Analytical Solutions for Effective Transverse Mechanical Properties and Performance of Radially Loaded Nanotube Based Nanocomposites

2009 ◽  
Author(s):  
Davood Askari ◽  
Mehrdad N. Ghasemi-Nejhad
Keyword(s):  
Exact Solutions ◽  
Poisson Ratio ◽  
Axial Strain ◽  
Radial Pressure ◽  
Stress Distributions ◽  
Closed Form Solutions ◽  
Analytical Formulae ◽  
And Performance ◽  
Plain Strain ◽  
Close Form

It is frequently reported that carbon nanotubes (CNTs) can be filled with various materials in different states to create nanocomposites. These nanocomposite tubes are often incorporated in another host material for further reinforcement to attain properties enhancements. The objective of this paper is to introduce exact analytical close form solutions for the prediction of effective transverse Young’s modulus and Poisson ratio of a matrix-filled nanotube (i.e., a representative element of nanotube reinforced nanocomposites) as well as its mechanical behavior (i.e., displacements, strains and stress distributions) when it is subjected to externally applied uniform radial pressure. In this work, both the nanotube and its filler material are considered to be generally cylindrical orthotropic. For no loss of generality, no plain strain condition is used and axial strain is also taken into consideration to obtain a more precise set of solutions. Analytical formulae are developed based on the principles of linear elasticity and continuum mechanics and then exact solutions are obtained for displacements, strains and stress distributions within the domain of each individual constituent. To validate and verify the accuracy of the closed form solutions obtained from the analytical approach, a 3-D model of a matrix-filled CNT is generated and solved for displacements, strains and stresses numerically, using finite element method. Excellent agreements were achieved between the results obtained from the analytical and numerical methods verifying the analytically obtained exact solutions.

Analytical Modeling of Mechanical Properties and Behavior of Nanotube-Based Nanocomposites

2013 ◽  
Author(s):  
Davood Askari ◽  
Mehrdad N. Ghasemi-Nejhad ◽  
Alexander L. Kalamkarov
Keyword(s):  
Exact Solutions ◽  
Closed Form ◽  
Axial Strain ◽  
Stress Distributions ◽  
Closed Form Solutions ◽  
Loading Case ◽  
Analytical Formulae ◽  
Plain Strain ◽  
And Behavior ◽  
Radial Loading

The objective of this paper is to introduce analytical closed form solutions for the prediction of effective axial and transverse Young’s modulus and Poisson ratios of a matrix-filled nanotube (i.e., a representative element of nanotube reinforced nanocomposites) as well as its mechanical behavior (i.e., displacements, strains and stress distributions) when it is subjected to externally applied uniform axial and radial loads. In this work, both the nanotube and its filler material are considered to be generally cylindrical orthotopic. For the derivation of exact solutions for radial loading case, no plain strain condition is assumed and effects of axial strain is taken into consideration to obtain a more precise set of solutions. Analytical formulae are developed based on the principles of linear elasticity and continuum mechanics and then exact solutions are obtained for displacements, strains and stress distributions within the domain of each individual constituent. To validate and verify the accuracy of the closed form solutions obtained from the analytical approach, a 3-D model of a matrix-filled nanotube is generated and solved for displacements, strains and stresses, numerically, using a finite element method. Excellent agreements were achieved between the results obtained from the analytical and numerical methods.

scholarly journals Generally cylindrical orthotropic constitutive modeling of matrix-filled carbon nanotubes: Transverse mechanical properties and responses

2018 ◽  
Vol 22 (7) ◽  
pp. 2330-2363
Author(s):  
Davood Askari ◽  
Mehrdad N. Ghasemi-Nejhad
Keyword(s):  
Closed Form ◽  
Poisson Ratio ◽  
Axial Strain ◽  
Three Dimensional ◽  
Element Analysis ◽  
Closed Form Solutions ◽  
Dimensional Finite Element ◽  
Analytical Formulae ◽  
Orthotropic Properties ◽  
Three Dimensional Finite Element

The main objective of this article is to introduce exact analytical closed-form solutions for the prediction of effective transverse Young’s modulus and Poisson ratio of a matrix-filled nanotube (i.e., a representative element of nanotube-based nanocomposites), as well as its mechanical behavior, when subjected to external loads. In this work, both the nanotube and its filler were considered to be generally cylindrical orthotropic. To ensure no loss of generality, the no plane strain condition was used, and the axial strain was taken into consideration to obtain a more precise set of solutions. Analytical formulae were developed based on the well-established principles of linear elasticity and continuum mechanics, considering effective orthotropic properties for both constituents as continuum tubes. To validate and verify the accuracy of the closed-form solutions obtained from the analytical approach, a three-dimensional finite element analysis was performed, and results were compared to those obtained from the analytical exact solutions. Excellent agreement was achieved, and the analytically obtained solutions were verified.

Evaluating Measured Tire Contact Stresses to Predict Pavement Response and Performance

2000 ◽  
Vol 1716 (1) ◽  
pp. 73-81 ◽  
Author(s):  
Reynaldo Roque ◽  
Leslie Ann Myers ◽  
Bjorn Birgisson
Keyword(s):  
Contact Stress ◽  
Contact Stresses ◽  
Embedded Sensors ◽  
Stress Distributions ◽  
Near Surface ◽  
Weak Bases ◽  
Truck Tires ◽  
Pavement Response ◽  
Pavement Structures ◽  
And Performance

Recent research has indicated that measured contact stress distributions under radial truck tires are highly complex. These stress distributions help to explain near-surface distresses that have become more prevalent since the inception of radial tires, indicating that realistic contact stresses must be considered when pavement response and performance are evaluated. However, because of the complexities involved in measuring contact stresses under tires, obtaining these measurements directly on real pavements is not possible. Consequently, contact stress measurements have been made on systems having rigid foundations with embedded sensors. Therefore, determining whether tire contact stresses measured on a rigid foundation are significantly different from contact stresses under the same tire on an actual pavement is critical. Finite element analyses conducted indicated that both vertical and lateral tire contact stresses measured on rigid foundations accurately represent the contact stresses for the same tire on typical asphalt pavement structures. Some minor differences were observed for thin (50-mm surface) pavements on weak bases, but the correspondence in terms of both distribution and magnitude was still very good. The conclusion was that contact stresses measured by devices with rigid foundations appear to be suitable for predicting response and performance of highway pavements.

Elastic-plastic stress distributions and limit angular velocities in rotating hyperbolic annular discs

2007 ◽  
Vol 221 (2) ◽  
pp. 137-142 ◽  
Author(s):  
N N Alexandrova ◽  
P M M Vila Real
Keyword(s):  
Rotational Speed ◽  
Yield Criterion ◽  
Circumferential Stress ◽  
Radial Pressure ◽  
Thickness Variation ◽  
Flow Rule ◽  
Stress Distributions ◽  
Elastic Plastic ◽  
Angular Velocities ◽  
Hyperbolic Form

Plastic analytical stress analysis of a rotating annular disc with its contours being free from the radial pressure and with specifically variable thickness is presented in terms of the Mises-yield criterion and its associated flow rule. The hyperbolic form of thickness variation is considered and optimized towards the maximum rotational speed and favourable stress combinations. Radial and circumferential stress distributions in the disc both in the intermediate elastic-plastic and in the limit plastic states are obtained. As a particular case, limit elastic angular velocity parameter is derived. The influences of rotational speed as well as the disc's thickness profile on the plastic solution and size of elastic-plastic zone are demonstrated and discussed. The results obtained may be used for the correct implementation of numerical codes and preliminary engineering design.

On the Approximate Solution of Viscous-Flow Problems

1963 ◽  
Vol 30 (2) ◽  
pp. 263-268 ◽  
Author(s):  
J. A. Schetz
Keyword(s):  
Approximate Solution ◽  
Exact Solutions ◽  
Viscous Flow ◽  
Closed Form ◽  
New Method ◽  
Two Dimensional ◽  
General Technique ◽  
Closed Form Solutions ◽  
Flow Problems

The need for a general technique for the approximate solution of viscous-flow problems is discussed. Existing methods are considered and a new method is presented which results in simple closed-form solutions. The accuracy of the method is demonstrated by comparisons with the results of known exact solutions, and finally the general technique is employed to determine a new solution for the fully expanded two-dimensional laminar nozzle problem.

Lie symmetry reductions, abound exact solutions and localized wave structures of solitons for a (2 + 1)-dimensional Bogoyavlenskii equation

2021 ◽  
pp. 2150252
Author(s):  
Sachin Kumar ◽  
Monika Niwas
Keyword(s):  
Exact Solutions ◽  
Closed Form ◽  
Evolution Equations ◽  
Dynamical Behavior ◽  
Lie Symmetry ◽  
Nonlinear Evolution Equations ◽  
Mathematical Methods ◽  
Closed Form Solutions ◽  
Symmetry Reductions ◽  
Engineering Sciences

By applying the two efficient mathematical methods particularly with regard to the classical Lie symmetry approach and generalized exponential rational function method, numerous exact solutions are constructed for a (2 + 1)-dimensional Bogoyavlenskii equation, which describes the interaction of Riemann wave propagation along the spatial axes. Moreover, we obtain the infinitesimals, all the possible vector fields, optimal system, and Lie symmetry reductions. The governing Bogoyavlenskii equation is converted into various nonlinear ordinary differential equations through two stages of Lie symmetry reductions. Accordingly, abundant exact closed-form solutions are obtained explicitly in terms of independent arbitrary functions, rational functions, trigonometric functions, and hyperbolic functions with arbitrary free parameters. The dynamical behavior of the resulting soliton solutions is presented through 3D-plots via numerical simulation. Eventually, single solitons, multi-solitons with oscillations, kink wave with breather-type solitons, and single lump-type solitons are obtained. The proposed mathematical techniques are effective, trustworthy, and reliable mathematical tools to work out new exact closed-form solutions of various types of nonlinear evolution equations in mathematical physics and engineering sciences.

Changes in Nanostructure of Wood Cell Wall during Deformation

2008 ◽  
Vol 599 ◽  
pp. 126-136 ◽  
Author(s):  
Marko Peura ◽  
Seppo Andersson ◽  
Ari Salmi ◽  
Timo Karppinen ◽  
Mika Torkkeli ◽  
...  
Keyword(s):  
Cell Wall ◽  
Poisson Ratio ◽  
Axial Strain ◽  
Microfibril Angle ◽  
Silver Birch ◽  
Wall Structure ◽  
Crystalline Cellulose ◽  
Tensile Behaviour ◽  
Angle Distribution ◽  
X Ray

The excellent mechanical properties of wood arise from its cellular and cell wall structure. X-ray scattering, ultrasound, and mechanical testing is combined to study the effects of strain on crystalline cellulose in wood. Results for dry and re-moistened softwood samples are reviewed and new results are presented for native, never-dried samples of Silver birch. When softwood is stretched parallel to the cell axis, the mean microfibril angle diminishes significantly in compression wood, but only slightly in clear wood. The cellulose chains in the crystallites elongate and their distance diminishes. In the never-dried Silver birch samples, axial strain caused the mode of the microfibril angle distribution to slightly decrease from the initial value of 14 degrees to 12 degrees. Unlike in softwood, in never-dried birch crystalline cellulose showed auxetic tensile behaviour. The distance of the chains increased and the X-ray Poisson ratio νca was negative, -0.3 ± 0.2. Dehydration of never-dried Silver birch caused no difference to the microfibril angle distribution.

Finite Element Analysis of Stress Distributions on the Diamond Pick

2011 ◽  
Vol 487 ◽  
pp. 184-188
Author(s):  
Shu Tao Huang ◽  
Li Zhou ◽  
J. Li
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Finite Element Modeling ◽  
Lateral Pressure ◽  
Normal Pressure ◽  
Three Dimension ◽  
Stress Distributions ◽  
Element Analysis ◽  
Modeling Software ◽  
And Performance

Commercial finite element modeling software ANSYS was used to calculate the stress distributions of diamond pick at different loads. The three-dimension model of the pick was built and the direction and magnitude of load were varied to determine their effect on the stress distributions of diamond pick. The results show that the stresses located on the pick increase with the increasing of the normal and lateral pressure, and if the maximum normal pressure and lateral pressure are not higher than 480 kN and 150 kN, respectively, the diamond pick will not be damaged. The results obtained can provide available data for pick selection, design and performance.

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