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.

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.

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.

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.

scholarly journals Analytical Solutions for Flow of a Dusty Fluid Between Two Porous Flat Plates

1994 ◽  
Vol 116 (2) ◽  
pp. 354-356 ◽  
Author(s):  
Ali J. Chamkha
Keyword(s):  
Exact Solutions ◽  
Closed Form ◽  
Skin Friction ◽  
Analytical Solutions ◽  
Velocity Profiles ◽  
Flat Plates ◽  
Friction Coefficients ◽  
Dusty Fluid ◽  
Closed Form Solutions

Equations governing flow of a dusty fluid between two porous flat plates with suction and injection are developed and closed-form solutions for the velocity profiles, displacement thicknesses, and skin friction coefficients for both phases are obtained. Graphical results of the exact solutions are presented and discussed.

EXACT SOLUTIONS FOR INTERFACIAL OUTFLOWS WITH STRAINING

2014 ◽  
Vol 55 (3) ◽  
pp. 232-244 ◽  
Author(s):  
LAWRENCE K. FORBES ◽  
MICHAEL A. BRIDESON
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Point Source ◽  
Exact Solutions ◽  
Closed Form ◽  
Line Source ◽  
Nonlinear Partial Differential Equation ◽  
Background Flow ◽  
Closed Form Solutions ◽  
Fluid Instabilities

AbstractIn models of fluid outflows from point or line sources, an interface is present, and it is forced outwards as time progresses. Although various types of fluid instabilities are possible at the interface, it is nevertheless of interest to know the development of its overall shape with time. If the fluids on either side are of nearly equal densities, it is possible to derive a single nonlinear partial differential equation that describes the interfacial shape with time. Although nonlinear, this equation admits a simple transformation that renders it linear, so that closed-form solutions are possible. Two such solutions are illustrated; for a line source in a planar straining flow and a point source in an axisymmetric background flow. Possible applications in astrophysics are discussed.

scholarly journals Closed-form solutions and conservation laws of a generalized Hirota–Satsuma coupled KdV system of fluid mechanics

Open Physics ◽  
2021 ◽  
Vol 19 (1) ◽  
pp. 18-25
Author(s):  
Chaudry Masood Khalique
Keyword(s):  
Solitary Wave ◽  
Fluid Mechanics ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Closed Form ◽  
Solitary Wave Solutions ◽  
Linear Ordinary Differential Equations ◽  
Closed Form Solutions ◽  
Wave Solutions ◽  
Simplest Equation Method

Abstract In this article, a generalized Hirota–Satsuma coupled Korteweg–de Vries (KdV) system is investigated from the group standpoint. This system represents an interplay of long waves with distinct dispersion correlations. Using Lie’s theory several symmetry reductions are performed and the system is reduced to systems of non-linear ordinary differential equations (NLODEs). Subsequently, the simplest equation method is invoked to find exact solutions of the NLODE systems, which then provides the solitary wave solutions for the system under discussion. Finally, we construct conservation laws of generalized Hirota–Satsuma coupled KdV system with the aid of general multiplier approach.

The Effect of Compressibility on the Stress Distributions in Thin Elastomeric Blocks and Annular Bushings

1992 ◽  
Vol 59 (4) ◽  
pp. 902-908 ◽  
Author(s):  
Yeh-Hung Lai ◽  
D. A. Dillard ◽  
J. S. Thornton
Keyword(s):  
Finite Element Analysis ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Stress Distributions ◽  
Element Analysis ◽  
Shape Factors ◽  
Closed Form Solutions ◽  
Apparent Stiffness ◽  
Bulk Compressibility

The effect of the bulk compressibility of elastomers on the response of rubber blocks and bushings bonded to platens is in vestigated. Closed-form solutions for the stresses and deformations within the elastomer are presented for the case of rigid adherends. It is shown that even with relatively small shape factors, the compressibility can significantly affect the apparent stiffness. A finite element analysis shows that the closed-form solution accurately predicts the stress distribution for rigid adherends, but also reveals that platen deformations in realistic systems may significantly alter the distributions.

scholarly journals Novel Analytical Technique to Find Closed Form Solutions of Time Fractional Partial Differential Equations

2022 ◽  
Vol 6 (1) ◽  
pp. 24
Author(s):  
Muhammad Shakeel ◽  
Nehad Ali Shah ◽  
Jae Dong Chung
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Exact Solutions ◽  
Closed Form ◽  
Fractional Order ◽  
Soliton Solutions ◽  
Wave Transformation ◽  
Order Partial Differential Equation ◽  
Partial Differential ◽  
Closed Form Solutions

In this article, a new method for obtaining closed-form solutions of the simplified modified Camassa-Holm (MCH) equation, a nonlinear fractional partial differential equation, is suggested. The modified Riemann-Liouville fractional derivative and the wave transformation are used to convert the fractional order partial differential equation into an integer order ordinary differential equation. Using the novel (G’/G2)-expansion method, several exact solutions with extra free parameters are found in the form of hyperbolic, trigonometric, and rational function solutions. When parameters are given appropriate values along with distinct values of fractional order α travelling wave solutions such as singular periodic waves, singular kink wave soliton solutions are formed which are forms of soliton solutions. Also, the solutions obtained by the proposed method depend on the value of the arbitrary parameters H. Previous results are re-derived when parameters are given special values. Furthermore, for numerical presentations in the form of 3D and 2D graphics, the commercial software Mathematica 10 is incorporated. The method is accurately depicted, and it provides extra general exact solutions.

Sign in / Sign up

Export Citation Format

Share Document