Thin plate theory including surface effects

Lü, Peng; He, Linghui; Lee, H.P.; Lu, C.

doi:10.1016/j.ijsolstr.2005.07.036

Cited by 376 publications

(137 citation statements)

References 20 publications

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“…where s The existence of the surface stresses of the PNP induces traction jumps exerted on the bulk of the plate, which has been commonly adopted in the surface elasticity model and surface piezoelectric model for nanostructures with a variety of configurations (Huang & Yu 2006;Lu et al 2006;Wang & Feng 2007He & Lilley 2008a,b;Yan & Jiang 2011a,b,c;Li et al 2011). According to the generalized Young-Laplace equations (Chen et al 2006b), these traction jumps T x , T y and T z with the consideration of plate deformation can be expressed as …”

Section: Formulationmentioning

confidence: 99%

“…The results in these studies suggest that accounting for axial strain relaxation may be necessary to improve the accuracy and predictive capability of analytical surface elastic theories. However, this surface-stress-induced relaxation phenomenon has not been accounted for in previous investigations of nanoplates with surface effects (Lim & He 2004;Lu et al 2006;, owing to their particular prescribed in-plane boundary conditions. Therefore, different in-plane constraints will be defined in this work in order to catch all the possible phenomena induced by the surface effects.…”

Section: Introductionmentioning

confidence: 99%

“…For example, Lim & He (2004) investigated surface effects on the large deflection of an ultra-thin film using von Karman plate theory. Lu et al (2006) used modified Kirchoff and Mindlin plate models to characterize the bending, vibration and buckling behaviour of nanoscale plates with surface effects. The transverse vibration of a rectangular nanoplate was investigated by , considering the influence of surface properties and temperature.…”

Section: Introductionmentioning

confidence: 99%

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Vibration and buckling analysis of a piezoelectric nanoplate considering surface effects and in-plane constraints

2012

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This work investigates the surface effects on the vibration and buckling behaviour of a simply supported piezoelectric nanoplate (PNP) by using a modified Kirchhoff plate model. Two kinds of in-plane constraints are defined for the PNP, and the surface effects are accounted in the modified plate theory through the surface piezoelectricity model and the generalized Young-Laplace equations. Simulation results show that the influence of surface effects on the plate resonant frequency depends on the in-plane constraints significantly. For the PNP with different in-plane constraints, the effects of the applied electric potential, the mode number, the plate aspect ratio and the plate thickness on the resonant frequency are examined with consideration of the surface effects. The possible mechanical buckling of the PNP is also studied, and it is found that the surface effects on the critical electric voltage for buckling are sensitive to the plate thickness and aspect ratio. Our results also reveal that there exists a critical transition point at which the combined surface effects on the critical electric voltage may vanish under certain conditions.

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Section: Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Vibration and buckling analysis of a piezoelectric nanoplate considering surface effects and in-plane constraints

2012

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“…However, the equilibrium will not be satisfied with this assumption, if the surface stress is considered. In this case, the stress component zz σ is expressed as follows [50]:…”

Section: Effect Of Surface Stressesmentioning

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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“…This is because the free surface plays a vital role for nano-sized structures, where the mechanical properties deviate significantly from their bulk forms because of high surface-to-volume ratios [35,36]. To date, extensive numerical simulations [37,38] and theoretical modeling [39][40][41] It should be noted that the Voronoi tessellation is a good approximation for the system with all periodic boundary conditions on three directions but overestimates the atomic volume on the top surface layer due to limited coordinate neighbors. Therefore in this case, we use the atomic volume estimated from the second layer as the approximation of the atomic volume in the first layer, i.e., the atomic volume and local volume of the first two layers are assumed to be the same.…”

Section: Simulationsmentioning

confidence: 99%

Fast evaluation of local elastic constants and its application to nanosized structures

2015

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We derive a method to determine the effective local elasticity tensor by combining the local stress, local strain, and global strain in conjunction with a linear least square solver. This method reduces to the standard stress-strain fluctuation method for the estimation of global moduli if the local stress and the local strain are substituted by global counterparts. The quality of the developed method is verified by the analysis of an FCC Lennard-Jones single crystal. By using this method, surface elastic behaviors of three nano-plates are investigated. Simulation results prove that both softening and stiffening effects could be detected, depending on the surface orientations and loading directions. This novel approach could be especially valuable for complicated morphologies where the physical properties of the local material are challenging or impractical to obtain.

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Thin plate theory including surface effects

Cited by 376 publications

References 20 publications

Vibration and buckling analysis of a piezoelectric nanoplate considering surface effects and in-plane constraints

Vibration and buckling analysis of a piezoelectric nanoplate considering surface effects and in-plane constraints

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

Fast evaluation of local elastic constants and its application to nanosized structures

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