Stability of size dependent functionally graded nanoplate based on nonlocal elasticity and higher order plate theories and different boundary conditions

Daneshmehr, Alireza; Rajabpoor, Amir; pourdavood, M.

doi:10.1016/j.ijengsci.2014.04.017

Cited by 95 publications

(14 citation statements)

References 47 publications

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“…Hosseini-Hashemi et al [175] derived Levy solutions for critical buckling loads and natural frequencies of isotropic nanoplates. Daneshmehr et al [176][177] extended the application of the nonlocal TSDT to the buckling [176] and free vibration analysis [177] of FG nanoplates.…”

Section: Nonlocal Models Based On the Tsdtmentioning

confidence: 99%

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

Thai

Nguyen

et al. 2017

Composite Structures

324

112

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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.

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Section: Nonlocal Models Based On the Tsdtmentioning

confidence: 99%

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

Thai

Nguyen

et al. 2017

Composite Structures

324

112

View full text Add to dashboard Cite

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“…Third-order shear deformation theory (TSDT) extends the FSDT by assuming that: – Shear strain and consequently shear stress are not constant through the plate thickness where for a moderately thick plate, TSDT leads to better results. – The strain equations do not need a shear correction factor. – The displacement field accommodates a quadratic variation of the transverse shear through the thickness and the vanishing of transverse shear stresses on the top and bottom surfaces of the plate. 15,30 …”

Section: Third-order Shear Deformation Theorymentioning

confidence: 99%

Orthotropic patterns of Pasternak foundation in smart vibration analysis of magnetostrictive nanoplate

Arani

Maraghi

Arani

2015

Proceedings of the Institution of Mechanical Engineers, Part C:

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In this research, free vibration of rectangular nanoplate made of magnetostrictive materials is studied while it is focused on elastic medium as an efficient stability factor. For this purpose, Pasternak foundation is developed by considering orthotropy angle where the effect of Pasternak shear modulus is investigated in different directions. Since the nanoplate is subjected to the coil, a feedback control system follows the effects of uniform magnetic field on vibration characteristics of magnetostrictive nanoplate. So, Reddy’s third-order shear deformation theory along with Eringen’s nonlocal continuum model are utilized in order to derive motion equations at nanoscale using Hamilton’s principle. Five coupled motion equations solved by differential quadrature method in two-dimensional space by considering different boundary conditions. Results indicate that with appropriative selection for orthotropy angle, normal, and shear Pasternak foundation modulus, it is possible to achieve optimal and desire values to more stability of magnetostrictive nanoplate. These findings can be used in automotive industry, communications equipment in nano- and microstructures.

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“…Thus, this theory is a suitable candidate for modeling of nanoscale structures [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. This theory is also extensively applied to investigate mechanical behaviors of FG nanoplates [35][36][37][38][39][40][41][42][43][44][45][46][47]. Note that these published papers on FG nanoplate have reported their linear vibration behavior.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear thermal vibration analysis of refined shear deformable FG nanoplates: two semi-analytical solutions

Barati

Shahverdi

2018

J Braz. Soc. Mech. Sci. Eng.

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This paper deals with the semi-analytical nonlinear thermal vibration analysis of functionally graded (FG) nanoplates modeled by four-variable refined plate theory. The nanoplate is resting on a nonlinear hardening elastic medium and subjected to uniform and nonlinear temperature rises. Temperature-dependent gradient material properties of the nanoplate are described via simple power-law model. A closed-form expression for nonlinear frequency is presented using a novel Hamiltonian approach as well as He's variational method. To the best of the author's knowledge, the nonlinear governing equations and their solution for a refined four-variable nanoplate are very rare in the literature. It is seen that the nonlinear vibration frequency is affected by the uniform temperature rise, nonlinear temperature rise, scale parameter, maximum amplitude, material gradation, foundation parameters and temperature-dependency. The presented formulation and solution approaches can be used in future investigations on macro to nanoscale plates.

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Stability of size dependent functionally graded nanoplate based on nonlocal elasticity and higher order plate theories and different boundary conditions

Cited by 95 publications

References 47 publications

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

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

Orthotropic patterns of Pasternak foundation in smart vibration analysis of magnetostrictive nanoplate

Nonlinear thermal vibration analysis of refined shear deformable FG nanoplates: two semi-analytical solutions

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