An explicit solution for bending of nanowires lying on Winkler–Pasternak elastic substrate medium based on the Euler–Bernoulli beam theory

Khajeansari, Amin; Baradaran, Gholam Hossein; Yvonnet, Julien

doi:10.1016/j.ijengsci.2011.11.004

Cited by 43 publications

(17 citation statements)

References 47 publications

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“…(17). These functions, for the different cases of boundary conditions, are listed in detail in Table 1, noting that   m/a,  n/b for m, n 1, 2, 3.…”

Section: Exact Solutionsmentioning

confidence: 99%

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Natural Frequency and Buckling of Orthotropic Nanoplates Resting on Two-Parameter Elastic Foundations with Various Boundary Conditions

Sobhy

2014

J. mech.

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In this article, the analyses of the natural frequency and buckling of orthotropic nanoplates, such as single-layered graphene sheets, resting on Pasternak's elastic foundations with various boundary conditions are presented. New functions for midplane displacements are suggested to satisfy the different boundary conditions. These functions are examined by comparing their results with the results obtained by using the functions suggested by Reddy (Reddy JN. Mechanics of Composite Materials and Structures: Theory and Analysis. Boca Raton, FL: CRC Press; 1997). Moreover, these functions are very simple comparing with Reddy's functions, leading to ease of calculations. The equations of motion of the nonlocal model are derived using the sinusoidal shear deformation plate theory (SPT) in conjunction with the nonlocal elasticity theory. The present SPT are compared with other plate theories. Explicit solution for buckling loads and vibration are obtained for single-layered graphene sheets with isotropic and orthotropic properties; and under biaxial loads. The formulation and the method of the solution are firstly validated by executing the comparison studies for the isotropic nanoplates with the results being in literature. Then, the influences of nonlocal parameter and the other parameters on the buckling and vibration frequencies are investigated.

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“…(17). These functions, for the different cases of boundary conditions, are listed in detail in Table 1, noting that   m/a,  n/b for m, n 1, 2, 3.…”

Section: Exact Solutionsmentioning

confidence: 99%

“…The substrate medium is simplified by an elastic foundation model. This idealization for the continuous interface media leads to a simple formulation and moreover makes the cost of computations much more less as compared with the simulation of the whole medium as a continuum model [17].…”

Section: Introductionmentioning

confidence: 99%

Natural Frequency and Buckling of Orthotropic Nanoplates Resting on Two-Parameter Elastic Foundations with Various Boundary Conditions

Sobhy

2014

J. mech.

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“…Due to their exciting properties, nanowires are promising candidates for detecting nano-objects with high sensitivity, and also they can be potentially employed in several fields, such as measurement systems [1,2], Micro/Nanoelectromechanical Systems (M/NEMS) [3], biological or gas sensing devices [4], flexible electronics and renewable energy technologies [5], integrated Shape Memory Alloy (SMA) [6], resonators and actuators [7,8] and multifunctional NEMSs.…”

Section: Introductionmentioning

confidence: 99%

Instability Characteristics of Free-Standing Nanowires Based on the Strain Gradient Theory with the Consideration of Casimir Attraction and Surface Effects

Sedighi

Ouakad

Khooran

2017

Metrology and Measurement Systems

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Size-dependent dynamic instability of cylindrical nanowires incorporating the effects of Casimir attraction and surface energy is presented in this research work. To develop the attractive intermolecular force between the nanowire and its substrate, the proximity force approximation (PFA) for small separations, and the Dirichlet asymptotic approximation for large separations with a cylinder-plate geometry are employed. A nonlinear governing equation of motion for free-standing nanowires − based on the Gurtin-Murdoch model − and a strain gradient elasticity theory are derived. To overcome the complexity of the nonlinear problem in hand, a Garlerkinbased projection procedure for construction of a reduced-order model is implemented as a way of discretization of the governing differential equation. The effects of length-scale parameter, surface energy and vacuum fluctuations on the dynamic instability threshold and adhesion of nanowires are examined. It is demonstrated that in the absence of any actuation, a nanowire might behave unstably, due to the Casimir induction force.

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“…The bending behavior of nano-scale structures has been the subject of several studies and, in particular, nanobeams under static transverse loads were studied in (Wang and Khajeansari et al, 2012). These studies took into account a number of effects such as shear deformation, surface stress, and elastic foundation but neglected the load and material uncertainties.…”

Section: Introductionmentioning

confidence: 99%

Static and Sensitivity Analysis of Nonlocal Nanobeams Subject to Load and Material Uncertainties by Convex Modeling

Radebe

Adali

2015

jtam

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At the nano-scale, loads acting on a nanobeam and its material properties are likely to be not known precisely, i.e., uncertain. In the present paper, the deflection of a nanobeam subject to load and material uncertainties is studied by convex modeling of the uncertainties. The level of uncertainty is taken to be bounded and the maximum deflection corresponding to the worst-case of loading or material properties is obtained, that is, the uncertainties are determined so as to maximize the deflection. The sensitivity of the deflection to the uncertainty in the material properties is also investigated. Numerical results are given relating the level of uncertainty to maximum deflection.

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An explicit solution for bending of nanowires lying on Winkler–Pasternak elastic substrate medium based on the Euler–Bernoulli beam theory

Cited by 43 publications

References 47 publications

Natural Frequency and Buckling of Orthotropic Nanoplates Resting on Two-Parameter Elastic Foundations with Various Boundary Conditions

Natural Frequency and Buckling of Orthotropic Nanoplates Resting on Two-Parameter Elastic Foundations with Various Boundary Conditions

Instability Characteristics of Free-Standing Nanowires Based on the Strain Gradient Theory with the Consideration of Casimir Attraction and Surface Effects

Static and Sensitivity Analysis of Nonlocal Nanobeams Subject to Load and Material Uncertainties by Convex Modeling

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