La Trobe
Bending_Vibration_Buckling_MircoFGbeams_Navier_R2.pdf (536.55 kB)

Size-dependent behaviour of functionally graded microbeams using various shear deformation theories based on the modified couple stress theory

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journal contribution
posted on 2021-01-15, 05:11 authored by LC Trinh, HX Nguyen, Thuc VoThuc Vo, TK Nguyen
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.


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.


Publication Date



Composite Structures




17p. (p. 556-572)





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