Eigenfrequencies of microtubules embedded in the cytoplasm by means of the nonlocal integral elasticity

Eptaimeros, K.G.; Koutsoumaris, C. Chr.; Karyofyllis, I. G.

doi:10.1007/s00707-019-02605-6

Cited by 9 publications

(2 citation statements)

References 68 publications

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“…The boundary effects were first compensated for in the framework of nonlocal damage [54,55], and then were re-discovered for nonlocal elasticity [56,57] by introducing a modified kernel, which satisfies the normalization condition. However, in the analysis of nanostructures, the compensation of the boundary effects is usually neglected and the mentioned modified kernel has been rarely implemented [58,59]. It is noteworthy that a few models capable of preserving corresponding uniform stress/strain field, such as the strain difference based [57,60] and stress-driven [61,62] nonlocal elasticity models, were also introduced.…”

Section: Introductionmentioning

confidence: 99%

“…Vibration analysis of carbon nanotube mass nanosensors resting on a nonlocal elastic foundation was performed through a nonlocal integral FE model [78]. Frequency response of a microtubule embedded in the cytoplasm of a cell was studied by an equivalent counterpart beam on the Pasternak elastic foundation through nonlocal integral elasticity [59]. An exact solution procedure and a sheer locking free FE formulation for the vibration of TP local/nonlocal integral nanobeams were proposed, and results of the exact and numerical solutions were compared [79].…”

Section: Introductionmentioning

confidence: 99%

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Free vibration analysis of nonlocal nanobeams: a comparison of the one-dimensional nonlocal integral Timoshenko beam theory with the two-dimensional nonlocal integral elasticity theory

Danesh

Javanbakht

2021

Mathematics and Mechanics of Solids

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Beam theories such as the Timoshenko beam theory are in agreement with the elasticity theory. However, due to the different nonlocal averaging processes, they are expected to yield different results in their nonlocal forms. In the present work, the free vibration behavior of nonlocal nanobeams is studied using the nonlocal integral Timoshenko beam theory (NITBT) and two-dimensional nonlocal integral elasticity theory (2D-NIET) with different kernels and their results are compared. A new kernel, termed the compensated two-phase (CTP) kernel, is introduced, which entirely compensates for the boundary effects and does not suffer from the ill-posedness of previous kernels. Using the finite element method, the free vibration analysis is performed for different boundary conditions based on the first three natural frequencies. For both the NITBT and 2D-NIET with both the two-phase (TP) and CTP kernels, the nonlocal parameter has a softening effect on the natural frequencies for all the boundary conditions, without observing the paradoxical behaviors of the nonlocal differential theory. For both theories, the softening effect of the nonlocal parameter is more pronounced for the TP kernel compared to the CTP kernel. The sensitivity of the 2D-NIET to the nonlocal parameter is found to be higher than that of the NITBT. Also, the softening effects for different vibration modes are compared to each other for both theories and both kernels. The obtained results can be extended for various important beam problems with nonlocal effects and help obtain a better understanding of applicable nonlocal theories.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of nonlocal nanobeams: a comparison of the one-dimensional nonlocal integral Timoshenko beam theory with the two-dimensional nonlocal integral elasticity theory

Danesh

Javanbakht

2021

Mathematics and Mechanics of Solids

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Discontinuous Galerkin FEMs for a gradient beam in static carbon nanotube applications

Eptaimeros

Koutsoumaris

2021

Math Methods in App Sciences

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The engineering applications of the innovative materials, such as carbon nanotubes (CNTs) and graphene sheets, constitute a developing branch of the modern science. CNTs, in particular, exhibit extraordinarily mechanical properties capable of making them a reliable material for the above applications. The simulation of the mechanical response of a CNT is effectively conducted by a generalized beam model. This work investigates the response of a CNT, subjected to a static loading, by means of a gradient beam model. Given that the existence of a boundary layer is demonstrated by the analytical solutions of the aforementioned problem, the interior penalty discontinuous Galerkin finite element methods (IPDGFEMs) are crucial to its solution. The hp‐version IPDGFEMs are developed in this study for the solution of a static gradient elastic beam in bending, derived from two different equilibrium formulations, for the first time. An a priori error analysis is also performed for the above method, and numerical simulations are then carried out. A comparison is finally drawn between the exact deflection and those of the IPDGFEM and the conforming C2‐continuous finite element method (C2CFEM) for a number of discretizations and each length scale that is investigated. The deduced results highlight the suitability, the efficiency, and the accuracy of the investigated models over the already existing ones, and they have considerable significance for the engineering design in the range of micro and nanodimensions.

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Eringen’s Nonlocal Integral Elasticity and Applications for Structural Models

Koutsoumaris

Eptaimeros²

2021

Springer Tracts in Mechanical Engineering

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Eigenfrequencies of microtubules embedded in the cytoplasm by means of the nonlocal integral elasticity

Cited by 9 publications

References 68 publications

Free vibration analysis of nonlocal nanobeams: a comparison of the one-dimensional nonlocal integral Timoshenko beam theory with the two-dimensional nonlocal integral elasticity theory

Free vibration analysis of nonlocal nanobeams: a comparison of the one-dimensional nonlocal integral Timoshenko beam theory with the two-dimensional nonlocal integral elasticity theory

Discontinuous Galerkin FEMs for a gradient beam in static carbon nanotube applications

Eringen’s Nonlocal Integral Elasticity and Applications for Structural Models

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