A Review on the Size-Dependent Models of Micro-beam and Micro-plate Based on the Modified Couple Stress Theory

Kong, Shengli

doi:10.1007/s11831-021-09567-w

Cited by 45 publications

(9 citation statements)

References 280 publications

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“…Where the coefficient of the variations of the partial derivatives of deformation variables u, v, w, f x and f y the stress and couple stress resultants using appendix A are shown by equations (11) and (12).…”

Section: Constitutive Lawsmentioning

confidence: 99%

“…The influence of sizedependent based on MCST, nonlocal elasticity, and modified deformation gradient method has been investigated [11] in the study of beams, plates, and shells. Numerical and analytical solutions of pull-in instability, static bending, buckling, and vibration of microbeams and microplates on the basis of MCST, CPT, and FSDT have been presented [12]. Numerical solutions of buckling of microplates have been studied [13] using Mindlin theory and a finite element model for various supports.…”

Section: Introductionmentioning

confidence: 99%

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Parametric study for modified couple stress theory on postbuckling of size-dependent FG saturated porous mindlin microplates

et al. 2023

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Using modified couple stress plate and Mindlin theories, the present study is a parametric study for revealing the effect of length scale parameter on postbuckling of saturated poroelastic rectangular microplates with pore distribution being functionally graded across thickness. The microplate postbuckling is a nonlinear eigenvalue problem with coupled partial differential equations of equilibrium. In order to find the mode shapes, the eigenfunctions have been approximated by some complete polynomial series expansions in accordance with the conventional Ritz approximation technique. After discretizing the governing equations throughout the microplate grid points, the assembled difference equations construct a nonlinear eigenvalue problem with coupled algebraic equations. The nontrivial coefficients of the expansions were calculated such that the eigenfunctions extremize the microplate potential energy for satisfying the equilibrium homogeneous equations. Variation of the potential energy have been derived with respect to the expansions coefficients from the vantage of using Maple software. By gradual reduction in the initial end shortening of the movable supports and solving the assembled difference equations via Newton-Raphson iterations, the critical postbuckling displacement imposed to the movable supports are found along with the nontrivial coefficients regarding eigenfunctions. The results of the parametric study have revealed how geometric parameters, pore distribution, the Skempton coefficient, porosity, and different boundary conditions modify the influence of length scale parameter on the microplate postbuckling.

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Section: Constitutive Lawsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Parametric study for modified couple stress theory on postbuckling of size-dependent FG saturated porous mindlin microplates

et al. 2023

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“…A number of researches has been performed for FGP microplates in which the modified coupled stress theory (MCT) are mostly used. By considering the rotation gradient in constitutive equations, the MCT with only one MLSP is known as the simplest theory accounted for the size effects [15]. Owing to its simplicity, many size-dependent FGP microplate models with different shear deformation theories based on the MCT have been developed [16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Static and vibration analysis of functionally graded microplate with porosities based on higher-order shear deformation and modified strain gradient theory

Tran

Nguyen

Nguyen³

et al. 2023

Vietnam J. Mech.

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Based on fundamental equations of the elasticity theory, a unified higher-order shear deformation theory is developed for bending and free vibration analysis of functionally graded (FG) microplates with porosities. The modified strain gradient theory is employed to capture the size effects. Bi-directional series with hybrid shape functions are used to solve the problems. Several important effects including thickness-to-material length scale parameters, side-to-thickness ratio, and boundary conditions on the deflections and natural frequencies of FG porous microplates are investigated.

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“…The Comprehensive Child Support Tool (CCST) has not been widely implemented. Kong [18] provided an overview of the existing size-dependent models for microbeams and microplates, focusing on the MCST approach. The beam systems based on the Modified Cantilever Shear Transfer (MCST) presented by various researchers were examined by Kwon and Lee [19].…”

Section: Introductionmentioning

confidence: 99%

Effect of non‐local modified couple stress theory on the responses of axially moving thermoelastic nano‐beams

Abouelregal

2023

Z Angew Math Mech

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The present study examines the lateral thermal vibrations of a nanobeam subjected to an axial motion while being influenced by a sinusoidal thermal load. The partial differential equation describing the system was obtained using the extended Hamiltonian principle. Also considered were the Euler‐Bernoulli (EB) beam, the nonlocal couple stress theory, and Eringen's nonlocal elasticity model. This type of axially moving beam has multiple applications in design, including industrial, civil, structural, chemical, and computer engineering. The Laplace transform technique is utilized to translate partial differential equations into a thermoelastic differential equation of the sixth order. This study investigates the impact of nanobeam size and velocity on thermo‐mechanical characteristics. To explore the impacts of axial velocity, pulse width, nonlocal index, material length scale coefficient, and phase lag coefficients on the examined studied fields, such as lateral vibration and temperature change for the moving nanobeam are calculated. The specified factors were discovered to impact the flexibility and dynamic response of the nanobeam substantially.

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A Review on the Size-Dependent Models of Micro-beam and Micro-plate Based on the Modified Couple Stress Theory

Cited by 45 publications

References 280 publications

Parametric study for modified couple stress theory on postbuckling of size-dependent FG saturated porous mindlin microplates

Parametric study for modified couple stress theory on postbuckling of size-dependent FG saturated porous mindlin microplates

Static and vibration analysis of functionally graded microplate with porosities based on higher-order shear deformation and modified strain gradient theory

Effect of non‐local modified couple stress theory on the responses of axially moving thermoelastic nano‐beams

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