Bending analysis of microtubules using nonlocal Euler–Bernoulli beam theory

doi:10.1016/J.APM.2010.11.004

Home
/
Papers
/
Bending analysis of microtubules using nonlocal Euler–Bernoulli beam theory

Journal Article•DOI•

Bending analysis of microtubules using nonlocal Euler–Bernoulli beam theory

Ömer Civalek¹, Çiğdem Demir¹•Institutions (1)

Akdeniz University¹

01 May 2011-Applied Mathematical Modelling (Elsevier)-Vol. 35, Iss: 5, pp 2053-2067

TL;DR: In this paper, an elastic beam model using nonlocal elasticity theory is developed for the bending analysis of microtubules (MTs) based on the Euler-Bernoulli beam theory.

read less

About: This article is published in Applied Mathematical Modelling.The article was published on 2011-05-01 and is currently open access. It has received 313 citations till now. The article focuses on the topics: Euler–Bernoulli beam theory & Bending stiffness.

...read moreread less

Citations

PDF

Open Access

More filters

Journal Article•DOI•

A nonlocal beam theory for bending, buckling, and vibration of nanobeams

[...]

Huu-Tai Thai¹•Institutions (1)

Hanyang University¹

01 Mar 2012-International Journal of Engineering Science

TL;DR: In this paper, a nonlocal shear deformation beam theory is proposed for bending, buckling, and vibration of nanobeams using the nonlocal differential constitutive relations of Eringen.

...read moreread less

459 citations

Journal Article•DOI•

Free vibration analysis of functionally graded size-dependent nanobeams

[...]

Mohamed A. Eltaher¹, Samir A. Emam¹, F.F. Mahmoud¹•Institutions (1)

Zagazig University¹

15 Mar 2012-Applied Mathematics and Computation

TL;DR: Free vibration analysis of functionally graded (FG) size-dependent nanobeam using finite element method to show the significance of the material distribution profile, nonlocal effect, and boundary conditions on the dynamic characteristics of nanobeams.

...read moreread less

322 citations

Journal Article•DOI•

Nonlinear vibration of the piezoelectric nanobeams based on the nonlocal theory

[...]

Liao-Liang Ke¹, Yue-Sheng Wang¹, Zheng-Dao Wang¹•Institutions (1)

Beijing Jiaotong University¹

01 May 2012-Composite Structures

TL;DR: In this article, the nonlinear vibration of the piezoelectric nanobeams based on the nonlocal theory and Timoshenko beam theory was investigated, and a detailed parametric study was conducted to study the influences of the non-local parameter, temperature change and external electric voltage on the size-dependent non-linear vibration characteristics of the PNE.

...read moreread less

307 citations

Journal Article•DOI•

A review of continuum mechanics models for size-dependent analysis of beams and plates

[...]

Huu-Tai Thai¹, Huu-Tai Thai², Thuc P. Vo³, Thuc P. Vo⁴, Trung-Kien Nguyen⁵, Seung-Eock Kim⁶ - Show less +2 more•Institutions (6)

La Trobe University¹, Ton Duc Thang University², Northumbria University³, Duy Tan University⁴, Ho Chi Minh City University of Technology⁵, Sejong University⁶

01 Oct 2017-Composite Structures

TL;DR: In this paper, a comprehensive review on the development of higher-order continuum models for capturing size effects in small-scale structures is presented, mainly focusing on the size-dependent beam, plate and shell models developed based on the nonlocal elasticity theory, modified couple stress theory and strain gradient theory.

...read moreread less

275 citations

Journal Article•DOI•

A review on nonlocal elastic models for bending, buckling, vibrations, and wave propagation of nanoscale beams

[...]

Mohamed A. Eltaher¹, M E Khater², Samir A. Emam³•Institutions (3)

Zagazig University¹, University of Waterloo², United Arab Emirates University³

01 Mar 2016-Applied Mathematical Modelling

TL;DR: In this paper, a review aimed at directing the light to research work concerned with bending, buckling, vibrations, and wave propagation of nanobeams modeled according to the nonlocal elasticity theory of Eringen.

...read moreread less

272 citations

1
2
3
4
…
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63

Collapse

References

PDF

Open Access

More filters

Journal Article•DOI•

On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves

[...]

A. Cemal Eringen

01 Sep 1983-Journal of Applied Physics

TL;DR: In this article, the integropartial differential equations of the linear theory of nonlocal elasticity are reduced to singular partial differential equations for a special class of physically admissible kernels.

...read moreread less

Abstract: Integropartial differential equations of the linear theory of nonlocal elasticity are reduced to singular partial differential equations for a special class of physically admissible kernels. Solutions are obtained for the screw dislocation and surface waves. Experimental observations and atomic lattice dynamics appear to support the theoretical results very nicely.

...read moreread less

3,929 citations

"Bending analysis of microtubules us..." refers background or methods in this paper

...As stated by Eringen [20], the linear theory of nonlocal elasticity leads to a set of integropartial differential equations for the displacement fields of homogeneous, isotropic bodies....
[...]
...In order to take into consideration the small size scale effect during the modeling and analysis stage, the theory of nonlocal elasticity proposed by Eringen [20] is used to modify the theory for vibration and buckling analyses of micro and nano scale beam devices....
[...]
...The nonlocal theory of elasticity proposed by Eringen [20] has been widely used in the past five years in many nano mechanical problems including dislocation, crack, wave propagation, vibration analysis of nanobeams, nanotubes, carbon nanotubes, and microtubules....
[...]

Book•

Mechanics of Motor Proteins and the Cytoskeleton

[...]

Jonathon Howard¹, RL Clark²•Institutions (2)

University of Washington¹, Duke University²

01 Feb 2001

TL;DR: The Motility Models: From Crossbridges to Motion chapter describes the building blocks of the Cytoskeleton and some of the mechanisms used in its manufacture are described.

...read moreread less

Abstract: Preface - Introduction - PART I: PHYSICAL PRINCIPLES - Mechanical Forces - Mass, Stiffness, and Damping of Proteins - Thermal Forces and Diffusion - Chemical Forces - Polymer Mechanics - PART II: CYTOSKELETON - Structures of Cytoskeletal Filaments - Mechanics of the Cytoskeleton - Polymerization of Cytoskeletal Filaments - Force Generation by Cytoskeletal Filaments - Active Polymerization - PART III: MOTOR PROTEINS - Structures of Motor Proteins - Speeds of Motors - ATP Hydrolysis - Steps and Forces - Motility Models: From Crossbridges to Motion - Afterword - Appendix - Bibliography - Index

...read moreread less

2,789 citations

"Bending analysis of microtubules us..." refers background in this paper

...Recently, much attention has been devoted to the mechanical behavior of micro/nano structures such as nanobeams, nanorods, nanotubes andmicrotubules [6–19]....
[...]

Journal Article•DOI•

Nonlocal theories for bending, buckling and vibration of beams

[...]

J. N. Reddy¹, J. N. Reddy²•Institutions (2)

Texas A&M University¹, National University of Singapore²

01 Feb 2007-International Journal of Engineering Science

TL;DR: In this article, the Euler-Bernoulli, Timoshenko, Reddy, and Levinson beam theories are reformulated using the nonlocal differential constitutive relations of Eringen.

...read moreread less

1,519 citations

Journal Article•DOI•

Application of generalized differential quadrature to solve two-dimensional incompressible navier-stokes equations

[...]

Chang Shu¹, Bryan E. Richards¹•Institutions (1)

University of Glasgow¹

15 Oct 1992-International Journal for Numerical Methods in Fluids

TL;DR: In this paper, a global method of generalised differential quadrature is applied to solve the two-dimensional incompressible Navier-Stokes equations in the vorticity-stream-function formulation.

...read moreread less

Abstract: A global method of generalised differential quadrature is applied to solve the two-dimensional incompressible Navier-Stokes equations in the vorticity-stream-function formulation. Numerical results for the flow past a circular cylinder were obtained using just a few grid points. A good agreement is found with the experimental data.

...read moreread less

807 citations

"Bending analysis of microtubules us..." refers methods in this paper

...Differential quadrature (DQ) method Differential quadrature (DQ) method is a relatively new numerical technique in applied mechanics [37–39]....
[...]

Journal Article•DOI•

Nonlocal continuum theories of beams for the analysis of carbon nanotubes

[...]

J. N. Reddy, Sze Dai Pang

22 Jan 2008-Journal of Applied Physics

TL;DR: The equations of motion of the Euler-Bernoulli and Timoshenko beam theories were reformulated using the nonlocal differential constitutive relations of Eringen [International Journal of Engineering Science 10, 1−16 (1972) as mentioned in this paper.

...read moreread less

Abstract: The equations of motion of the Euler–Bernoulli and Timoshenko beam theories are reformulated using the nonlocal differential constitutive relations of Eringen [International Journal of Engineering Science 10, 1–16 (1972)]. The equations of motion are then used to evaluate the static bending, vibration, and buckling responses of beams with various boundary conditions. Numerical results are presented using the nonlocal theories to bring out the effect of the nonlocal behavior on deflections, buckling loads, and natural frequencies of carbon nanotubes.

...read moreread less

642 citations

"Bending analysis of microtubules us..." refers background or methods or result in this paper

...In the present manuscript we used values proposed by researchers [22,34]....
[...]
...Exact analytical solution is also obtained by the analytical formula given by Reddy and Pang [22] for comparison....
[...]
...VðxÞ 1⁄4 EI L @ wðxÞ @x3 ðe0aÞqA L EI x @wðxÞ @x " # : ð29Þ For a uniformly distributed load, the related equations can be written as [22]...
[...]
...It is also accepted that some mechanical properties such as vibration, bending and buckling of beam like micro structures based on nonlocal elasticity theory are entirely different from their counterparts based on the classical (macro) beam theory [22–36]....
[...]
...Excellent agreement has been achieved between the present results and the results obtained by analytical formula given by Reddy and Pang [22]....
[...]