M. Q. Chau^1,2, X. Han¹, Y. C. Bai¹, C. Jiang¹

CMC-Computers, Materials & Continua, Vol.27, No.2, pp. 128-142, 2012, DOI:10.32604/cmc.2012.027.128

Abstract The first-order reliability method (FORM) is one of the most widely used structural reliability analysis techniques due to its simplicity and efficiency. However, direct using FORM seems disability to work well for complex problems, especially related to high-dimensional variables and computation intensive numerical models. To expand the applicability of the FORM for more practical engineering problems, a response surface (RS) approach based FORM is proposed for structural reliability analysis. The radial basis function (RBF) is employed to approximate the implicit limit-state functions combined with Latin Hypercube Sampling (LHS) strategy. To guarantee the numerical stability, the improved HL-RF (iHL-RF) algorithm is… More >

Cheng-Hung San¹, Chuang-Pin Chiu¹, Che-Wun Hong^1,2

CMC-Computers, Materials & Continua, Vol.26, No.3, pp. 167-186, 2011, DOI:10.3970/cmc.2011.026.167

Abstract An improvement in the catalytic process of oxygen reduction reactions is of prime importance for further progress in low temperature fuel cell performance. This paper intends to investigate this problem from a fundamental quantum mechanics viewpoint. For this purpose, a hybrid density functional theory is employed to analyze the catalytic mechanism of the oxygen reduction at the fuel cell cathode. Major steps in the oxygen reduction that include the oxygen adsorption on solid metal clusters (e.g. Cu and Pt) and complete four proton transfer steps are simulated. Proton transfer processes from hydroniums to the adsorbed oxygen molecules to produce water… More >

Hao Dong¹, Yufeng Nie^1,2, Zihao Yang¹, Yang Zhang¹, Yatao Wu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.111, No.5, pp. 395-419, 2016, DOI:10.3970/cmes.2016.111.395

Abstract In this paper, we discuss the numerical accuracy of asymptotic homogenization method (AHM) and multiscale finite element method (MsFEM) for periodic composite materials. Through numerical calculation of the model problems for four kinds of typical periodic composite materials, the main factors to determine the accuracy of first-order AHM and second-order AHM are found, and the physical interpretation of these factors is given. Furthermore, the way to recover multiscale solutions of first-order AHM and MsFEM is theoretically analyzed, and it is found that first-order AHM and MsFEM provide similar multiscale solutions under some assumptions. Finally, numerical experiments verify that MsFEM is… More >

Chung-Fu Chen¹, Yi-Chia Cheng¹, Che-Wun Hong^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.109-110, No.3, pp. 263-283, 2015, DOI:10.3970/cmes.2015.109.263

Abstract Based on the Hellmann-Feynman theorem, which integrates the molecular dynamics simulation with computational quantum mechanics, this research simulates the ionic transport in the LiCl-KCl molten salt materials using so called “first principles molecular dynamics (FPMD)” technique without employing an empirical potential model. The main purpose of this computational FPMD focuses on the evaluation of important transport properties, such as diffusion coefficient, ionic conductivity, shear viscosity, and thermal conductivity, using the Green-Kubo relationship. All simulation results agree well with experimental data published in existing literatures within an acceptable range. FPMD calculations are proved to be a powerful tool for prediction of… More >

W.H. Chen¹, H.C. Cheng^2,3, C.F. Yu^1,3

CMES-Computer Modeling in Engineering & Sciences, Vol.109-110, No.1, pp. 1-13, 2015, DOI:10.3970/cmes.2015.109.001

Abstract This study aims at exploring the interfacial adhesion strength between solder bump and four typical under bump metallurgies (UBMs), i.e., Cu/Ni, Cu/TiW, Cu/Ni/Cr and /Cu/V/Cr, at atomistic scale. The average bond length and interfacial adhesion stress of the Sn-3.5Ag/Cu/Ni, Sn-3.5Ag/Cu/TiW, Sn-3.5Ag/Cu/Ni/Cr and Sn-3.5Ag/Cu/V/Cr micro-bump interconnects are calculated through the firstprinciples density functional theory (DFT) calculation to estimate the interfacial adhesion strength between the solder bump and UBMs. In addition, by investigating the electric field effect on the average bond length and adhesive stress, the combination of solder bump and UBM with better interfacial adhesion strength and electromigration resistance ability can… More >

Xu Yong^1,2, Feng Jing¹, Xu Wei¹, Gu Rencai¹

CMES-Computer Modeling in Engineering & Sciences, Vol.106, No.5, pp. 309-322, 2015, DOI:10.3970/cmes.2015.106.309

Abstract In this paper, bifurcation analysis and numerical simulations are performed on the FitzHugh-Nagumo system in the presence of Lévy stable noise. The stationary probability density functions are obtained to examine the influences of noise intensity and stability index. Results show that under the influences of noise intensity and stability index, the dynamic of the FitzHugh-Nagumo model can be well characterized through the concept of stochastic bifurcation, consisting in qualitative changes of the stationary probability distribution. Then, the mean passage time between the resting and action state is investigated as functions of noise intensity and stability index of the external signal… More >

S. Masuri¹, K. K. Tamma²

CMES-Computer Modeling in Engineering & Sciences, Vol.106, No.3, pp. 147-168, 2015, DOI:10.3970/cmes.2015.106.147

Abstract The objective in this paper is to extend the previously developed twoparameter GS4-1 (Generalized Single System Single Solve for 1st order transient systems) computational framework from parabolic to hyperbolic type of applications pertaining to first order linear transient systems. In particular, attention is paid to the selective control feature inherit in the framework, which is the new feature that enables different amounts of high frequency damping for the primary variable and its time derivative, allowing for physically accurate solutions of all variables in the system. This is in contrast to having only limited, often indiscriminate, control of the high frequency… More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.98, No.4, pp. 375-407, 2014, DOI:10.3970/cmes.2014.098.375

Abstract In this paper we study the nonlinear dynamical system x^·=f(x,t) from a newly developed theory, viewing the time-varying function of sign(||f||²||x||²− 2(f·x)²) = −sign(cos 2θ) as a key factor, where θ is the intersection angle between x and f. It together with sign(cos θ) can reveal the complexity of nonlinear Duffing oscillator and a quadratic ship rolling oscillator. The barcode is formed by plotting sign(||f||²||x||²− 2(f·x)²) with respect to time. We analyze the barcode to point out the bifurcation of subharmonic motions and the range of chaos in the parameter space. The bifurcation diagram obtained by plotting the percentage… More >

Wen-Hwa Chen^1,2, Ching-Feng Yu¹, Hsien-Chie Cheng^2,3

CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.2, pp. 119-131, 2014, DOI:10.3970/cmes.2014.100.119

Abstract The aim of the study is to investigate the interactions between Sn adatoms in a solder bump and three typical Sn-based intermetallic compounds (IMCs) surface, i.e., Cu₃Sn, Cu₆Sn₅, and Ni₃Sn₄, at the atomistic scale. The adsorption energy, average bond length, and bond population of the Sn/Cu₃Sn, Sn/Cu₆Sn₅,and Sn/Ni₃Sn₄ systems are calculated through the first-principles density functional theory (DFT) calculation to investigate how the Sn adatoms influence the IMC surface. The calculated results show that the Sn atoms on the Cu₃Sn (0 0 1) surface hold the largest adsorption energy, average bond length and bond population, implying that the Cu₃Sn (0… More >

Leiting Dong^1,2, Satya N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.89, No.5, pp. 417-458, 2012, DOI:10.3970/cmes.2012.089.417

Abstract Two-dimensional weakly-singular Symmetric Galerkin Boundary Elements (SGBEMs) are developed, following the work of [Han and Atluri (2003)], using non-hypersingular integral equations for tractions. Specifically, the present 2D SGBEM is used to compute the stress intensity factors for arbitrary-shaped line cracks, including embedded, edge, branching, and intersecting cracks. The computed stress intensity factors show high accuracy, even with very coarse meshes. The non-collinear mixed-mode fatigue growth analysis of cracks requires a very minimal effort¡ªsimply extending the cracks by adding an element to each crack tip, in the direction of the crack-growth as determined by a physics-based criterion. Moreover, by rearranging the… More >