Simple solution for buckling of orthotropic circular cylindrical shells

Zou, R.D.; Foster, C. G.

doi:10.1016/0263-8231(94)00026-v

Cited by 20 publications

(12 citation statements)

References 5 publications

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“…11 and 12. From these figures, it can be seen that the results of Zou and Table 1 Parameters of equivalent shell model E = 920 GPa G = 375 GPa m = 0.225 h = 0.218 nm Foster (1995) are very close to those of both numerical approaches. When the nanotube is comparatively long, the non-axisymmetric buckling mode happens, and the wavenumber along the axial direction becomes higher.…”

Section: Simple Continuum Theoretical Models For Prediction Of Bucklisupporting

confidence: 81%

“…When the nanotube is comparatively long, the non-axisymmetric buckling mode happens, and the wavenumber along the axial direction becomes higher. Furthermore, when the wavenumber is much higher, i.e., k ) 1, the axisymmetric buckling mode happens and the results of Zou and Foster (1995) tend to be the same with the results of Timoshenko's shell buckling theory. Also, when the nanotube is very short, the wavenumber increases along the circumferential direction, it is identical to that of one-directional bending of thin plate or elemental strip.…”

Section: Simple Continuum Theoretical Models For Prediction Of Bucklisupporting

confidence: 74%

“…When the diameter is from 40 to 50 nm, m and k are very large, the results of Zou and Foster (1995) in Eq. (13) are close to that of Timoshenko's theory.…”

Section: Verifications By Experimental Resultsmentioning

confidence: 97%

“…(12) Cylindrical shell (Zou and Foster,(1995)) n=1 Cylindrical shell (Zou and Foster,(1995) Cylindrical shell (Zou and Foster,(1995)) n=1 Cylindrical shell (Zou and Foster,(1995) regime is that we have compared our results of MSMA with those of MD (Sears and Batra, 2004) for some cases in Figs. 3(b) and 8(b).…”

Section: Simple Continuum Theoretical Models For Prediction Of Bucklimentioning

confidence: 94%

“…These figures illustrate that the results of the present FEM shell model are very close to those of the FEM beam model of the present MSMA at a variety of stages. When the half-wavenumber along the axial direction of shell is taken as n = 2 and n = 1, respectively, the results of Zou and Foster (1995) for various kinds of half-wavenumber along the circumferential direction are shown in Figs. 11 and 12.…”

Section: Simple Continuum Theoretical Models For Prediction Of Bucklimentioning

confidence: 99%

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Prediction of buckling characteristics of carbon nanotubes

Nunoya

Pan

et al. 2007

International Journal of Solids and Structures

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In this paper, to investigate the buckling characteristics of carbon nanotubes, an equivalent beam model is first constructed. The molecular mechanics potentials in a C-C covalent bond are transformed into the form of equivalent strain energy stored in a three dimensional (3D) virtual beam element connecting two carbon atoms. Then, the equivalent stiffness parameters of the beam element can be estimated from the force field constants of the molecular mechanics theory. To evaluate the buckling loads of multi-walled carbon nanotubes, the effects of van-der Waals forces are further modeled using a newly proposed rod element. Then, the buckling characteristics of nanotubes can be easily obtained using a 3D beam and rod model of the traditional finite element method (FEM). The results of this numerical model are in good agreement with some previous results, such as those obtained from molecular dynamics computations. This method, designated as molecular structural mechanics approach, is thus proved to be an efficient means to predict the buckling characteristics of carbon nanotubes. Moreover, in the case of nanotubes with large length/diameter, the validity of Euler's beam buckling theory and a shell model with the proper material properties defined from the results of present 3D FEM beam model is investigated to reduce the computational cost. The results of these simple theoretical models are found to agree well with the existing experimental results.

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Section: Simple Continuum Theoretical Models For Prediction Of Bucklisupporting

confidence: 81%

Section: Simple Continuum Theoretical Models For Prediction Of Bucklisupporting

confidence: 74%

“…When the diameter is from 40 to 50 nm, m and k are very large, the results of Zou and Foster (1995) in Eq. (13) are close to that of Timoshenko's theory.…”

Section: Verifications By Experimental Resultsmentioning

confidence: 97%

Section: Simple Continuum Theoretical Models For Prediction Of Bucklimentioning

confidence: 94%

Section: Simple Continuum Theoretical Models For Prediction Of Bucklimentioning

confidence: 99%

See 3 more Smart Citations

Prediction of buckling characteristics of carbon nanotubes

Nunoya

Pan

et al. 2007

International Journal of Solids and Structures

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Microstructure‐based modeling of primary cilia mechanics

Mostafazadeh,

Resnick,

Young

et al. 2024

Cytoskeleton

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A primary cilium, made of nine microtubule doublets enclosed in a cilium membrane, is a mechanosensing organelle that bends under an external mechanical load and sends an intracellular signal through transmembrane proteins activated by cilium bending. The nine microtubule doublets are the main load‐bearing structural component, while the transmembrane proteins on the cilium membrane are the main sensing component. No distinction was made between these two components in all existing models, where the stress calculated from the structural component (nine microtubule doublets) was used to explain the sensing location, which may be totally misleading. For the first time, we developed a microstructure‐based primary cilium model by considering these two components separately. First, we refined the analytical solution of bending an orthotropic cylindrical shell for individual microtubule, and obtained excellent agreement between finite element simulations and the theoretical predictions of a microtubule bending as a validation of the structural component in the model. Second, by integrating the cilium membrane with nine microtubule doublets and simulating the tip‐anchored optical tweezer experiment on our computational model, we found that the microtubule doublets may twist significantly as the whole cilium bends. Third, besides being cilium‐length‐dependent, we found the mechanical properties of the cilium are also highly deformation‐dependent. More important, we found that the cilium membrane near the base is not under pure in‐plane tension or compression as previously thought, but has significant local bending stress. This challenges the traditional model of cilium mechanosensing, indicating that transmembrane proteins may be activated more by membrane curvature than membrane stretching. Finally, we incorporated imaging data of primary cilia into our microstructure‐based cilium model, and found that comparing to the ideal model with uniform microtubule length, the imaging‐informed model shows the nine microtubule doublets interact more evenly with the cilium membrane, and their contact locations can cause even higher bending curvature in the cilium membrane than near the base.

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Nonlocal orthotropic shell model applied on wave propagation in microtubules

Wang

Gao

2016

Applied Mathematical Modelling

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Simple solution for buckling of orthotropic circular cylindrical shells

Cited by 20 publications

References 5 publications

Prediction of buckling characteristics of carbon nanotubes

Prediction of buckling characteristics of carbon nanotubes

Microstructure‐based modeling of primary cilia mechanics

Nonlocal orthotropic shell model applied on wave propagation in microtubules

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