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  • Open Access

    ARTICLE

    A State Space Approach for the Analysis of Doubly Curved Functionally Graded Elastic and Piezoelectric Shells

    Chih-Ping Wu1,2, Kuo-Yen Liu2

    CMC-Computers, Materials & Continua, Vol.6, No.3, pp. 177-200, 2007, DOI:10.3970/cmc.2007.006.177

    Abstract Based on the three-dimensional (3D) piezoelectricity, we present the exact solutions of simply-supported, doubly curved functionally graded (FG) elastic and piezoelectric shells using a state space approach. A set of the dimensionless coordinates and field variables is introduced in the present formulation to prevent from the ill-conditioned problem in the relevant computation. By means of direct elimination, we reduce the twenty-two basic differential equations to a set of eight state variable equations (or state equations) with variable coefficients of the thickness coordinate. By means of the successive approximation method, we artificially divide the shell into… More >

  • Open Access

    ARTICLE

    A simple and accurate four-node quadrilateral element using stabilized nodal integration for laminated plates

    H. Nguyen-Van1, N. Mai Duy2, T. Tran-Cong 3

    CMC-Computers, Materials & Continua, Vol.6, No.3, pp. 159-176, 2007, DOI:10.3970/cmc.2007.006.159

    Abstract This paper reports the development of a simple but efficient and accurate four-node quadrilateral element for models of laminated, anisotropic plate behaviour within the framework of the first-order shear deformation theory. The approach incorporates the strain smoothing method for mesh-free conforming nodal integration into the conventional finite element techniques. The membrane-bending part of the element stiffness matrix is calculated by the line integral on the boundaries of the smoothing elements while the shear part is performed using an independent interpolation field in the natural co-ordinate system. Numerical results show that the element offered here is More >

  • Open Access

    ARTICLE

    Numerical Analysis of the Effect of Diffusion and Creep Flow on Cavity Growth

    J. Oh1, N. Katsube2, F.W. Brust3

    CMC-Computers, Materials & Continua, Vol.6, No.3, pp. 129-158, 2007, DOI:10.3970/cmc.2007.006.129

    Abstract In this paper, intergranular cavity growth in regimes, where both surface diffusion and deformation enhanced grain boundary diffusion are important, is studied. In order to continuously simulate the cavity shape evolution and cavity growth rate, a fully-coupled numerical method is proposed. Based on the fully-coupled numerical method, a gradual cavity shape change is predicted and this leads to the adverse effect on the cavity growth rate. As the portion of the cavity volume growth due to jacking and viscoplastic deformation in the total cavity volume growth increases, spherical cavity evolves to V-shaped cavity. The obtained More >

  • Open Access

    ARTICLE

    A Consistent Computation of Magnetization Reversal under a Circularly Polarized Field and an Anisotropy Field

    Chein-Shan Liu1

    CMC-Computers, Materials & Continua, Vol.6, No.2, pp. 117-128, 2007, DOI:10.3970/cmc.2007.006.117

    Abstract In this paper the Landau-Lifshitz equation is subjected to a circularly polarized field in the plane, as well as both a dc field and an anisotropy field along the vertical easy axis perpendicular to the plane. The representation of Landau-Lifshitz equation in the Minkowski space is a Lie-type system. By performing a computation through the Lie-group solvers we can develop a consistent numerical method, which satisfies the consistency condition exactly, and thus can retain the invariant behavior. Then, we use the consistent numerical method to investigate the magnetization reversal, whose switching criterion is displayed through More >

  • Open Access

    ARTICLE

    Flexural-Torsional Buckling and Vibration Analysis of Composite Beams

    E.J. Sapountzakis1, G.C. Tsiatas2

    CMC-Computers, Materials & Continua, Vol.6, No.2, pp. 103-116, 2007, DOI:10.3970/cmc.2007.006.103

    Abstract In this paper the general flexural-torsional buckling and vibration problems of composite Euler-Bernoulli beams of arbitrarily shaped cross section are solved using a boundary element method. The general character of the proposed method is verified from the formulation of all basic equations with respect to an arbitrary coordinate system, which is not restricted to the principal one. The composite beam consists of materials in contact each of which can surround a finite number of inclusions. It is subjected to a compressive centrally applied load together with arbitrarily transverse and/or torsional distributed or concentrated loading, while… More >

  • Open Access

    ARTICLE

    Cased Hole Flexural Modes in Anisotropic Formations

    Ping’en Li1, Xianyue Su1,2, Youquan Yin1

    CMC-Computers, Materials & Continua, Vol.6, No.2, pp. 93-102, 2007, DOI:10.3970/cmc.2007.006.093

    Abstract Based on the perturbation method, for flexural wave in cased hole in anisotropic formation, the alteration in the phase velocity caused by the differences in elastic constants between anisotropic formation of interest and a reference, or unperturbed isotropic formation is obtained. Assuming the cased hole is well bonded, the Thomson-Haskell transfer matrix method is applied to calculate the dispersion relation of flexural wave in cased hole in unperturbed isotropic formation. Both the cases of a fast and slow formation are considered where the symmetry axis of a transversely isotropic (TI) formation makes an angle with… More >

  • Open Access

    ARTICLE

    A General Equation for Stress Concentration in Countersunk Holes

    Kunigal N. Shivakumar1, Anil Bhargava2, Sameer Hamoush3

    CMC-Computers, Materials & Continua, Vol.6, No.2, pp. 71-92, 2007, DOI:10.3970/cmc.2007.006.071

    Abstract A detailed and accurate three-dimensional finite element stress analysis was conducted on countersunk rivet holes in a plate subjected to tension loading. The analysis included a wide range of countersunk depths, plate thicknesses, countersunk angles and plate widths. The study confirmed some of the previous results, addressed their differences, provided many new results, and investigated countersunk angle and width effects. Using the detailed FE results and the limiting conditions, a general equation for stress concentration was developed and verified. More >

  • Open Access

    ARTICLE

    An Adaptive Multi-resolution Method for Solving PDE's

    V. Kozulić1, H. Gotovac1, B. Gotovac1

    CMC-Computers, Materials & Continua, Vol.6, No.2, pp. 51-70, 2007, DOI:10.3970/cmc.2007.006.051

    Abstract In this paper, we present a multi-resolution adaptive algorithm for solving problems described by partial differential equations. The technique is based on the collocation method using Fup basis functions, which belong to a class of Rvachev's infinitely differentiable finite functions. As it is possible to calculate derivation values of Fup basis functions of high degree in a precise yet simple way, so it is possible to efficiently apply strong formulation procedures. The mesh free method developed in this work is named Adaptive Fup Collocation Method (AFCM). The distribution of collocation points within the observed area… More >

  • Open Access

    ARTICLE

    Evaluations of the BGA Solder Ball Shape by Using Energy Method

    Heng Cheng Lin1,2, Chieh Kung3, Rong Sheng Chen2

    CMC-Computers, Materials & Continua, Vol.6, No.1, pp. 43-50, 2007, DOI:10.3970/cmc.2007.006.043

    Abstract Presented herein are the evaluation results of the BGA solder ball shape using energy method, two types of solder, viz. Sn37Pb and Sn80Pb, are selected .The geometry of the solder bump is firstly estimated using free computer software, the Surface Evolver, an interactive program which is an energy-based approach for the study of liquid droplet surfaces shaped by surface tension and other energies. The solder bump is then numerically constructed in a finite element model that simulates a BGA package. The influences of both upper and bottom solder pad radii, the surface tension on the… More >

  • Open Access

    ARTICLE

    Robust Reduction Method for Biomolecules Modeling

    Kilho Eom1, Jeong-Hee Ahn2, Seung-Chul Baek2, Jae-In Kim2, Sungsoo Na2,3

    CMC-Computers, Materials & Continua, Vol.6, No.1, pp. 35-42, 2007, DOI:10.3970/cmc.2007.006.035

    Abstract This paper concerns the application and demonstration of robust reduction methodology for biomolecular structure modeling, which is able to estimate dynamics of large proteins. The understanding of large protein dynamics is germane to gain insight into biological functions related to conformation change that is well described by normal modes. In general, proteins exhibit the complicated potential field and the large degrees of freedom, resulting in the computational prohibition for large protein dynamics. In this article, large protein dynamics is investigated with modeling reduction schemes. The performance of hierarchical condensation methods implemented in the paper is More >

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