On functionally graded Timoshenko nonisothermal nanobeams

Čanađija, Marko; Barretta, Raffaele; Sciarra, Francesco Marotti de

doi:10.1016/j.compstruct.2015.09.030

Cited by 53 publications

(22 citation statements)

References 34 publications

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“…The first step again involves separation of the strain into a part that describes dilatation due to free expansion (or contraction) of a beam ε th (x, z) = α∆θ(x, z) and the one caused by the stresses ε el , Eq. (8). In contrast to the earlier works on the nonlocal beam mechanics cited in the Introduction, the present approach is stress-driven.…”

Section: Stress-driven Nonlocal Thermoelasticitymentioning

confidence: 90%

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Stress-driven modeling of nonlocal thermoelastic behavior of nanobeams

Barretta

Čanađija

Sciarra

2018

International Journal of Engineering Science

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128

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A consistent stress-driven nonlocal integral model for nonisothermal structural analysis of elastic nano-and microbeams is proposed. Most nonlocal models of literature are strain-driven and it was shown that such approaches can lead toward a number of difficulties. Following recent contributions within the isothermal setting, the developed model abandons the classical strain-driven methodology in favour of the modern stress-driven elasticity theory by G. Romano and R. Barretta. This effectively circumvents issues associated with strain-driven formulations. The new thermoelastic nonlocal integral model is proven to be equivalent to an adequate set of differential equations, accompanied by higher-order constitutive boundary conditions, when the special Helmholtz averaging kernel is adopted in the convolution.The example section provides several applications, thus enabling insight into performance of the formulation. Exact nonlocal solutions are established,

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Section: Stress-driven Nonlocal Thermoelasticitymentioning

confidence: 90%

“…Although such a claim can be made for the problems involving isothermal deformation processes, when the nonisothermal problems are concerned the results are not so numerous. For a short review of the existing nonisothermal models, see [8] for statical and [36] for dynamical problems.…”

Section: Introductionmentioning

confidence: 99%

Stress-driven modeling of nonlocal thermoelastic behavior of nanobeams

Barretta

Čanađija

Sciarra

2018

International Journal of Engineering Science

Self Cite

128

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“…Those investigations were carried out for bending ( [3][4][5][6][7][8][9]), buckling ( [10][11][12][13][14]) and vibration analyses ( [15][16][17][18][19][20]). The nonlocal elasticity theory was also employed to study the size-dependant behaviours of functional graded nanobeams ( [21][22][23][24][25][26][27][28][29][30][31][32][33][34]). It is well-known that the EBT underestimates deflection and overestimates buckling load and natural frequencies of thick beam due to neglecting the shear deformation effects.…”

Section: Introductionmentioning

confidence: 99%

A simple shear deformation theory for nonlocal beams

Thai

et al. 2018

Composite Structures

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In this paper, a simple beam theory accounting for shear deformation effects with one unknown is proposed for static bending and free vibration analysis of isotropic nanobeams. The sizedependent behaviour is captured by using the nonlocal differential constitutive relations of Eringen. The governing equation of the present beam theory is obtained by using equilibrium equations of elasticity theory. The present theory has strong similarities with nonlocal Euler-Bernoulli beam theory in terms of the governing equation and boundary conditions. Analytical solutions for static bending and free vibration are derived for nonlocal beams with various types of boundary conditions. Verification studies indicate that the present theory is not only more accurate than Euler-Bernoulli beam theory, but also comparable with Timoshenko beam theory.

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“…biosensors, micro-resonators, atomic force microscopes (AFMs) and actuators [1][2][3][4]. MEMS/NEMS may be actuated using several sources of energy such as electrostatic [5], electromagnetic [6], piezoelectric [7] and may be made of metals or polymer, silicon-based structures or functionally graded materials (FGM) [8][9][10][11][12][13]. Electrostatic actuation has demonstrated good energy density and efficiency.…”

Section: Introductionmentioning

confidence: 99%

Static and Dynamic Pull-In Instability of Nano-Beams Resting on Elastic Foundation Based on the Nonlocal Elasticity Theory

Sedighi

Sheikhanzadeh

2017

Chin. J. Mech. Eng.

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This paper provides the static and dynamic pullin behavior of nano-beams resting on the elastic foundation based on the nonlocal theory which is able to capture the size effects for structures in micron and sub-micron scales. For this purpose, the governing equation of motion and the boundary conditions are driven using a variational approach. This formulation includes the influences of fringing field and intermolecular forces such as Casimir and van der Waals forces. The differential quadrature (DQ) method is employed as a high-order approximation to discretize the governing nonlinear differential equation, yielding more accurate results with a considerably smaller number of grid points. In addition, a powerful analytical method called parameter expansion method (PEM) is utilized to compute the dynamic solution and frequency-amplitude relationship. It is illustrated that the first two terms in series expansions are sufficient to produce an acceptable solution of the mentioned structure. Finally, the effects of basic parameters on static and dynamic pull-in instability and natural frequency are studied.

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On functionally graded Timoshenko nonisothermal nanobeams

Cited by 53 publications

References 34 publications

Stress-driven modeling of nonlocal thermoelastic behavior of nanobeams

Stress-driven modeling of nonlocal thermoelastic behavior of nanobeams

A simple shear deformation theory for nonlocal beams

Static and Dynamic Pull-In Instability of Nano-Beams Resting on Elastic Foundation Based on the Nonlocal Elasticity Theory

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