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Applied Mathematics and Mechanics

, Volume 39, Issue 7, pp 923–952 | Cite as

Instability of functionally graded micro-beams via micro-structure-dependent beam theory

  • Xiaobai Li
  • Li Li
  • Yujin Hu
Article
  • 95 Downloads

Abstract

This paper focuses on the buckling behaviors of a micro-scaled bi-directional functionally graded (FG) beam with a rectangular cross-section, which is now widely used in fabricating components of micro-nano-electro-mechanical systems (MEMS/NEMS) with a wide range of aspect ratios. Based on the modified couple stress theory and the principle of minimum potential energy, the governing equations and boundary conditions for a micro-structure-dependent beam theory are derived. The present beam theory incorporates different kinds of higher-order shear assumptions as well as the two familiar beam theories, namely, the Euler-Bernoulli and Timoshenko beam theories. A numerical solution procedure, based on a generalized differential quadrature method (GDQM), is used to calculate the results of the bi-directional FG beams. The effects of the two exponential FG indexes, the higher-order shear deformations, the length scale parameter, the geometric dimensions, and the different boundary conditions on the critical buckling loads are studied in detail, by assuming that Young’s modulus obeys an exponential distribution function in both length and thickness directions. To reach the desired critical buckling load, the appropriate exponential FG indexes and geometric shape of micro-beams can be designed according to the proposed theory.

Keywords

bi-directional functionally graded (FG) material buckling modified couple stress theory micro-beam 

Chinese Library Classification

O343.7 O343.9 

2010 Mathematics Subject Classification

74K10 74S30 

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© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mechanical Science and EngineeringHuazhong University of Science and TechnologyWuhanChina

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