Abstract
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.
Highlights
Graded materials (FGM) are increasingly used in the many fields of industrial engineering including automotive, nuclear power plant, aerospace
The modified couple stress theory is considered as a prominent one since it includes asymmetric couple stress tensor and there only one material length scale parameter is used in the constitutive equations
In order to take into account the shear deformations, the Timoshenko or the First-order Beam Theory (FBT) which is appropriate for thick beams is introduced
Summary
Graded materials (FGM) are increasingly used in the many fields of industrial engineering including automotive, nuclear power plant, aerospace. The modified couple stress theory is considered as a prominent one since it includes asymmetric couple stress tensor and there only one material length scale parameter is used in the constitutive equations Utilising these striking features of the modified couple stress theory, a number of research works have been conducted to investigate the size-dependent behaviours of FG microbeams with various theories. In the effort to seek a better solution for beam problems, various quasi-3D theories ([28,29,30,31,32,33]) and Carrera Unified Formulation theory ([34, 35]), which include both shear and thickness stretching effects are developed. An unified framework for various beam theories are proposed to investigate the sizedependent bending, vibration and buckling behaviours of FG microbeams based on the modified couple stress theory.
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