Developing a Novel Finite Elastic Approach in Strain Gradient Theory for Microstructures

Farahmand, Hamed; Arabnejad, Saeid

doi:10.1615/intjmultcompeng.v8.i4.70

Cited by 13 publications

(7 citation statements)

References 13 publications

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“…The other higher-order elasticity models reveal that magnitude of the length scale parameter is of the same order as diameter of the basic building block in a microstructure, e.g., the grain in metals or ceramics, the osteon in bones or the cell in foams [28].…”

Section: Strain Gradient Elasticity Theorymentioning

confidence: 99%

“…The aforementioned higher-order theories of elasticity can be found in the works of Tiersten and Bleustein [21], Vardoulakis and Sulem [22] and Lakes [23], Papargyri-Beskou and Beskos [24] and Farahmand et al [25][26][27]. Imposing the SG term with length scale parameter in conventional elasticity as a constraint was first discussed by Farahmand and Arabnejad [28]. Lazopoulos [29] studied the bending analysis of thin plates due to the Kirchhoff plate theory and SGT.…”

Section: Introductionmentioning

confidence: 99%

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Analytical solutions of bending and free vibration of moderately thick micro-plate via two-variable strain gradient theory

Farahmand

2020

J Braz. Soc. Mech. Sci. Eng.

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In this paper, the strain gradient theory (SGT) and two-variable refined plate theory are implemented simultaneously to analyze bending and free vibration of micro-plate. The proposed theory is called two-variable strain gradient theory (TV-SGT). The TV-SGT, which can be used for both thin and moderately thick micro-plates, predicts parabolic variation of transverse shear stresses across the plate thickness and does not need the shear correction factor. The governing equations are obtained using a variational approach and solved analytically to find the deflection of simply supported micro-plate under uniformly distributed loading and natural frequency of this plate. Thereby, the effects of length scale parameters and dimensions on the bending deflection and natural frequency of the micro-plate are investigated. Results show that, strengthen micro-plate has higher shear rigidity. Moreover, it is inferred that TV-SGT is well defined to analyze the micro-plate.

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Section: Strain Gradient Elasticity Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analytical solutions of bending and free vibration of moderately thick micro-plate via two-variable strain gradient theory

Farahmand

2020

J Braz. Soc. Mech. Sci. Eng.

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“…Imposing the strain gradient term with length scale parameter in conventional elasticity as a constraint was discussed by Aifantis (1999) and Farahmand and Arabnejad (2010). Comparison of experimental results from torsion and bending tests of beams with the theoretical ones obtained from the study and other higher-order elasticity models reveal that magnitude of the gradient coefficient g (internal length) is of the same order as the diameter of the basic building block in a microstructure, e.g.…”

Section: Strain Gradient Rlsticity Theorymentioning

confidence: 99%

Navier Solution for Buckling Analysis of Size-Dependent Functionally Graded Micro-Plates

Farahmand

Naseralavi

Iranmanesh

et al. 2016

Lat. Am. j. solids struct.

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In the present paper, buckling analysis of functionally graded rectangular micro-plates, on the basis of strain gradient theory with one length scale parameter is studied. Considering the Kirchhoff plate theory and the principle of minimum total potential energy, governing equations of micro-plate subjected to in-plane loads are extracted. In accordance with functionally graded distribution of material properties through the thickness, higher order governing equation of sixth order is derived. Consequently, the stability equation is solved analytically for simply supported micro-plates and the effects of material properties, micro-structure parameters, dimensions and loading conditions are expounded on the critical buckling load. Developing the strain gradient theory for buckling analysis of micro-plates made of functionally graded material is a significant novelty of the presented study.

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“…The Gibbs equation (18), the expression for entropy production (19), and Eq. (20) serve as a basis for the formulation of constitutive relations of the model of local-gradient thermoelasticity.…”

Section: Balance Equationsmentioning

confidence: 99%

Relations of gradient thermomechanics taking into account the irreversibility and inertia of local mass displacement

Kondrat¹,

Hrytsyna²

2012

J Math Sci

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We have obtained the complete set of relations of the gradient-type nonlocal theory that describes the processes of heat conduction, deformation, and local mass displacement with regard for its inertia and irreversibility. In this case, the constitutive relation for the vector of local mass displacement, referred to density, is rheological. The equation for potential ′ μ π , characterizing the effect of local mass displacement on the internal energy of the body, has a dynamic character due to the presence of terms with the first-and second-order time derivatives of potential ′ μ π , the spherical component of strain tensor, and temperature.

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Developing a Novel Finite Elastic Approach in Strain Gradient Theory for Microstructures

Cited by 13 publications

References 13 publications

Analytical solutions of bending and free vibration of moderately thick micro-plate via two-variable strain gradient theory

Analytical solutions of bending and free vibration of moderately thick micro-plate via two-variable strain gradient theory

Navier Solution for Buckling Analysis of Size-Dependent Functionally Graded Micro-Plates

Relations of gradient thermomechanics taking into account the irreversibility and inertia of local mass displacement

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