Wall Thickness and Radial Breathing Modes of Single-Walled Carbon Nanotubes

2008 ◽  
Vol 75 (6) ◽  
Author(s):  
R. C. Batra ◽  
S. S. Gupta
Keyword(s):  
Boundary Conditions ◽  
Wall Thickness ◽  
Mechanical Response ◽  
Free Vibrations ◽  
Spectral Lines ◽  
Bending Vibrations ◽  
Element Analysis ◽  
Linear Elasticity Theory ◽  
Single Walled Carbon ◽  
3D Fea

We postulate that an equivalent continuum structure (ECS) of a single-walled carbon nanotube (SWCNT) is a hollow cylinder with mean radius and length equal to that of the SWCNT, and find the thickness of the ECS so that its mechanical response in free vibrations is the same as that of the SWCNT. That is, for mechanical deformations, the ECS is energetically equivalent to the SWCNT. We use MM3 potential to study axial, torsional, radial breathing and bending vibrations of several traction free–traction free SWCNTs of different helicities and diameters and compare them with the corresponding vibrational modes and frequencies of traction free–traction free ECSs obtained by using the three-dimensional linear elasticity theory and the finite element analysis (3D-FEA). The consideration of free ends eliminates the effects of boundary conditions and avoids resolving equivalence between boundary conditions in the analyses of SWCNTs and their ECSs. It is found that the wall thickness of the ECS (and hence of a SWCNT) is ∼1 Å and Young’s modulus of the material of the ECS (and hence of the SWCNT) is ∼3.3 TPa. Both quantities are independent of the helicity and the diameter of the SWCNT. We also study radial breathing mode (RBM) vibrations with the molecular dynamics and the 3D-FEA simulations, and compare them with experimental findings. Accuracy in the assignment of spectral lines for RBMs in the Raman spectroscopy is discussed.

Computational Design and Analysis of Nitinol-Based Arch Wedge Support

2018 ◽  
Author(s):  
Tyler Stranburg ◽  
Yucheng Liu ◽  
Harish Chander ◽  
Adam Knight
Keyword(s):  
Boundary Conditions ◽  
Mechanical Response ◽  
Computational Study ◽  
Experimental Testing ◽  
Permanent Deformation ◽  
Computational Design ◽  
Element Analysis ◽  
Human Movements ◽  
First Time ◽  
Human Motions

A nitinol-based arch wedge support (AWS) was designed using computational approach. Finite element analysis (FEA) was performed to on this design to assess the influence of loading, boundary conditions, and thickness on the mechanical response of the computer-aid design (CAD) model. Five loading conditions caused by different human movements, two boundary conditions, and three thicknesses are involved in this computational study. FEA results showed that the presented AWS design can resist forces caused by different human motions without generating any permanent deformation. The study features the first time to design and evaluate a thin-walled nitinol AWS model. The results of this study form the background of prototyping and experimental testing of the design in the next phase.

scholarly journals ВІЛЬНІ КОЛИВАННЯ ОРТОТРОПНИХ ПЛАСТИН

2020 ◽  
Vol 138 (5) ◽  
pp. 53-61
Author(s):  
Д. В. Лазарєва ◽  
І. В. Курган
Keyword(s):  
Differential Equation ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Boundary Conditions ◽  
Orthotropic Plate ◽  
Free Vibrations ◽  
Element Analysis ◽  
Method Of Boundary Elements ◽  
Rectangular Orthotropic Plate ◽  
Numerical Analytical Method

The solution of the problem of free vibrations of a rectangular orthotropic plate by the methods of boundary and finite elements under any boundary conditions. Transformation of the two-dimensional differential equation of free vibrations of an orthotropic rectangular plate to one-dimensional. Determination of the complete system of its fundamental solutions using the numerical-analytical method of boundary elements. Implementation of the algorithm on the example of a specific plate and comparison with the results of finite element analysis in ANSYS. The solution to the problem of natural vibrations of a rectangular orthotropic plate is obtained without any restrictions on the nature of the fixing of its sides. A transcendental frequency equation is obtained whose roots give the full spectrum of natural frequencies. The modeling and calculations of the orthotropic plate by the finite element method are performed. An analysis of the numerical results obtained by the author's method shows a very good convergence with the results of finite element analysis. For a plate with rigid fastening of three sides with a free fourth side, the discrepancy is slightly higher than for a plate with a hinged support along the contour. Under both variants of the boundary conditions, the frequency spectrum calculated by the boundary element method is lower than in the finite element calculations. Analytical expressions of fundamental functions are obtained that correspond to all possible solutions to the differential equation of free oscillations. For the first time, a solution to the problem of free vibrations of a rectangular orthotropic plate is presented by the numerical-analytical method of boundary elements. The results allow us to solve the problem of free vibrations of a rectangular orthotropic plate by two methods under any boundary conditions, including inhomogeneous ones.

Formulation of Problem of Free Vibration Analysis of Isotropic Homogeneous Rectangular Mindlin Plates Having Variable Thickness With General Elastic Boundary Conditions

2017 ◽  
Author(s):  
Sangle Sourabh ◽  
Verma Shesha ◽  
Mali Kiran
Keyword(s):  
Shear Stress ◽  
Boundary Conditions ◽  
Variable Thickness ◽  
Ritz Method ◽  
Free Vibration Analysis ◽  
Free Vibrations ◽  
Element Analysis ◽  
Elastic Boundary ◽  
Constant Shear Stress ◽  
Transverse Deflection

This work presents a formulation for the free vibrations of isotropic homogeneous rectangular Mindlin plates with variable thickness. These plates are subjected to general boundary supports in present study. To obtain arbitrarily supported boundary conditions, new form of trigonometric series expansion functions is used as the admissible functions for transverse deflection and rotation due to bending. In order to account the constant shear stress assumption, a shear stress correction factor is taken into consideration. The Rayleigh-Ritz Method is employed in this formulation. The boundaries are assumed to have three set of springs to achieve required boundary condition. Thus the changes in boundary conditions can be easily obtained by varying the stiffness of these springs, without actually making any changes in the shape functions. In this study, FEA (Finite Element Analysis) has been carried out for the Mindlin plates, for simply supported and constrained on two opposite sides.

scholarly journals Shape Sensing of a Complex Aeronautical Structure with Inverse Finite Element Method

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1388
Author(s):  
Daniele Oboe ◽  
Luca Colombo ◽  
Claudio Sbarufatti ◽  
Marco Giglio
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Strain Field ◽  
Element Analysis ◽  
Inverse Finite Element Method ◽  
Shape Sensing ◽  
Definition Of ◽  
High Level ◽  
Element Method

The inverse Finite Element Method (iFEM) is receiving more attention for shape sensing due to its independence from the material properties and the external load. However, a proper definition of the model geometry with its boundary conditions is required, together with the acquisition of the structure’s strain field with optimized sensor networks. The iFEM model definition is not trivial in the case of complex structures, in particular, if sensors are not applied on the whole structure allowing just a partial definition of the input strain field. To overcome this issue, this research proposes a simplified iFEM model in which the geometrical complexity is reduced and boundary conditions are tuned with the superimposition of the effects to behave as the real structure. The procedure is assessed for a complex aeronautical structure, where the reference displacement field is first computed in a numerical framework with input strains coming from a direct finite element analysis, confirming the effectiveness of the iFEM based on a simplified geometry. Finally, the model is fed with experimentally acquired strain measurements and the performance of the method is assessed in presence of a high level of uncertainty.

scholarly journals Effects of Loading and Boundary Conditions on the Performance of Ultrasound Compressional Viscoelastography: A Computational Simulation Study to Guide Experimental Design

Materials ◽  
2021 ◽  
Vol 14 (10) ◽  
pp. 2590
Author(s):  
Che-Yu Lin ◽  
Ke-Vin Chang
Keyword(s):  
Boundary Conditions ◽  
Simulation Study ◽  
Viscoelastic Properties ◽  
Measurement Accuracy ◽  
Computational Simulation ◽  
Vertical Direction ◽  
Fixation Method ◽  
Element Analysis ◽  
Sample Container

Most biomaterials and tissues are viscoelastic; thus, evaluating viscoelastic properties is important for numerous biomedical applications. Compressional viscoelastography is an ultrasound imaging technique used for measuring the viscoelastic properties of biomaterials and tissues. It analyzes the creep behavior of a material under an external mechanical compression. The aim of this study is to use finite element analysis to investigate how loading conditions (the distribution of the applied compressional pressure on the surface of the sample) and boundary conditions (the fixation method used to stabilize the sample) can affect the measurement accuracy of compressional viscoelastography. The results show that loading and boundary conditions in computational simulations of compressional viscoelastography can severely affect the measurement accuracy of the viscoelastic properties of materials. The measurement can only be accurate if the compressional pressure is exerted on the entire top surface of the sample, as well as if the bottom of the sample is fixed only along the vertical direction. These findings imply that, in an experimental validation study, the phantom design should take into account that the surface area of the pressure plate must be equal to or larger than that of the top surface of the sample, and the sample should be placed directly on the testing platform without any fixation (such as a sample container). The findings indicate that when applying compressional viscoelastography to real tissues in vivo, consideration should be given to the representative loading and boundary conditions. The findings of the present simulation study will provide a reference for experimental phantom designs regarding loading and boundary conditions, as well as guidance towards validating the experimental results of compressional viscoelastography.

scholarly journals Vibration of rotating circular cylindrical shells with distributed springs

2021 ◽  
Vol 37 ◽  
pp. 346-358
Author(s):  
Fuchun Yang ◽  
Xiaofeng Jiang ◽  
Fuxin Du
Keyword(s):  
Boundary Conditions ◽  
Galerkin Method ◽  
Shell Theory ◽  
Rotation Speed ◽  
Cylindrical Shells ◽  
Free Vibrations ◽  
Governing Equations ◽  
Natural Response ◽  
Circular Cylindrical Shells ◽  
The Galerkin Method

Abstract Free vibrations of rotating cylindrical shells with distributed springs were studied. Based on the Flügge shell theory, the governing equations of rotating cylindrical shells with distributed springs were derived under typical boundary conditions. Multicomponent modal functions were used to satisfy the distributed springs around the circumference. The natural responses were analyzed using the Galerkin method. The effects of parameters, rotation speed, stiffness, and ratios of thickness/radius and length/radius, on natural response were also examined.

scholarly journals Discrete element analysis of the punching behaviour of a secured drapery system: from laboratory characterization to idealized in situ conditions

2021 ◽  
Author(s):  
Antonio Pol ◽  
Fabio Gabrieli ◽  
Lorenzo Brezzi
Keyword(s):  
Mechanical Response ◽  
Steel Wire ◽  
Discrete Element ◽  
Wire Mesh ◽  
Steel Plates ◽  
Loading Conditions ◽  
Element Analysis ◽  
In Situ Conditions ◽  
Wire Meshes

AbstractIn this work, the mechanical response of a steel wire mesh panel against a punching load is studied starting from laboratory test conditions and extending the results to field applications. Wire meshes anchored with bolts and steel plates are extensively used in rockfall protection and slope stabilization. Their performances are evaluated through laboratory tests, but the mechanical constraints, the geometry and the loading conditions may strongly differ from the in situ conditions leading to incorrect estimations of the strength of the mesh. In this work, the discrete element method is used to simulate a wire mesh. After validation of the numerical mesh model against experimental data, the punching behaviour of an anchored mesh panel is investigated in order to obtain a more realistic characterization of the mesh mechanical response in field conditions. The dimension of the punching element, its position, the anchor plate size and the anchor spacing are varied, providing analytical relationships able to predict the panel response in different loading conditions. Furthermore, the mesh panel aspect ratio is analysed showing the existence of an optimal value. The results of this study can provide useful information to practitioners for designing secured drapery systems, as well as for the assessment of their safety conditions.

scholarly journals Mechanics of tubular helical assemblies: ensemble response to axial compression and extension

2021 ◽  
Author(s):  
Jacopo Quaglierini ◽  
Alessandro Lucantonio ◽  
Antonio DeSimone
Keyword(s):  
Boundary Conditions ◽  
Elastic Properties ◽  
Central Region ◽  
Mechanical Response ◽  
Different Boundary Conditions ◽  
Kirchhoff Rods ◽  
Model Versus ◽  
The Individual ◽  
Opposite Chirality

Abstract Nature and technology often adopt structures that can be described as tubular helical assemblies. However, the role and mechanisms of these structures remain elusive. In this paper, we study the mechanical response under compression and extension of a tubular assembly composed of 8 helical Kirchhoff rods, arranged in pairs with opposite chirality and connected by pin joints, both analytically and numerically. We first focus on compression and find that, whereas a single helical rod would buckle, the rods of the assembly deform coherently as stable helical shapes wound around a common axis. Moreover, we investigate the response of the assembly under different boundary conditions, highlighting the emergence of a central region where rods remain circular helices. Secondly, we study the effects of different hypotheses on the elastic properties of rods, i.e., stress-free rods when straight versus when circular helices, Kirchhoff’s rod model versus Sadowsky’s ribbon model. Summing up, our findings highlight the key role of mutual interactions in generating a stable ensemble response that preserves the helical shape of the individual rods, as well as some interesting features, and they shed some light on the reasons why helical shapes in tubular assemblies are so common and persistent in nature and technology. Graphic Abstract We study the mechanical response under compression/extension of an assembly composed of 8 helical rods, pin-jointed and arranged in pairs with opposite chirality. In compression we find that, whereas a single rod buckles (a), the rods of the assembly deform as stable helical shapes (b). We investigate the effect of different boundary conditions and elastic properties on the mechanical response, and find that the deformed geometries exhibit a common central region where rods remain circular helices. Our findings highlight the key role of mutual interactions in the ensemble response and shed some light on the reasons why tubular helical assemblies are so common and persistent.

Scanner influence on the mechanical response of QCT-based finite element analysis of long bones

2019 ◽  
Vol 86 ◽  
pp. 149-159 ◽  
Author(s):  
Yekutiel Katz ◽  
Gal Dahan ◽  
Jacob Sosna ◽  
Ilan Shelef ◽  
Evgenia Cherniavsky ◽  
...  
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Mechanical Response ◽  
Long Bones ◽  
Element Analysis
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