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  • Open Access


    Identification of dynamical systems with fractional derivative damping models using inverse sensitivity analysis

    R Sivaprasad1,2, S Venkatesha1, C S Manohar1,3

    CMC-Computers, Materials & Continua, Vol.9, No.3, pp. 179-208, 2009, DOI:10.3970/cmc.2009.009.179

    Abstract The problem of identifying parameters of time invariant linear dynamical systems with fractional derivative damping models, based on a spatially incomplete set of measured frequency response functions and experimentally determined eigensolutions, is considered. Methods based on inverse sensitivity analysis of damped eigensolutions and frequency response functions are developed. It is shown that the eigensensitivity method requires the development of derivatives of solutions of an asymmetric generalized eigenvalue problem. Both the first and second order inverse sensitivity analyses are considered. The study demonstrates the successful performance of the identification algorithms developed based on synthetic data on one, two and a 33… More >

  • Open Access


    Eigen-vibrations of Plates made of Functionally Graded Material

    H. Altenbach1, V. A. Eremeyev2

    CMC-Computers, Materials & Continua, Vol.9, No.2, pp. 153-178, 2009, DOI:10.3970/cmc.2009.009.153

    Abstract Within the framework of the direct approach to the plate theory we consider natural oscillations of plates made of functionally graded materials taking into account both the rotatory inertia and the transverse shear stiffness. It is shown that in some cases the results based on the direct approach differ significantly from the classical estimates. The reason for this is the non-classical computation of the transverse shear stiffness. More >

  • Open Access


    A Quasi-Boundary Semi-Analytical Method for Backward in Time Advection-Dispersion Equation

    Chein-Shan Liu1, Chih-Wen Chang2, Jiang-Ren Chang2,3

    CMC-Computers, Materials & Continua, Vol.9, No.2, pp. 111-136, 2009, DOI:10.3970/cmc.2009.009.111

    Abstract In this paper, we take the advantage of an analytical method to solve the advection-dispersion equation (ADE) for identifying the contamination problems. First, the Fourier series expansion technique is employed to calculate the concentration field C(x, t) at any time t< T. Then, we consider a direct regularization by adding an extra term αC(x,0) on the final condition to carry off a second kind Fredholm integral equation. The termwise separable property of the kernel function permits us to transform itinto a two-point boundary value problem. The uniform convergence and error estimate of the regularized solution Cα(x,t) are provided and a… More >

  • Open Access


    Construction of Green's function using null-field integral approach for Laplace problems with circular boundaries

    Jeng-Tzong Chen1,2, Jia-Nan Ke1, Huan-Zhen Liao1

    CMC-Computers, Materials & Continua, Vol.9, No.2, pp. 93-110, 2009, DOI:10.3970/cmc.2009.009.093

    Abstract A null-field approach is employed to derive the Green's function for boundary value problems stated for the Laplace equation with circular boundaries. The kernel function and boundary density are expanded by using the degenerate kernel and Fourier series, respectively. Series-form Green's function for interior and exterior problems of circular boundary are derived and plotted in a good agreement with the closed-form solution. The Poisson integral formula is extended to an annular case from a circle. Not only an eccentric ring but also a half-plane problem with an aperture are demonstrated to see the validity of the present approach. Besides, a… More >

  • Open Access


    Simulation of delamination by means of cohesive elements using an explicit finite element code

    E.V. González1, P. Maimí1, A. Turon1, P.P. Camanho2, J. Renart1

    CMC-Computers, Materials & Continua, Vol.9, No.1, pp. 51-92, 2009, DOI:10.3970/cmc.2009.009.051

    Abstract This paper presents the formulation of a tri-dimensional cohesive element implemented in a user-written material subroutine for explicit finite element analysis. The cohesive element simulates the onset and propagation of the delamination in advanced composite materials. The delamination model is formulated by using a rigorous thermodynamic framework which takes into account the changes of mixed-mode loading conditions. The model is validated by comparing the finite element predictions with experimental data obtained in interlaminar fracture tests under quasi-static loading conditions. More >

  • Open Access


    Strategic Estimation of Kinetic Parameters in VGO Cracking

    Praveen Ch.1, Shishir Sinha1,2

    CMC-Computers, Materials & Continua, Vol.9, No.1, pp. 41-50, 2009, DOI:10.3970/cmc.2009.009.041

    Abstract Fluid catalytic cracking (FCC) unit plays most important role in the economy of a modern refinery that it is use for value addition to the refinery products. Because of the importance of FCC unit in refining, considerable effort has been done by scientists till now on the modelling of this unit for better understanding and improved productivity. To model a FCC unit we have to know the unknown kinetic parameters of the governing equations.
    The basic aim of this paper is to prove that MATLABTM can be used as a tool to find unknown kinetic parameters of governing equations for… More >

  • Open Access


    A Discrete Fourier Transform Framework for Localization Relations

    D.T. Fullwood1, S.R. Kalidindi2, B.L. Adams1, S. Ahmadi1

    CMC-Computers, Materials & Continua, Vol.9, No.1, pp. 25-40, 2009, DOI:10.3970/cmc.2009.009.025

    Abstract Localization relations arise naturally in the formulation of multi-scale models. They facilitate statistical analysis of local phenomena that may contribute to failure related properties. The computational burden of dealing with such relations is high and recent work has focused on spectral methods to provide more efficient models. Issues with the inherent integrations in the framework have led to a tendency towards calibration-based approaches. In this paper a discrete Fourier transform framework is introduced, leading to an extremely efficient basis for the localization relations. Previous issues with the Green's function integrals are resolved, and the method is validated against finite element… More >

  • Open Access


    A Chain Approach of Boundary Element Row-Subdomains for Simulating the Failure Processes in Heterogeneous Brittle Materials

    Zhenhan Yao1, Lingfei Gao1

    CMC-Computers, Materials & Continua, Vol.9, No.1, pp. 1-24, 2009, DOI:10.3970/cmc.2009.009.001

    Abstract To improve the effectiveness of the lattice model for simulating the failure processes of heterogeneous brittle materials, each lattice element is refined as a subdomain with homogenous material, and is modeled by the boundary element method in this paper. For simplicity, each subdomain is modeled with constant boundary elements. To enhance the efficiency, a row of sub-domains is formed, and then a chain structure of such row-subdomain is constructed. The row-equation systems are solved one by one, and then back substituted, to obtain the final solution. Such a chain subdomain approach of the boundary element method not only reduces the… More >

  • Open Access


    An Analytical Method for Computing the One-Dimensional Backward Wave Problem


    CMC-Computers, Materials & Continua, Vol.13, No.3, pp. 219-234, 2009, DOI:10.3970/cmc.2009.013.219

    Abstract The present paper reveals a new computational method for the illposed backward wave problem. The Fourier series is used to formulate a first-kind Fredholm integral equation for the unknown initial data of velocity. Then, we consider a direct regularization to obtain a second-kind Fredholm integral equation. The termwise separable property of kernel function allows us to obtain an analytical solution of regularization type. The sufficient condition of the data for the existence and uniqueness of solution is derived. The error estimate of the regularization solution is provided. Some numerical results illustrate the performance of the new method. More >

  • Open Access


    Numerical Modeling of Grain Structure in Continuous Casting of Steel

    A.Z. Lorbiecka1, R.Vertnik2, H.Gjerkeš1, G. Manojlovič2, B.Senčič2, J. Cesar2, B.Šarler1,3

    CMC-Computers, Materials & Continua, Vol.8, No.3, pp. 195-208, 2008, DOI:10.3970/cmc.2008.008.195

    Abstract A numerical model is developed for the simulation of solidification grain structure formation (equiaxed to columnar and columnar to equiaxed transitions) during the continuous casting process of steel billets. The cellular automata microstructure model is combined with the macroscopic heat transfer model. The cellular automata method is based on the Nastac's definition of neighborhood, Gaussian nucleation rule, and KGT growth model. The heat transfer model is solved by the meshless technique by using local collocation with radial basis functions. The microscopic model parameters have been adjusted with respect to the experimental data for steel 51CrMoV4. Simulations have been carried out… More >

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