns. Composites Part B, 2009, 40, 393–403.

11.

Huang

Buckling of functionally graded circular columns including shear deformation. Mater. Des, 2010, 31, 3159–3166.

12.

Yang

Chen

Free vibration and buckling analyses of functionally graded beams with edge cracks. Compos. Struct, 2008, 83, 48–60.

13.

Morimoto

Tanigawa

Kawamura

Thermal buckling of functionally graded rectangular plates subjected to partial heating. Int. J. Mech. Sci, 2006, 48, 926–937.

14.

Abrate

Functionally graded plates behave like homogeneous plates. Composites Part B, 2008, 39, 151–158.

15.

Zhang

Zhou

A theoretical analysis of FGM thin plates based on physical neutral surface. Comput. Mater. Sci, 2008, 44, 716–720.

16.

Zhang

Dai

Stress analysis of functionally gradient beam using effective principal axes. Int. J. Mech. Mater. Des, 2005, 2, 157–164.

17.

Kang

Bending of functionally graded cantilever beam with power-law non-linearity subjected to an end force. Int. J. Nonlinear Mech, 2009, 44, 696–703.

18.

Taeprasartsit

Using a homogeneous beam element to analyse functionally graded beams. Proc. IMechE, Part C: J. Mechanical Engineering Science, 2010, 224, 789–795.

19.

Simitses

Hodges

Fundamentals of structural stability, 2006, Oxford, UK, Butterworth-Heinemann.

20.

Wakashima

Hirano

Niino

. Functionally gradient materials (FGM) architecture: a new type of ceramic-metal assemblage designed for hot structural components. Proceedings of the ESA Symposium on Space applications of advanced structural materials, ESTEC, Noordwijk, The Netherlands, 21–23 March 1990 (Ed. Burke

), 1990, pp. 97–102 (The Agency, Paris, France).