Size dependent buckling analysis of functionally graded micro beams based on modified couple stress theory

被引:180
|
作者
Nateghi, A. [1 ]
Salamat-talab, M. [2 ]
Rezapour, J. [3 ]
Daneshian, B. [4 ]
机构
[1] Univ Tehran, Coll Engn, Sch Mech Engn, Tehran, Iran
[2] Iran Univ Sci & Technol, Dept Mech Engn, Tehran, Iran
[3] Islamic Azad Univ, Lahijan Branch, Dept Mech Engn, Lahijan, Iran
[4] Islamic Azad Univ, Lahijan Branch, Dept Math, Lahijan, Iran
关键词
Buckling; Size dependency; Modified couple stress theory; Shear deformation; GDQ method; GENERALIZED DIFFERENTIAL QUADRATURE; FREE-VIBRATION ANALYSIS; TIMOSHENKO; ELASTICITY; FREQUENCY;
D O I
10.1016/j.apm.2011.12.035
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
Buckling analysis of functionally graded micro beams based on modified couple stress theory is presented. Three different beam theories, i.e. classical, first and third order shear deformation beam theories, are considered to study the effect of shear deformations. To present a profound insight on the effect of boundary conditions, beams with hinged-hinged, clamped-clamped and clamped-hinged ends are studied. Governing equations and boundary conditions are derived using principle of minimum potential energy. Afterwards, generalized differential quadrature (GDQ) method is applied to solve the obtained differential equations. Some numerical results are presented to study the effects of material length scale parameter, beam thickness, Poisson ratio and power index of material distribution on size dependent buckling load. It is observed that buckling loads predicted by modified couple stress theory deviates significantly from classical ones, especially for thin beams. It is shown that size dependency of FG micro beams differs from isotropic homogeneous micro beams as it is a function of power index of material distribution. In addition, the general trend of buckling load with respect to Poisson ratio predicted by the present model differs from classical one. (C) 2011 Elsevier Inc. All rights reserved.
引用
收藏
页码:4971 / 4987
页数:17
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