A size-dependent FG micro-plate model incorporating higher-order shear and normal deformation effects based on a modified couple stress theory

Nguyen

et al. 2017

Composite Structures

326

112

This paper presents a comprehensive review on the development of higher-order continuum models for capturing size effects in small-scale structures. The review mainly focus on the size-dependent beam, plate and shell models developed based on the nonlocal elasticity theory, modified couple stress theory and strain gradient theory due to their common use in predicting the global behaviour of small-scale structures. In each higher-order continuum theory, various size-dependent models based on the classical theory, first-order shear deformation theory and higher-order shear deformation theory were reviewed and discussed. In addition, the development of finite element solutions for size-dependent analysis of beams and plates was also highlighted. Finally a summary and recommendations for future research are presented. It is hoped that this review paper will provide current knowledge on the development of higher-order continuum models and inspire further applications of these models in predicting the behaviour of micro-and nano-structures.

Section: Modified Couple Stress Models Based On Hsdtsmentioning

confidence: 99%

Section: Modified Couple Stress Models Based On Hsdtsmentioning

confidence: 99%

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A review of continuum mechanics models for size-dependent analysis of beams and plates

Nguyen

et al. 2017

Composite Structures

326

112

“…Fundamental frequencies of Al/Al2O3 microplates are compared with those of Lei et al [38] in Table 5 and presented in Fig. 2 for various slenderness and material length scale ratios.…”

Section: B Vibration and Buckling Analysismentioning

confidence: 99%

Size-dependent behaviour of functionally graded sandwich microplates under mechanical and thermal loads

Trinh

Composites Part B: Engineering

et al. 2017

This paper presents the static bending, free vibration and buckling behaviours of functionally graded sandwich microplates under mechanical and thermal loads. Governing equations of both higher-order shear deformation and quasi-3D theories are derived based on the variational principle and modified couple stress theory. Apart from mechanical load, the temperature profiles considered are either uniform or linear distribution through the thickness, which results in changes of material properties and stress resultants. Numerical results are obtained using Navier solutions. The difference between quasi-3D and 2D models in dealing with mechanical and thermal load is discussed. Temperature-dependent and temperature-independent material properties are examined. The effects of geometry and power-law index together with mechanical loads and various temperature distributions on the size-dependent behaviours of functionally graded sandwich plates are also investigated.

“…The MCST sinusoidal shear deformation model was also developed by Thai and Vo [47] for deflections and natural frequencies of simply supported microplates. Some other refined plate models [48,49] and quasi-3D [50][51][52] were also employed the MCST for FG microplates. In addition, the thermal effects are examined for the FG microplates in many publications.…”

Section: Introductionmentioning

confidence: 99%

State-space Levy solution for size-dependent static, free vibration and buckling behaviours of functionally graded sandwich plates

Trinh

Composites Part B: Engineering

et al. 2018

The size-dependent static, free vibration and buckling behaviours of functionally graded (FG) sandwich plates are analysed in this study. Utilising the modified couple stress theory and variational principle, governing equations of motion are developed with a refined shear deformation theory. The rectangular plates embedded on two opposite simply-supported edges with the arbitrary combinations of the other two. Based on the state-space Levy solution, the deflections, stresses, natural frequencies and critical buckling loads are analytically solved for the closed-form formulations. The effects of material distribution and graded schemes, geometric parameters and boundary conditions are also investigated to examine the size-dependent behaviours of FG sandwich microplates.