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  • Open Access

    ARTICLE

    Stability of Solder Bridging for Area Array Type Packaging

    Wen-Hwa Chen1,2, Shu-Ru Lin2, Kuo-Ning Chiang2,3

    CMC-Computers, Materials & Continua, Vol.2, No.3, pp. 151-162, 2005, DOI:10.3970/cmc.2005.002.151

    Abstract As ultra-fine-pitch technologies are adopted to enhance the performance of electronic packaging, solder bridging becomes an urgently serious defect. This work presents a computational model using the Surface Evolver program to analyze the stability of solder bridging for area array type packaging. Several factors that affect the stability of solder bridging spanning two identical circular pads are considered herein, including the pad size, the total volume of solder bumps, the pitch between adjacent pads, the contact angle between the molten solder alloy and the pad, the contact angle between the molten solder alloy and the… More >

  • Open Access

    ARTICLE

    Three-dimensional Finite Element Buckling Analysis of Honeycomb Sandwich Composite Shells with Cutouts

    J. Li, Z. H. Xiang, M. D. Xue1

    CMC-Computers, Materials & Continua, Vol.2, No.2, pp. 139-150, 2005, DOI:10.3970/cmc.2005.002.139

    Abstract This paper investigates the buckling response of honeycomb sandwich composite shells with cutouts under axial compression. The Wilson's incompatible solid Finite Element (FE) is used around cutouts to obtain the detail stress distribution there. While to reduce the computational expense, a special multilayered relative degrees-of-freedom (DOF) shell FE is used to model the regions far from the cutouts. The efficiency and accuracy of this modeling scheme are illustrated by two benchmarks. Then parametric studies are carried out to reveal how the buckling response is influenced by the area, the shape and the orientation of cutouts. More >

  • Open Access

    ARTICLE

    A Three-Dimensional Asymptotic Theory of Laminated Piezoelectric Shells

    Chih-Ping Wu, Jyh-Yeuan Lo, Jyh-Ka Chao1

    CMC-Computers, Materials & Continua, Vol.2, No.2, pp. 119-138, 2005, DOI:10.3970/cmc.2005.002.119

    Abstract An asymptotic theory of doubly curved laminated piezoelectric shells is developed on the basis of three-dimensional (3D) linear piezoelectricity. The twenty-two basic equations of 3D piezoelectricity are firstly reduced to eight differential equations in terms of eight primary variables of elastic and electric fields. By means of nondimensionalization, asymptotic expansion and successive integration, we can obtain recurrent sets of governing equations for various order problems. The two-dimensional equations in the classical laminated piezoelectric shell theory (CST) are derived as a first-order approximation to the 3D piezoelectricity. Higher-order corrections as well as the first-order solution can More >

  • Open Access

    ARTICLE

    Bond Graph Modelling and Simulation of Static Recrystallization Kinetics in Multipass Hot Steel Rolling

    S.K. Pal1, D.A. Linkens2

    CMC-Computers, Materials & Continua, Vol.2, No.2, pp. 113-118, 2005, DOI:10.3970/cmc.2005.002.113

    Abstract In hot rolling, the final thickness of the strip is achieved through plastic deformation of the original stock by a series of counter-rotating rollers. In this work, static recrystallization kinetics in between two stages of steel rolling has been modelled, and simulation studies have also been performed to find out the effect of entry temperature on the recrystallization kinetics. A viable bond graph model has been developed to study the kinetics of the process. Low-carbon steel has been considered for this purpose. More >

  • Open Access

    ARTICLE

    A CFD/CSD Model for Transonic Flutter

    Tong-qing Guo, Zhi-liang Lu1

    CMC-Computers, Materials & Continua, Vol.2, No.2, pp. 105-112, 2005, DOI:10.3970/cmc.2005.002.105

    Abstract In this paper, a rapid deforming technique is developed to generate dynamic, three-dimensional, multi-block, mesh. The second-order Runge-Kutta time-marching method is used to solve the structural equations of motion. A dual-time method and finite volume discretization are applied for the unsteady Euler/Navier-Stokes equations to calculate the aerodynamic forces, in which the physical time step is synchronous with the structural equations of motion. The Spalart-Allmaras turbulence model is adopted for a turbulent flow. Due to mass dissimilarity, exiting in flutter calculations for a compressible flow, methods of variable mass and variable stiffness are developed to calculate More >

  • Open Access

    ARTICLE

    Analytical Approach to Cell Geometry Description

    P. Dabnichki1, A. Zhivkov2

    CMC-Computers, Materials & Continua, Vol.2, No.2, pp. 97-104, 2005, DOI:10.3970/cmc.2005.002.097

    Abstract A novel method for geometric reconstruction of smooth pseudo-rotational objects based on elliptic functions is developed. Based on the apparatus of theta functions analytical expressions for the main geometric invariants are derived. Reconstruction of asymmetric and irregular objects is illustrated. The advantages of the proposed technique lay in the following: i) reconstruction is computationally very fast and would allow a qualitative change in the current research practices, i.e. real-time monitoring and analysis of the responses of large cell samples ii) the accuracy of the method is very high and can be flexibly varied iii) the More >

  • Open Access

    ARTICLE

    Chance-Constrained Optimization of Pumping in Coastal Aquifers by Stochastic Boundary Element Method and Genetic Algorithm

    B. Amaziane1, A. Naji2, D. Ouazar3, A. H.-D. Cheng4

    CMC-Computers, Materials & Continua, Vol.2, No.2, pp. 85-96, 2005, DOI:10.3970/cmc.2005.002.085

    Abstract In this paper the optimization of groundwater pumping in coastal aquifers under the threat of saltwater intrusion is investigated. The aquifer is inhomogeneous and contains several hydraulic conductivities zones. The aquifer data such as the hydraulic conductivities are uncertain, but with their expected mean and standard deviation values given. A stochastic boundary element method based on the perturbation technique is employed as the simulation tool. The stochastic optimization is handled by the chance-constrained programming. Genetic algorithm is selected as the optimization tool. Numerical examples of deterministic and stochastic problems are provided to demonstrate the feasibility More >

  • Open Access

    ARTICLE

    MLPG Method Based on Rankine Source Solution for Simulating Nonlinear Water Waves

    Q.W. Ma1

    CMES-Computer Modeling in Engineering & Sciences, Vol.9, No.2, pp. 193-210, 2005, DOI:10.3970/cmes.2005.009.193

    Abstract Recently, the MLPG (Meshless Local Petrov-Galerkin Method) method has been successfully extended to simulating nonlinear water waves [Ma, (2005)]. In that paper, the author employed the Heaviside step function as the test function to formulate the weak form over local sub-domains, acquiring an expression in terms of pressure gradient. In this paper, the solution for Rankine sources is taken as the test function and the local weak form is expressed in term of pressure rather than pressure gradient. Apart from not including pressure gradient, velocity gradient is also eliminated from the weak form. In addition, More >

  • Open Access

    ARTICLE

    3-D Modeling of a composite material reinforced with multiple thickly coated particles using the infinite element method

    D.S. Liu1,2 , C.Y. Chen2 , D.Y. Chiou3

    CMES-Computer Modeling in Engineering & Sciences, Vol.9, No.2, pp. 179-192, 2005, DOI:10.3970/cmes.2005.009.179

    Abstract A three-dimensional heterogeneous infinite element method (HIEM) for modeling inclusions with interphases in composite materials is presented. This special element is formulated based on the conventional finite element method (FEM) using the similarity stiffness property and matrix condensation operations. An HIE-FE coupling scheme is also developed and implemented using the commercial software ABAQUS to conduct the elastostatic analysis. The proposed approach was validated first to study heterogeneous material containing one spherical inclusion. The displacement and stress variations around the inclusion vicinity are verified against conventional FEM. The proposed approach was next applied to analyze the effective More >

  • Open Access

    ARTICLE

    A Combination of Group Preserving Scheme and Runge-Kutta Method for the Integration of Landau-Lifshitz Equation

    Chein-Shan Liu, Yu-Ling Ku

    CMES-Computer Modeling in Engineering & Sciences, Vol.9, No.2, pp. 151-178, 2005, DOI:10.3970/cmes.2005.009.151

    Abstract In this paper we are concerned with the integration of a semi-discretized version of the Landau-Lifshitz equation, which is fundamental to describe the magnetization dynamics in micro/nano-scale magnetic systems. The resulting ordinary differential equations at the interior grid points are numerically integrated by a combination of the group preserving scheme derived by Liu (2004a) and the fourth-order Runge-Kutta method, abbreviated as GPS-RK4. The new method not only conserves the magnetization magnitude and has the fourth-order accuracy, but also preserves the Lyapunov property of the Landau-Lifshitz equation, namely the free energy is decreasing with time. In More >

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