Finite element analysis of vibrating micro-beams and -plates using a three-dimensional micropolar element

Ansari, R.; Norouzzadeh, A.; Shakouri, Amir; Bazdid-Vahdati, M.; Rouhi, H.

doi:10.1016/j.tws.2017.12.036

Cited by 39 publications

(17 citation statements)

References 57 publications

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“…To derive the governing equations using equation (6), variations of different forms of energies as presented previously are to be considered. The derivations of the variational forms of various strain energies and potential energy in connection with equation 6are straightforward as they contain derivatives with respect to space coordinates only and hence are not mentioned here.…”

Section: Governing Equationsmentioning

confidence: 99%

“…Based on modified couple stress theory and von Ka´rma´n geometric non-linearity, Ke et al 5 studied the non-linear free vibration of FGM microbeams. Employing the micropolar theory, Ansari et al 6 reported the free vibration behavior of microscale beams and plates considering a three dimensional formulation. Based on Timoshenko beam theory (TBT) and Gurtin-Murdoch continuum elasticity, Ansari et al 7 presented the vibration and instability characteristics of fluid-conveying nanoscale pipes.…”

Section: Introductionmentioning

confidence: 99%

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Non-linear forced vibration analysis of higher-order shear-deformable functionally graded material beam in thermal environment subjected to harmonic excitation and resting on non-linear elastic foundation

Paul¹,

Das

2018

The Journal of Strain Analysis for Engineering Design

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Geometrically non-linear forced vibration analysis of higher-order shear-deformable functionally graded material beam under harmonic excitation and supported on three-parameter non-linear elastic foundation is presented. The beam is immovably clamped and is considered to be under static thermal loading due to uniform temperature rise. Reddy's third-order shear-deformable beam theory in conjunction with von Kármán geometric non-linearity is considered to derive the governing equations employing Hamilton's principle, and Ritz method is followed for approximating the displacement and rotation fields. A numerical algorithm based on iterative substitution method and Broyden's method is proposed to predict the stable regions of frequency-response behavior. The frequency-response curves are presented in normalized plane for variations of load-amplitude, elastic foundation parameters, temperature rise, gradation index and functionally graded material composition, and their effects are discussed in detail. It is found that the load-amplitude, elastic foundation parameters, thermal loading and some of the functionally graded material compositions significantly affect the frequency response; whereas, the effect of gradation index is found to be relatively small. A comparative frequency-response curve between Voigt model and Mori-Tanaka scheme of functionally graded material modeling is presented, and it shows negligible difference between these two models. The present problem under thermal environment is studied for the first time through this work, and the proposed model and the numerical algorithm provide a simplified approach to study the non-linear frequency-response behavior.

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Section: Governing Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Non-linear forced vibration analysis of higher-order shear-deformable functionally graded material beam in thermal environment subjected to harmonic excitation and resting on non-linear elastic foundation

Paul¹,

Das

2018

The Journal of Strain Analysis for Engineering Design

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“…Godio et al (2015) proposed a displacement-based finite element model for micropolar plates, Ansari et al (2017) proposed a nonlinear finite element model for micropolar plates where the nonlinear micropolar strains were considered. Ansari et al (2018) used 3-D micropolar elements to study the vibrations of micro-beams and micro-plates. To the authors' knowledge there has not been a geometric nonlinear finite element formulation for micropolar plates which have been enriched with von Kármán nonlinearity to account for moderate macrorotations in a relatively simple way.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear finite element analysis of lattice core sandwich plates

Nampally¹,

Karttunen²,

Reddy³

2020

International Journal of Non-Linear Mechanics

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A displacement-based, geometrically nonlinear finite element model is developed for lattice core sandwich panels modeled as 2-D equivalent single-layer (ESL), first-order shear deformation theory (FSDT) micropolar plates. The nonlinearity is due to the moderate macrorotations of the plate which are modeled by including the von Kármán strains in the micropolar strain measures. Weak form Galerkin method with linear Lagrange interpolations is used to develop the displacementbased finite element model. Selective reduced integration is used to eliminate shear locking and membrane locking. The novel finite element model is used to study the nonlinear bending and linear free vibrations of web-core and pyramid core sandwich panels. Clamped and free edge boundary conditions are considered for the first time for the 2-D micropolar ESL-FSDT plate theory. The present 2-D finite element results are in good agreement with the corresponding detailed 3-D FE results for the lattice core sandwich panels. The 2-D element provides computationally costeffective solutions; in a nonlinear bending example, the number of elements required for the 2-D micropolar plate is of the order 10 3 , whereas for the corresponding 3-D model the order is 10 5 .

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“…With the revived interest in micropolar elasticity (Eringen and Suhubi, 1964), considerable work has been put into developing appropriate finite element models for micropolar continua in general; see, for example, (Li and Xie, 2004;Pothier and Rencis, 1994;Roman and Steinberg, 2013;Zhou and Cusatis, 2015). To list a few recent finite element models for micropolar plates we mention the works of Ansari et al (2018Ansari et al ( , 2016 and Godio et al (2014). Various finite element models have been proposed for the bending analysis of micropolar beams as well.…”

Section: Introductionmentioning

confidence: 99%

“…Regueiro and Duan (2015) derived a finite element model for a micropolar Timoshenko beam with the microrotation assumed to be equal to the cross-sectional rotation. More recently, Karttunen et al (2018a) proposed nodally-exact 1-D finite element to analyze micropolar Timoshenko beams and Ansari et al (2018) proposed a 27-node 3-D finite element for the analysis of beams. Only linear strains were considered in developing the finite element models in all the above mentioned papers.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear finite element analysis of lattice core sandwich beams

Nampally

Karttunen

Reddy

2019

European Journal of Mechanics - A/Solids

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A geometrically nonlinear finite element model is developed for the bending analysis of micropolar Timoshenko beams using the principle of virtual displacements and linear Lagrange interpolation functions. The nonlinearity enters the model via a nonlinear von Kármán strain term that allows the micropolar beam to undergo moderate rotations. The nonlinear micropolar Timoshenko beam is used as an equivalent single layer model to study four different lattice core sandwich beams. A two-scale energy method is used to derive the micropolar constitutive equations for web, hexagonal, Y-frame and corrugated core topologies. Various bending cases are studied numerically using the developed 1-D finite element model. Reduced integration techniques are used to overcome the shear and membrane locking. The present 1-D results are in good agreement with the corresponding 2-D finite element beam frame results for global bending.

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Finite element analysis of vibrating micro-beams and -plates using a three-dimensional micropolar element

Cited by 39 publications

References 57 publications

Non-linear forced vibration analysis of higher-order shear-deformable functionally graded material beam in thermal environment subjected to harmonic excitation and resting on non-linear elastic foundation

Non-linear forced vibration analysis of higher-order shear-deformable functionally graded material beam in thermal environment subjected to harmonic excitation and resting on non-linear elastic foundation

Nonlinear finite element analysis of lattice core sandwich plates

Nonlinear finite element analysis of lattice core sandwich beams

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