A new method for bending and buckling analysis of rectangular nano plate: full modified nonlocal theory

Mousavi, Z.; Shahidi, Seyed Alireza; Boroomand, B.

doi:10.1007/s11012-016-0606-9

Cited by 12 publications

(4 citation statements)

References 36 publications

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“…3 (d). Else, Mousavi et al [83] presented a novel methodology (fully modified NLC) to examine the static analyses of NPs. Moreover, Ebrahimi and Barati [84] examined the NLC thermal stability of embedded METE nonhomogeneous NPs, shown in Fig.…”

Section: Various Composite Nano/microplatesmentioning

confidence: 99%

Computational Linear and Nonlinear Free Vibration Analyses of Micro/Nanoscale Composite Plate-Type Structures With/Without Considering Size Dependency Effect: A Comprehensive Review

Al Mahmoud,

Safaei,

Sahmani

et al. 2024

Arch Computat Methods Eng

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Recently, the mechanical performance of various mechanical, electrical, and civil structures, including static and dynamic analysis, has been widely studied. Due to the neuroma's advanced technology in various engineering fields and applications, developing small-size structures has become highly demanded for several structural geometries. One of the most important is the nano/micro-plate structure. However, the essential nature of highly lightweight material with extraordinary mechanical, electrical, physical, and material characterizations makes researchers more interested in developing composite/laminated-composite-plate structures. To comprehend the dynamical behavior, precisely the linear/nonlinear-free vibrational responses, and to represent the enhancement of several parameters such as nonlocal, geometry, boundary condition parameters, etc., on the free vibrational performance at nano/micro scale size, it is revealed that to employ all various parameters into various mathematical equations and to solve the defined governing equations by analytical, numerical, high order, and mixed solutions. Thus, the presented literature review is considered the first work focused on investigating the linear/nonlinear free vibrational behavior of plates on a small scale and the impact of various parameters on both dimensional/dimensionless natural/fundamental frequency and Eigen-value. The literature is classified based on solution type and with/without considering the size dependency effect. As a key finding, most research in the literature implemented analytical or numerical solutions. The drawback of classical plate theory can be overcome by utilizing and developing the elasticity theories. The nonlocality, weight fraction of porosity, or the reinforcements, and its distribution type of elastic foundation significantly influence the frequencies.

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Section: Various Composite Nano/microplatesmentioning

confidence: 99%

Computational Linear and Nonlinear Free Vibration Analyses of Micro/Nanoscale Composite Plate-Type Structures With/Without Considering Size Dependency Effect: A Comprehensive Review

Al Mahmoud,

Safaei,

Sahmani

et al. 2024

Arch Computat Methods Eng

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“…Given the fact that experimental methods are difficult and costly at the nanoscale, three numerical simulation methods such as atomistic, hybrid atomistic–continuum mechanics, and continuum mechanics have received much attention. 14,21 Due to the limitations concerning time and the maximum number of atoms in the simulation, the first two methods are costlier than modeling based on continuum mechanics. Since classical continuum theories cannot capture the size effects, nonclassical continuum theories have been proposed to assess the significant size effects in small scale.…”

Section: Introductionmentioning

confidence: 99%

Mindlin’s strain gradient theory for vibration analysis of FG-CNT-reinforced composite nanoplates resting on Kerr foundation in thermal environment

Shahraki

Riahi

Izadinia

et al. 2019

Journal of Thermoplastic Composite Materials

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This article examines the application of simplified Mindlin’s strain gradient theory to free vibration analysis of functionally graded carbon nanotube–reinforced composite (FG-CNTRC) thick rectangular nanoplates resting on Kerr elastic foundation in thermal environment. The theory contains only one length scale parameter corresponding to strain gradient effects. Also, a quasi-3D hyperbolic theory considering transverse shear deformation and thickness stretching effects is employed to present the formulation. In this study, properties of the carbon nanotubes (CNTs) and the polymeric matrix are assumed to be temperature dependent. Distribution of CNTs across the thickness of the nanoplate is considered to be uniform (UD) or functionally graded (FG-X, FG-V, and FG-O). According to Hamilton’s principle and the generalized differential quadrature method, the governing equations and associated boundary conditions are obtained and discretized, respectively. The natural frequencies of FG-CNTRC nanoplates are determined by solving eigenvalue problem. The numerical results of the present formulation are compared with those available in the literature to explain the accuracy of the suggested theories. Then, parametric studies are presented to examine the effects of elastic foundation coefficients, size parameter, temperature change, volume fraction and dispersion profile of CNTs, aspect ratio, length-to-thickness ratio, and different boundary conditions on vibration behavior of FG-CNTRC nanoplates. The results confirmed that size parameter and changes in temperature play an important role in determining natural frequencies. In addition, the shear layer parameter of Kerr foundation has more influence with respect to the coefficients of the upper and lower layers.

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“…The existing 2D nonlocal models for thin elastic plates are usually based on the above mentioned differential constitutive relations, e.g., see Lu et al (2007), Duan and Wang (2007), Aghababaei and Reddy (2009), Pradhan and Phadikar (2009), Malekzadeh et al (2011), Xu et al (2014), Thai et al (2014), Jung and Han (2014), and Mousavi et al (2017). In these models, 3D → 2D reduction is carried out using ad-hoc assumptions neglecting the variation of nonlocal properties across the thickness.…”

Section: Introductionmentioning

confidence: 99%

“…The existing two-dimensional non-local models for thin elastic plates are usually based on the above-mentioned differential constitutive relations (e.g. [20][21][22][23][24][25][26][27][28]). In these models, threedimensional → two-dimensional reduction is carried out using ad-hoc assumptions neglecting the variation of non-local properties across the thickness.…”

Section: Introductionmentioning

confidence: 99%

A non-local asymptotic theory for thin elastic plates

2017

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The 3D dynamic nonlocal elasticity equations for a thin plate are subject to asymptotic analysis assuming the plate thickness to be much greater than a typical microscale size. The integral constitutive relations, incorporating the variation of an exponential nonlocal kernel across the thickness, are adopted. Long-wave low-frequency approximations are derived for both bending and extensional motions. Boundary layers specific for nonlocal behaviour are revealed near the plate faces. It is established that the effect of the boundary layers leads to first-order corrections to the bending and extensional stiffness in the classical 2D plate equations.

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A new method for bending and buckling analysis of rectangular nano plate: full modified nonlocal theory

Cited by 12 publications

References 36 publications

Computational Linear and Nonlinear Free Vibration Analyses of Micro/Nanoscale Composite Plate-Type Structures With/Without Considering Size Dependency Effect: A Comprehensive Review

Computational Linear and Nonlinear Free Vibration Analyses of Micro/Nanoscale Composite Plate-Type Structures With/Without Considering Size Dependency Effect: A Comprehensive Review

Mindlin’s strain gradient theory for vibration analysis of FG-CNT-reinforced composite nanoplates resting on Kerr foundation in thermal environment

A non-local asymptotic theory for thin elastic plates

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