This study investigates the mechanical behaviours of functionally graded (FG) microbeams based on the modified couple stress theory. The material properties of these beams are varied through beam's depth and calculated by using classical rule of mixture and Mori–Tanaka scheme. The displacement fields are presented by using a unified framework which covers various theories including classical beam theory, first-order beam theory, third-order beam theory, sinusoidal beam theory, and quasi-3D beam theories. The governing equations of bending, vibration and buckling problems are derived using the Hamilton's principle and then solved by using Navier solutions with simply-supported boundary conditions. A number of numerical examples are conducted to show the validity and accuracy of the proposed approaches. Effects of Poisson's ratio, material length scale parameter, power-law index, estimation methods of material properties and slenderness ratio on deflections, stresses, natural frequencies and critical buckling loads of FG microbeams are examined.
Funding
The authors would like to thank Dr. Huu-Tai Thai at La Trobe University for discussion and Matlab codes. The first, second and third authors gratefully acknowledge research support fund from Northumbria University. The fourth author gratefully acknowledges financial support from Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. 107.02-2015.07.
History
Publication Date
2016-01-01
Journal
Composite Structures
Volume
154
Pagination
17p. (p. 556-572)
Publisher
Elsevier
ISSN
0263-8223
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