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Effect of CNT Agglomeration on the Electrical Conductivity and Percolation Threshold of Nanocomposites: A Micromechanics-based Approach
Get PDFThe addition of carbon nanotubes (CNTs) to a matrix material is expected to lead to an increase in the effective electrical properties of nanocomposites. However, a CNT entanglement caused by the matrix viscosity and the high aspect ratio of the nanotubes often inhibits the formation of a conductive network. In the present study, the micromechanics-based model is utilized to investigate the effect of CNT agglomeration on the electrical conductivity and percolation threshold of nanocomposites. A series of parametric studies considering various shapes and curviness distributions of CNTs are carried out to examine the effects of entanglement on the electrical performance of nanocomposites. Comparisons between experimental results and the present predictions are made to evaluate the predictive capability of the proposed model. In addition, the present model is incorporated into the commercial finite element software ANSYS HFSS to simulate the electromagnetic interference (EMI) shielding effectiveness of nanocomposites
Numerical Solution for the Variable Order Time Fractional Diffusion Equation with Bernstein Polynomials
Get PDFIn this paper, Bernstein polynomials method is proposed for the numerical solution of a class of variable order time fractional diffusion equation. Coimbra variable order fractional operator is adopted, as it is the most appropriate and desirable definition for physical modeling. The Coimbra variable order fractional operator can also be regarded as a Caputo-type definition. The main characteristic behind this approach in this paper is that we derive two kinds of operational matrixes of Bernstein polynomials. With the operational matrixes, the equation is transformed into the products of several dependent matrixes which can also be viewed as the system of linear equations after dispersing the variable. By solving the linear equations, the numerical solutions are acquired. Only a small number of Bernstein polynomials are needed to obtain a satisfactory result. Numerical examples are provided to show that the method is computationally efficient
A State Space Differential Reproducing Kernel Method for the Buckling Analysis of Carbon Nanotube-Reinforced Composite Circular Hollow Cylinders
Get PDFA state space differential reproducing kernel (DRK) method is developed for the three-dimensional (3D) buckling analysis of simply-supported, carbon nanotube-reinforced composite (CNTRC) circular hollow cylinders and laminated composite ones under axial compression. The single-walled carbon nanotubes (CNTs) and polymer are used as the reinforcements and matrix, respectively, to constitute the CNTRC cylinder. Three different distributions of CNTs varying in the thickness direction are considered (i.e., the uniform distribution and functionally graded rhombus-, and X-type ones), and the through-thickness distributions of effective material properties of the cylinder are determined using the rule of mixtures. The 3D linear buckling theory is used, in which a set of membrane stresses is assumed to exist in the cylinder just before instability occurs, and this is regarded as the initial stresses introduced in the formulation. The Euler-Lagrange equations perturbed from the state of neutral equilibrium are derived using the Reissner mixed variational theorem. The primary field variables, displacement and transverse stress components, are expanded as the single Fourier series in the circumferential coordinate, and then interpolated in the axial coordinate using DRK interpolation functions. Finally, the state space equations of this problem are obtained, which represent a system of ordinary differential equations in the thickness coordinate. The state space DRK solutions of the critical load parameters of the cylinder can thus be obtained by means of the transfer matrix method combined with the successive approximation one, and the convergence and accuracy of the state space DRK solutions are validated by comparing these solutions with exact 3D ones available in the literature and approximate 3D ones obtained using the ANSYS software
Differential Quadrature and Cubature Methods for Steady-State Space-Fractional Advection-Diffusion Equations
Get PDFSpace-fractional advection-diffusion equation is a promising tool to describe the solute anomalous transport in underground water, and it has been extended to multi-dimensions with the help of weighted, fractional directional diffusion operator [Benson, Wheatcraft and Meerschaert (2000)]. Due to the nonlocal property of the space-fractional derivative, it is always a challenge to develop an efficient numerical solution method. The present paper extends the polynomialbased differential quadrature and cubature methods to the solution of steady-state spatial fractional advection-diffusion equations on a rectangular domain. An improved differential cubature method is proposed which accelerates the solution process considerably. Owing to the global interpolation nature these methods are more accurate and efficient than the finite element method. Numerical convergence is investigated thru one- and two- dimensional benchmark problems. The convergence can be improved after well-organized explicit formulas for weighting coefficients are obtained
Flexural Wave Dispersion in Bi-material Compound Solid and Hollow Circular Cylinders
Get PDFFlexural wave dispersion in a bi-material solid and hollow circular cylinders is investigated with the use of the three-dimensional linear theory of elastodynamics. It is assumed that on the interface surface of the cylinders the complete contact conditions satisfy. The analytical solution of the corresponding field equations is presented and, using these solutions, the dispersion equations for the cases under consideration are obtained. The dispersion equations are solved numerically and based on these solutions, dispersion curves are constructed for the concrete selected pairs of materials such as Tungsten (inner cylinder material) + Aluminum (outer cylinder material) and Steel (inner cylinder material) + Aluminum (outer cylinder material). The numerical results are obtained for the first and second lowest modes. According to these numerical results the influence of the problem parameters, such as the thicknesses of the external and inner cylinders and the materials of the inner cylinder material, on the character of the dispersion curves is analyzed
Erratum to: "Finite Element Analysis of Discrete Circular Dislocations" [CMES, vol. 60, no. 2, pp. 181-198, 2010]
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On Solving Three-dimensional Laplacian Problems in a Multiply Connected Domain Using the Multiple Scale Trefftz Method
Get PDFThis paper proposes the numerical solution of three-dimensional Laplacian problems in a multiply connected domain using the collocation Trefftz method with multiple source points. A numerical solution for three-dimensional Laplacian problems was approximated by superpositioning T-complete functions formulated from 36 independent functions satisfying the governing equation in the cylindrical coordinate system. To deal with complicated problems for multiply connected domain, we adopted the generalized multiple source point boundary collocation Trefftz method which allows many source points in the Trefftz formulation without using the decomposition of the problem domain. In addition, to mitigate a severely ill-conditioned system of linear equations, this study adopted the newly developed multiple scale Trefftz method and the dynamical Jacobian-inverse free method. Numerical solutions were conducted for five three-dimensional groundwater flow problems in a simply connected domain, an infinite domain, a doubly connected domain, and a multiply connected domain. The results revealed that the proposed method can obtain accurate numerical solutions for three-dimensional Laplacian problems in a multiply connected domain, yielding a superior convergence in numerical stability to that of the conventional Trefftz method
A Precise Integration Method for Modeling GPR Wave Propagation in Layered Pavement Structure
Get PDFConstruction of electromagnetic wave propagation model in layered pavement structure is a key step in back analysis of ground penetrating radar (GPR) echo signal. The precise integration method (PIM) is a highly accurate, efficient, and unconditionally stable algorithm for solving 1-order ordinary differential equations. It is quite suitable for dealing with problems of wave propagation in layered media. In this paper, forward simulation of GPR electromagnetic wave propagating in homogeneous layered pavement structure is developed by employing PIM. To verify the performance of the proposed algorithm, simulated GPR signal is compared with the measured one. Excellent agreement is achieved
A Stochastic Multi-Scale Model for Prediction of the Autogenous Shrinkage Deformations of Early-age Concrete
Get PDFAutogenous shrinkage is defined as the bulk deformation of a closed, isothermal, cement-based material system, which is not subjected to external forces. It is associated with the hydration process of the cement paste. From the viewpoint of engineering practice, autogenous shrinkage deformations result in an increase of tensile stresses, which may lead to cracking of early-age concrete. Since concrete is a multi-phase composite with different material compositions and microscopic configurations at different scales, autogenous shrinkage does not only depend on the hydration of the cement paste, but also on the mechanical properties of the constituents and of their distribution. In this paper, a stochastic multi-scale model for early-age concrete is presented, which focuses on the prediction of autogenous shrinkage deformations. In this model, concrete is divided into three different levels according to the requirement of separation of scales. These levels are the cement paste, the mortar, and the concrete. A specific representative volume element (RVE) for each scale is described by introducing stochastic parameters. Different scales are linked by means of the asymptotic expansion theory. A set of autogenous shrinkage experiments on the cement paste, the mortar, and the concrete is conducted and used for validation of the developed multi-scale model. Furthermore, the influence of the type and the volume fraction of the aggregate on autogenous shrinkage is studied. Besides, a combined optimum of fine and coarse aggregates is determined. The analysis results show that the proposed model can effectively estimate the autogenous shrinkage deformations of concrete at early-age by taking the influence of the material composition and configuration into consideration
Generalized RayleighWave Dispersion Analysis in a Pre-stressed Elastic Stratified Half-space with Imperfectly Bonded Interfaces
Get PDFWithin the framework of the piecewise homogeneous body model the influence of the shear-spring type imperfect contact conditions on the dispersion relation of the generalized Rayleigh waves in the system consisting of the initially stressed covering layer and initially stressed half plane is investigated. The second version of the small initial deformation theory of the three-dimensional linearized theory of elastic waves in initially stressed bodies is applied and the elasticity relations of the materials of the constituents are described by the Murnaghan potential. The magnitude of the imperfectness of the contact conditions is estimated through the shear-spring type parameter. Consequently, the influence of the imperfectness of the contact conditions on the generalized Rayleigh wave propagation velocity is studied through the influence of the values of this parameter. Numerical results on the action of the imperfectness of the contact conditions and the influence of the initial stresses in the constituents on the wave dispersion curves are presented and discussed. In particular, it is established that the magnitude of action of the imperfectness of the contact conditions under the influence of the initial stresses on the wave propagation velocity cannot be limited with corresponding ones obtained in the case where the contact between the constituents is complete and in the case where this contact is full slipping one. The possible application of the obtained results on the geophysical and geotechnical engineering is also discussed