A Finite-Deformation Shell Theory for Carbon Nanotubes Based on the Interatomic Potential—Part II: Instability Analysis

2008 ◽  
Vol 75 (6) ◽  
Author(s):  
J. Wu ◽  
K. C. Hwang ◽  
J. Song ◽  
Y. Huang
Keyword(s):  
Carbon Nanotubes ◽  
Internal Pressure ◽  
Critical Load ◽  
Finite Deformation ◽  
Shell Theory ◽  
Interatomic Potential ◽  
External Pressure ◽  
External Pressures ◽  
Tension And Compression ◽  
Potential Part

Based on the finite-deformation shell theory for carbon nanotubes established from the interatomic potential in Part I of this paper, we have studied the instability of carbon nanotubes subjected to different loadings (tension, compression, internal and external pressures, and torsion). Similar to the conventional shells, carbon nanotubes may undergo bifurcation under compression/torsion/external pressure. Our analysis, however, shows that carbon nanotubes may also undergo bifurcation in tension and internal pressure, though the bifurcation modes for tension and compression are very different, and so are the modes for the internal and external pressures. The critical load for instability and bifurcation depends on the interatomic potential used.

A Finite-Deformation Shell Theory for Carbon Nanotubes Based on the Interatomic Potential—Part I: Basic Theory

2008 ◽  
Vol 75 (6) ◽  
Author(s):  
J. Wu ◽  
K. C. Hwang ◽  
Y. Huang ◽  
J. Song
Keyword(s):  
Carbon Nanotubes ◽  
Boundary Conditions ◽  
Constitutive Relation ◽  
Finite Deformation ◽  
Shell Theory ◽  
Interatomic Potential ◽  
Bending Moments ◽  
Equilibrium Equations ◽  
Potential Part ◽  
Asymmetric Stress

A finite-deformation shell theory for carbon nanotubes (CNTs) is established directly from the interatomic potential for carbon to account for the effect of bending and curvature. Its constitutive relation accounts for the nonlinear multibody atomistic interactions and therefore can model the important effect of CNT chirality and radius. The equilibrium equations and boundary conditions are obtained for the symmetric stresses and bending moments, which are different from many existing shell theories that involve asymmetric stress and bending moments. The theory is used in Part II of this paper to study the instability of carbon nanotubes subjected to different loadings.

Buckling Analyses of Double-Wall Carbon Nanotubes: A Shell Theory Based on the Interatomic Potential

2010 ◽  
Vol 77 (6) ◽  
Author(s):  
W. B. Lu ◽  
J. Wu ◽  
X. Feng ◽  
K. C. Hwang ◽  
Y. Huang
Keyword(s):  
Carbon Nanotubes ◽  
Shell Theory ◽  
Interatomic Potential ◽  
Outer Wall ◽  
Critical Buckling Strain ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes ◽  
Double Wall ◽  
The Continuum ◽  
Vdw Interaction

Based on the finite-deformation shell theory for carbon nanotubes established from the interatomic potential and the continuum model for van der Waals (vdW) interactions, we have studied the buckling of double-walled carbon nanotubes subjected to compression or torsion. Prior to buckling, the vdW interactions have essentially no effect on the deformation of the double-walled carbon nanotube. The critical buckling strain of the double-wall carbon nanotubes is always between those for the inner wall and for the outer wall, which means that the vdW interaction decelerates buckling of one wall at the expenses of accelerating the buckle of the other wall.

Buckling of Thick Orthotropic Cylindrical Shells Under External Pressure

1993 ◽  
Vol 60 (1) ◽  
pp. 195-202 ◽  
Author(s):  
G. A. Kardomateas
Keyword(s):  
Critical Load ◽  
Shell Theory ◽  
Cylindrical Shells ◽  
Three Dimensional ◽  
Stability Loss ◽  
External Pressure ◽  
Elasticity Solution ◽  
Composite Shells

An elasticity solution to the problem of buckling of orthotropic cylindrical shells subjected to external pressure is presented. In this context, the structure is considered a three-dimensional body. The results show that the shell theory predictions can produce nonconservative results on the critical load of composite shells with moderately thick construction. The solution provides a means of accurately assessing the limitations of shell theories in predicting stability loss.

scholarly journals Depressurization-Induced Nucleation in the “Polylactide-Carbon Dioxide” System: Self-Similarity of the Bubble Embryos Expansion

Polymers ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1115
Author(s):  
Dmitry Zimnyakov ◽  
Marina Alonova ◽  
Ekaterina Ushakova
Keyword(s):  
Initial Rate ◽  
Initial Pressure ◽  
External Pressure ◽  
Self Similarity ◽  
Embryo Formation ◽  
Linear Behavior ◽  
Joint Influence ◽  
External Pressures ◽  
Adiabatic Cooling ◽  
Self Similar

Self-similar expansion of bubble embryos in a plasticized polymer under quasi-isothermal depressurization is examined using the experimental data on expansion rates of embryos in the CO2-plasticized d,l-polylactide and modeling the results. The CO2 initial pressure varied from 5 to 14 MPa, and the depressurization rate was 5 × 10−3 MPa/s. The constant temperature in experiments was in a range from 310 to 338 K. The initial rate of embryos expansion varied from ≈0.1 to ≈10 µm/s, with a decrease in the current external pressure. While modeling, a non-linear behavior of CO2 isotherms near the critical point was taken into account. The modeled data agree satisfactorily with the experimental results. The effect of a remarkable increase in the expansion rate at a decreasing external pressure is interpreted in terms of competing effects, including a decrease in the internal pressure, an increase in the polymer viscosity, and an increase in the embryo radius at the time of embryo formation. The vanishing probability of finding the steadily expanding embryos for external pressures around the CO2 critical pressure is interpreted in terms of a joint influence of the quasi-adiabatic cooling and high compressibility of CO2 in the embryos.

Fitness for Service Assessments of Bulging and Out-of-Round Structures

2004 ◽  
Author(s):  
Peter Carter ◽  
D. L. Marriott ◽  
M. J. Swindeman
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Internal Pressure ◽  
Structural Model ◽  
External Pressure ◽  
Element Analysis ◽  
Structural Imperfection ◽  
Level 2

This paper examines techniques for the evaluation of two kinds of structural imperfection, namely bulging subject to internal pressure, and out-of-round imperfections subject to external pressure, with and without creep. Comparisons between comprehensive finite element analysis and API 579 Level 2 techniques are made. It is recommended that structural, as opposed to material, failures such as these should be assessed with a structural model that explicitly represents the defect.

Data Collection and Analysis for the Creation of a Digital Shadow During the Production of Thermoplastic Composite Layers in Unbonded Flexible Pipes

2018 ◽  
Author(s):  
Martin Schäkel ◽  
John McNab ◽  
Neville Dodds ◽  
Tido Peters ◽  
Henning Janssen ◽  
...  
Keyword(s):  
External Pressure ◽  
Thermoplastic Composite ◽  
Sensor Data ◽  
Consolidation Process ◽  
Specific Strength ◽  
Additional Information ◽  
Flexible Pipes ◽  
Potential Part ◽  
Path Dependent ◽  
Unbonded Flexible Pipes

Unbonded flexible pipes present a mature technology for the efficient recovery and transport of hydrocarbons offshore. The substitution of metallic reinforcement layers in the multi-layered structure by thermoplastic fiber-reinforced polymer (FRP) presents a solution for self-weight issues of especially long pipes, as FRP materials display high specific strength and modulus while being resistant to external pressure and corrosion. The production of these layers is automated by the laser-assisted tape winding process without the need of additional curing steps. During the manufacturing process, several data like process temperature and consolidation pressure are continuously monitored by non-contact sensors to ensure process stability without interfering in the consolidation process. To gain additional information about the temperature distribution within the multi-layered laminate, contact temperature sensors were introduced in the tape winding process. By this method the temperature of subjacent tapes can be assessed during the continued winding process. Additionally, this paper features a new approach of utilizing winding path data for relating the time-dependent sensor data to the exact position on the produced part. The visualization of path-dependent sensor data opens up possibilities of linking quality monitoring results to manufacturing insufficiencies and potential part defects.

A Theoretical and Experimental Analysis of the Bending Behavior of Unbonded Flexible Pipes

2014 ◽  
Author(s):  
Tatiana Vargas-Londoño ◽  
José Renato M. de Sousa ◽  
Carlos Magluta ◽  
Ney Roitman
Keyword(s):  
Internal Pressure ◽  
Cross Section ◽  
Structural Response ◽  
Experimental Tests ◽  
Theoretical Models ◽  
External Pressure ◽  
Local Behavior ◽  
Flexible Pipes ◽  
Floating System ◽  
Bending Loads

Due to its compound cross-section, the prediction of the structural response of flexible pipes to loads such as their self-weight, internal and external pressure, movements imposed by the floating system and environmental loads such as currents, waves and wind is quite complex. All these loads generate stresses and strains in the cross section of the pipe that have to be properly evaluated in order to ensure integrity of the line. Research has been done on the local behavior of flexible pipes under combined axisymmetric loads as well as under bending loads. However, there is a lack of research combining both axisymmetric and bending loads, as also in the study of the strains in the tensile amour layers of the pipes, aspects which are important for the calibration of theoretical models to predict such behavior. Based on that, this study aims to evaluate the local behavior of flexible pipes under combinations of axisymmetric (tension, and internal pressure) and bending loads via a series of experimental tests in a 9.13″ I.D pipe. In the experimental tests, the behavior of the pipe was studied for three load combinations: i) bending combined with tension; ii) bending combined with internal pressure; and iii) bending combined with tension and internal pressure. Based on these tests, the authors obtained the strains in the tensile armor layer, axial elongation due to tension, axial reaction forces due to internal pressure, and deflection due to bending. These measurements were used to calibrate a theoretical model devoted to simulate the pipe’s response, getting accurate results for stiffness and stresses of the pipe in each scenario.

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