A. Chakraborty¹

CMES-Computer Modeling in Engineering & Sciences, Vol.40, No.2, pp. 105-132, 2009, DOI:10.3970/cmes.2009.040.105

Abstract A mathematical model is presented in this work that describes the behavior of porous piezoelectric materials subjected to mechanical load and electric field. The model combines Biot's theory of poroelasticity and the classical theory of piezoelectric material wherein it is assumed that piezoelectric coupling exists only with the solid phase of the porous medium. This model is used to analyze the stress and electric wave generated in bone and porous Lead-Zirconate-Titanate (PZT) due to high frequency pulse loading. The governing partial differential equations are solved in the frequency domain by transforming them into a polynomial eigenvalue structure. This approach permits… More >

Shaw-Jyh Shin¹, Chen-Hung Huang², Y.C. Shiah³

CMES-Computer Modeling in Engineering & Sciences, Vol.40, No.1, pp. 83-104, 2009, DOI:10.3970/cmes.2009.040.083

Abstract Owing to the CTE (Coefficient of Thermal Expansion) mismatch among solder joints, IC (Integrated Circuit) chip, and PCB (Printed Circuit Board), electronic packages shall experience fatigue failure after going though a period of thermal cycling. As a major means to enhance the reliability of the solder joints, underfill is often dispensed to fill the gap between the die and the substrate. This study aims at investigating how the underfill may affect the thermal fatigue life of WLCSP (Wafer Level Chip Scale Package) by means of FEA (finite element analysis). In this study, the thermal fatigue life of the WLCSP was… More >

A. Takei¹, S. Yoshimura¹, H. Kanayama²

CMES-Computer Modeling in Engineering & Sciences, Vol.40, No.1, pp. 63-82, 2009, DOI:10.3970/cmes.2009.040.063

Abstract This paper describes a large-scale finite element analysis (FEA) for a high-frequency electromagnetic field of Maxwell equations including the displacement current. A stationary Helmholtz equation for the high-frequency electromagnetic field analysis is solved by considering an electric field and an electric scalar potential as unknown functions. To speed up the analysis, the hierarchical domain decomposition method (HDDM) is employed as a parallel solver. In this study, the Parent-Only type (Parallel processor mode: P-mode) of the HDDM is employed. In the P-mode, Parent processors perform the entire FEA. In this mode, all CPUs can be used without idling in an environment… More >

Sergia Colli¹, Massimiliano Gei¹, Davide Bigoni^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.40, No.1, pp. 29-62, 2009, DOI:10.3970/cmes.2009.040.029

Abstract Incremental plane strain deformations superimposed upon a uniformly stressed and deformed nonlinear elastic (compressible) body are treated by developing {\it ad hoc} boundary integral equations that, discretized, lead to a novel boundary element technique. The approach is a generalization to compressible elasticity of results obtained by Brun, Capuani, and Bigoni (2003, Comput. Methods Appl. Mech. Engrg. 192, 2461-2479), and is based on a Green's function here obtained through the plane-wave expansion method. New expressions for Green's tractions are determined, where singular terms are solved in closed form, a feature permitting the development of a optimized numerical code. An application of… More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.40, No.1, pp. 1-28, 2009, DOI:10.3970/cmes.2009.040.001

Abstract We consider an inverse problem of Laplace equation by recoverning boundary value on the inner circle of a two-dimensional annulus from the overdetermined data on the outer circle. The numerical results can be used to determine the Robin coefficient or crack's position inside a disk from the measurements of Cauchy data on the outer boundary. The Fourier series is used to formulate the first kind Fredholm integral equation for the unknown data f(θ) on the inner circle. Then we consider a Lavrentiev regularization, by adding an extra term αf(θ) to obtain the second kind Fredholm integral equation. The termwise separable… More >

Chunhai Kou¹, Ye Yan², Jian Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.39, No.3, pp. 301-318, 2009, DOI:10.3970/cmes.2009.039.301

Abstract In the paper, stability for fractional order differential equations is studied. Then the result obtained is applied to analyse the stability of equilibrium for the model of HIV. More >

Donghuan Liu¹, Xiaoping Zheng^1,2, Yinghua Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.39, No.3, pp. 263-300, 2009, DOI:10.3970/cmes.2009.039.263

Abstract A discontinuous Galerkin (DG) finite element method for the heat conduction problems with local high gradient and thermal contact resistance is presented. The DG formulation is constructed by employing the stabilization term and the Bassi-Rebay numerical flux term. The stabilization term is defined by a penalization of the temperature jump at the interface. By eliminating the penalization term of the temperature jump in the region of local high gradient and imperfect contact interfaces, the present DG method is applied to solve problems involving local high gradient and thermal contact resistance where the numerical flux is obtained from the definition of… More >

W. Attaporn¹, H. Koguchi²

CMES-Computer Modeling in Engineering & Sciences, Vol.39, No.3, pp. 237-262, 2009, DOI:10.3970/cmes.2009.039.237

Abstract In the present study, a stress singularity field along free edges meeting at a corner in a three-dimensional joint structure is investigated. The order of stress singularity is determined using an eigen analysis based on a finite element method. Intensities of stress singularity not only at the corner but also along the free edge of interface are determined directly without any post-processing by a new FEM formulation referred to as a three-dimensional enriched FEM. Result in the present analysis is also compared with that in another numerical method. It was slightly larger than the intensity of stress singularity, which was… More >

E. Tonti¹, F. Zarantonello¹

CMES-Computer Modeling in Engineering & Sciences, Vol.39, No.3, pp. 201-236, 2009, DOI:10.3970/cmes.2009.039.201

Abstract The theory of elasticity is usually formulated using differential calculus. We will show that it is possible to give an algebraic or discrete or finite formulation, by starting directly from experimental laws, i.e. by avoiding any discretization process of the differential equations. This direct formulation can be immediately used for numerical solution in elasticity problems and, from a theoretical point of view, it shows some interesting features which are hidden in the differential formulation or are not considered at all. More >

Chun-Lang Yeh¹

CMES-Computer Modeling in Engineering & Sciences, Vol.39, No.2, pp. 179-200, 2009, DOI:10.3970/cmes.2009.039.179

Abstract In this research, the atomization process of a nanojet is investigated by molecular dynamics simulation. Liquid argon nanojet made of 44000 Lennard-Jones molecules is examined under various simulation parameters to study their influence on the nanojet atomization process. Snapshots of the molecules, evolution of the density field, and evolution of the intermolecular force are analyzed. The present simulation results can provide insight into the fundamental mechanism of the atomization process and will be helpful for the design of nanojet devices such as nano-printer or nano-sprayer. More >