Multi-objective optimization of functionally graded materials, thickness and aspect ratio in micro-beams embedded in an elastic medium

Taati, Ehsan; Sina, Nima

doi:10.1007/s00158-017-1895-x

Cited by 13 publications

(7 citation statements)

References 35 publications

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“…By substituting Eqs. (15), (18) and (19) into Eq. (14) and performing integration by parts the following weak form is derived…”

Section: Euler-bernoulli Beam Theory Based On Nonlocal Elasticitymentioning

confidence: 99%

“…In fact, Eringen's theory assumes that the stress of a specific point in a continuum body is related to the strains at all points of that continuum, not only those near the considered point. In the recent years, many studies have analysed the vibrations and buckling of intact nanostructures on the basis of nonlocal elasticity [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]; since the list of these investigations is very long, only some of the latest studies are mentioned here. Also, in the field of electro-mechanical structures, Zhu et al, investigated the influence of the surface energy on the vibration [24] and buckling [25] behaviour of piezoelectric nano-shells.…”

Section: Introductionmentioning

confidence: 99%

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Thermal vibration analysis of cracked nanobeams embedded in an elastic matrix using finite element analysis

Aria

Friswell

Rabczuk

2019

Composite Structures

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“…By substituting Eqs. (15), (18) and (19) into Eq. (14) and performing integration by parts the following weak form is derived…”

Section: Euler-bernoulli Beam Theory Based On Nonlocal Elasticitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Thermal vibration analysis of cracked nanobeams embedded in an elastic matrix using finite element analysis

Aria

Friswell

Rabczuk

2019

Composite Structures

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“…Consequently, manufacturing technologies were extended to make functionally graded (FG) layers in micron and submicron dimensions with the desired electrical and mechanical properties at their bottom and top sides. Therefore, many researchers have focused on the thermal [38][39][40] and mechanical [41][42][43][44] behavior of FG micro-and nanostructures. With the rapid advancement of manufacturing technology, CNTs are used as the favorite reinforcements for polymer nanolayers utilized in different engineering applications.…”

Section: Carbon Nanotubes Reinforced Compositesmentioning

confidence: 99%

Bending, buckling and free vibration of nonlocal FG-carbon nanotube-reinforced composite nanobeams: exact solutions

2019

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This paper investigates the bending, buckling and free vibration behaviors of functionally graded carbon nanotubereinforced composite (FG-CNTRC) nanobeams by considering small-scale effect. The governing equations of motion of a Timoshenko beam under a general loading are derived utilizing the nonlocal elasticity theory. The equations governing bending and stretching behavior of CNTRC nanobeams are uncoupled to a fifth-order ordinary differential equation with respect to the rotation of cross-section for the static cases of bending and buckling. This uncoupling makes it possible to develop exact solutions for transverse deflection and buckling load of CNTRC nanobeams. Using differential operator method, the decoupled sixth-order differential equations in terms of the kinematic variables are obtained for vibration analysis. By setting the coefficients matrix in the corresponding system of homogenous algebraic equations to zero, an algebraic frequency equation is derived. Finally, based on the presented closed-form solutions, parametric studies are carried out to assess the effects of CNT distribution, nonlocal parameter and type of boundary conditions on the deflection, buckling and natural frequency of CNTRC nanobeams. Findings show that nonlocal effect on the mechanical behavior of nanobeams is strongly dependent on boundary conditions and loadings. It is seen that cantilever nanobeams become harder by taking into account nonlocal effect, contrary to clamped and simply supported nanobeams. In addition, the influence of CNT distribution on the mechanical behavior of cantilever beams is more significant than that of simply supported and clamped beams.

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“…Such long range interactions occur between charged atoms or molecules in a solid. Recently, many works have been focused on mechanical analysis of micro‐and nanostructures namely: static, vibration, bucking and postbuckling, dynamic and thermomechanical behavior based on the non‐classical continuum theories.…”

Section: Introductionmentioning

confidence: 99%

“…Such long range interactions occur between charged atoms or molecules in a solid. Recently, many works have been focused on mechanical analysis of micro-and nanostructures namely: static, [5][6][7][8][9] vibration, [10][11][12][13][14][15] bucking and postbuckling, [16][17][18][19] dynamic [20][21][22][23][24][25] and thermomechanical [26][27][28][29] behavior based on the non-classical continuum theories.On the other hand, in the proximity between material objects which are in order of a few microns down to nanometers e.g., electrodes in NEMS, a regime is governed in which intermolecular forces such as the van der Waals and Casimir forces become operative. [30][31][32] In such devices, the nanoscale surface forces are able to overcome elastic restoring reactions in the electrodes and consequently lead to the sheets' sticking during the fabrication process.…”

mentioning

confidence: 99%

On dynamic pull‐in instability of electrostatically actuated multilayer nanoresonators: A semi‐analytical solution

Taati

2019

Z Angew Math Mech

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Based on the nonlocal Euler–Bernoulli beam theory, a theoretical approach is developed to investigate the effects of small scale and intermolecular force on the dynamic pull‐in behavior of electrostatically actuated nanoresonators. To this purpose, nanoresonators are modeled as multilayer beams with rectangular cross‐sections and fixed‐fixed and fixed‐free end conditions which are embedded in an elastic medium containing Winkler and Pasternak elastic foundations. Also, the effects of nonlocal parameter, fringing field due to the finite width of beams, Casimir or van der Waals intermolecular forces, nonlinear term induced by mid‐plane stretching and Winkler and Pasternak elastic foundations are considered in the mathematical modeling of pull‐in behavior. Finally, a hybrid semi‐analytical method is proposed to solve the nonlinear partial differential equation in two steps using the separation of variable technique. First, the Galerkin method is used to reduce a nonlinear ordinary differential equation with respect to time variable. Next, the parameter expansion method is applied to solve ensuing equation and obtain the time history response of transverse deflection. As case studies, the numerical results including curves of voltage‐normalized frequency, time history of normalized maximum deflection and phase portrait of two six‐layer cantilever and fully fixed beams are presented and discussed in detail. Findings indicate that the effect of small scale on the pull‐in voltages is more significant for both boundary conditions, in comparison with the intermolecular force. Also, it is seen that the pull‐in voltages of cantilever beams become larger by considering the nonlocal effect, contrary to the case of fully fixed beams.

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Multi-objective optimization of functionally graded materials, thickness and aspect ratio in micro-beams embedded in an elastic medium

Cited by 13 publications

References 35 publications

Thermal vibration analysis of cracked nanobeams embedded in an elastic matrix using finite element analysis

Thermal vibration analysis of cracked nanobeams embedded in an elastic matrix using finite element analysis

Bending, buckling and free vibration of nonlocal FG-carbon nanotube-reinforced composite nanobeams: exact solutions

On dynamic pull‐in instability of electrostatically actuated multilayer nanoresonators: A semi‐analytical solution

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