Yiming Chen¹, Liqing Liu¹, Xuan Li¹ and Yannan Sun¹

CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.1, pp. 81-100, 2014, DOI:10.3970/cmes.2014.097.081

Abstract In 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… More >

F. Mechighel^1,2,3, N. Armour⁴, S. Dost⁴, M. Kadja³

CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.1, pp. 53-80, 2014, DOI:10.3970/cmes.2014.097.053

Abstract Numerical simulations were carried out to explain the behavior exhibited in experimental work on the dissolution process of silicon into a germanium melt. The experimental work utilized a material configuration similar to that used in the Liquid Phase Diffusion (LPD) and Melt-Replenishment Czochralski (Cz) growth systems. The experimental dissolution system was modeled by considering axisymmetric and three-dimensional (3-D) domains. In both cases, the governing equations, namely conservation of mass, momentum balance, energy balance, and solute transport balance, were solved using the Finite Element Method.
Measured concentration profiles and dissolution heights from the experiment samples showed that the application of a… More >

Lei Lu^1,2, Jun-Sheng Duan^2,3

CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.1, pp. 35-52, 2014, DOI:10.3970/cmes.2014.097.035

Abstract In this paper, we investigate the problem of selecting of the convergence parameter c in the Adomian decomposition method. Through the curves of the n-term approximations Φ_n(t;c) versus c for different specified values of n and t, we demonstrate how to determine the value of c such that the decomposition series has a larger effective region of convergence. More >

Z. D. Han¹, S. N. Atluri^2,3

CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.1, pp. 1-34, 2014, DOI:10.3970/cmes.2014.097.001

Abstract The concept of a stress tensor [for instance, the Cauchy stress σ, Cauchy (1789-1857); the first Piola-Kirchhoff stress P, Piola (1794-1850), and Kirchhoff (1824-1889); and the second Piola-Kirchhoff stress, S] plays a central role in Newtonian continuum mechanics, through a physical approach based on the conservation laws for linear and angular momenta. The pioneering work of Noether (1882-1935), and the extraordinarily seminal work of Eshelby (1916- 1981), lead to the concept of an “energy-momentum tensor” [Eshelby (1951)]. An alternate form of the “energy-momentum tensor” was also given by Eshelby (1975) by taking the two-point deformation gradient tensor as an independent… More >

Yin Xiao-Liang¹, Wu Yi-Zhong^1,2, Wan Li¹, Xiong Hui-Yuan³

CMES-Computer Modeling in Engineering & Sciences, Vol.103, No.6, pp. 429-462, 2014, DOI:10.3970/cmes.2014.103.429

Abstract The use of multi-dimensional global approximation for a complex black-box function (such as a simulation or an analysis model) is steadily growing in the past decade. It can be applied in many fields such as parameter experiment, sensibility analyses real-time simulation, and design/control optimization. However, the widespread use of approximation methods is hampered by the lack of the ability to approximate a complex simulation model which characterizes the dynamic feature with multiple inputs and multiple outputs (MIMO) in a large domain. In this paper, a novel global approximation method for simulation models based on the RBF response surface set is… More >

Jia Dongyao^1,2, Zhu Huaihua¹, Ai Yanke¹, Zou Shengxiong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.103, No.6, pp. 411-427, 2014, DOI:10.3970/cmes.2014.103.411

Abstract The existing study on the image segmentation methods based on the image of vehicle lights is insufficient both at home and abroad, and its segmentation efficiency and accuracy is low as well. On the basis of the analysis of the regional characteristics of vehicle lights and a level set model, an image segmentation method for complex vehicle lights based on adaptive significance level set contour model is proposed in this paper. Adaptive positioning algorithm of the significant initial contour curve based on two-dimensional convex hull is designed to obtain the initial position of evolution curve, thus the adaptive ability of… More >

A.E. Kampitsis¹, E.J. Sapountzakis²

CMES-Computer Modeling in Engineering & Sciences, Vol.103, No.6, pp. 367-409, 2014, DOI:10.3970/cmes.2014.103.367

Abstract In this paper a Boundary Element Method (BEM) is developed for the geometrically nonlinear inelastic analysis of Timoshenko beams of arbitrary doubly symmetric simply or multiply connected constant cross-section, resting on inelastic tensionless Winkler foundation. The beam is subjected to the combined action of arbitrarily distributed or concentrated transverse loading and bending moments in both directions as well as to axial loading, while its edges are subjected to the most general boundary conditions. To account for shear deformations, the concept of shear deformation coefficients is used. A displacement based formulation is developed and inelastic redistribution is modeled through a distributed… More >

B.J. Yang¹, K.J. Cho¹, G.M. Kim¹, H.K. Lee^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.103, No.5, pp. 343-365, 2014, DOI:10.3970/cmes.2014.103.343

Abstract The 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… More >

S. Saha Ray¹, A. K. Gupta²

CMES-Computer Modeling in Engineering & Sciences, Vol.103, No.5, pp. 315-341, 2014, DOI:10.3970/cmes.2014.103.315

Abstract In this paper, an efficient numerical schemes based on the Haar wavelet method are applied for finding numerical solution of nonlinear third-order modified Korteweg-de Vries (mKdV) equation as well as modified Burgers' equations. The numerical results are then compared with the exact solutions. The accuracy of the obtained solutions is quite high even if the number of calculation points is small. More >

J. Labaki¹, E. Mesquita², R. K. N. D. Rajapakse³

CMES-Computer Modeling in Engineering & Sciences, Vol.103, No.5, pp. 281-313, 2014, DOI:10.3970/cmes.2014.103.281

Abstract This paper introduces a numerical model to investigate the vibratory response of elastic and rigid circular plates embedded in viscoelastic, transversely isotropic, three-dimensional layered media. In the present numerical scheme, the boundary-value problem corresponding to the case of time-harmonic concentrated and distributed axisymmetric vertical ring loads within a layered half-space is formulated according to an exact stiffness method. Its solution results in the required influence functions for the modeling of the present problem. The case of an embedded flexible plate is formulated in terms of a variational method. The deflection profile of the plate is written in terms of generalized… More >