H. T. Xiao^1,2,3, Y. Y. Xie^1,2, Z. Q. Yue⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.109-110, No.1, pp. 55-80, 2015, DOI:10.3970/cmes.2015.109.055

Abstract This paper examines the problem of a square-shaped crack embedded in a layered half-space whose external surface is subject to a uniform loading over a rectangular area. Two novel numerical methods and the superposition principle in fracture mechanics are employed for the analysis of the crack problem. The numerical methods are based on the fundamental solution of a multilayered elastic medium and are, respectively, applied to calculate the stress fields of layered halfspace without cracks and the discontinuous displacements of crack surfaces in layered halfspace. The stress intensity factor (SIF) values are calculated using discontinuous displacements and the influence 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 >

Jason F. Hammond¹, Elizabeth J. Stewart², John G. Younger³, Michael J.Solomon², David M. Bortz^4,5

CMES-Computer Modeling in Engineering & Sciences, Vol.98, No.3, pp. 295-340, 2014, DOI:10.32604/cmes.2014.098.295

Abstract The overall goal of this work is to develop a numerical simulation which correctly describes a bacterial biofilm fluid-structure interaction and separation process. In this, the first of a two-part effort, we fully develop a convergent scheme and provide numerical evidence for the method order as well as a full 3D separation simulation. We use an immersed boundary-based method (IBM) to model and simulate a biofilm with density and viscosity values different from than that of the surrounding fluid. The simulation also includes breakable springs connecting the bacteria in the biofilm which allows the inclusion of erosion and detachment into… More >

H.T. Zhu ¹

CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.3, pp. 281-298, 2014, DOI:10.3970/cmes.2014.097.281

Abstract This study is concerned with a solution procedure to obtain the probability density function (PDF) of a vibro-impact Duffing oscillator under fully correlated external and parametric Gaussian white noises. The proposed solution procedure consists of three steps. In the first step, the Zhuravlev non-smooth coordinate transformation is adopted to introduce an additional impulsive damping term, in which the original vibro-impact oscillator is converted into a new oscillator without any barrier. After that, the PDF of the new oscillator is obtained by solving the Fokker-Planck equation with the exponential-polynomial closure method. Last, the PDF of the original oscillator is formulated in… More >

Guoqing Yang¹, Baotong Li^2,3, Yang Wang², Jun Hong²

CMES-Computer Modeling in Engineering & Sciences, Vol.103, No.4, pp. 251-279, 2014, DOI:10.3970/cmes.2014.103.251

Abstract Mechanical behaviors arising at the contact interface largely depend on its surface topographies, particularly when it comes to rough surfaces. A numerical simulation based on an appropriate characterization of rough surfaces especially in terms of three dimensional can be of great significance when it comes to capturing the deformation patterns of micro-scale contacts. In this paper, a simple and practical scheme is developed to generate 3D rough surfaces and to analyze and evaluate the contact characteristics. Firstly amplitude and spatial statistical characterizations of asperities are introduced to avert from the redundancy of topography data caused by traditional measuring methods. A… More >

Po-Wei Li¹, Chia-Ming Fan^1,2, Chun-Yu Chen¹, Cheng-Yu Ku¹

CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.5, pp. 319-350, 2014, DOI:10.3970/cmes.2014.101.319

Abstract A combination of the generalized finite difference method (GFDM), the implicit Euler method and the Newton-Raphson method is proposed to efficiently and accurately analyze the density-driven groundwater flows. In groundwater hydraulics, the problems of density-driven groundwater flows are usually difficult to be solved, since the mathematical descriptions are a system of time- and space-dependent nonlinear partial differential equations. In the proposed numerical scheme, the GFDM and the implicit Euler method were adopted for spatial and temporal discretizations of governing equations. The GFDM is a newly-developed meshless method and is truly free from time-consuming mesh generation and numerical quadrature. Based on… 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 >

Xiaokui Yue¹, Yong Xu², Jianping Yuan¹

CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.4, pp. 277-291, 2013, DOI:10.3970/cmes.2013.093.277

Abstract In this paper, a stochastic averaging method is derived for a class of non-linear stochastic systems under parametrical Poisson white noise excitation, which may be used to model the beam-beam interaction models in particle accelerators. The averaged Generalized Fokker-Planck equation is derived and the approximate stationary solution of the averaged Generalized Fokker-Planck equation is solved by using perturbation method. The present method applied in this paper can reduce the dimensions of stochastic ODE from 2n to n, which simplify the complex stochastic ODE, and then the analytical stationary solutions can be obtained. An example is employed to demonstrate the procedure… More >

Jian Hua Rong^1,2,3, Zhi Jun Zhao⁴, Yi Min Xie⁵, Ji Jun Yi^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.90, No.3, pp. 211-231, 2013, DOI:10.3970/cmes.2013.090.211

Abstract Similar periodic structures have been widely used in engineering. In order to obtaining the optimal similar periodic structures, a topology optimization method of similar periodic structures with multiple displacement constraints is proposed in this paper. Firstly, in the proposed method, the design domain is divided into sub-domains. Secondly, a penalty term considering discrete conditions of density variables is introduced into the objective function, and the reciprocal density exponents of structural elements are taken as design variables. A topological optimization model of a similar periodic continuum structure with the objective function being the structural mass and the constraint functions being structural… More >