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  • Open Access

    ARTICLE

    Virtual Delamination Testing through Non-Linear Multi-Scale Computational Methods: Some Recent Progress

    O. Allix1, P. Gosselet1, P. Kerfriden2, K. Saavedra3

    CMC-Computers, Materials & Continua, Vol.32, No.2, pp. 107-132, 2012, DOI:10.3970/cmc.2012.032.107

    Abstract This paper deals with the parallel simulation of delamination problems at the meso-scale by means of multi-scale methods, the aim being the Virtual Delamination Testing of Composite parts. In the non-linear context, Domain Decomposition Methods are mainly used as a solver for the tangent problem to be solved at each iteration of a Newton-Raphson algorithm. In case of strongly non linear and heterogeneous problems, this procedure may lead to severe difficulties. The paper focuses on methods to circumvent these problems, which can now be expressed using a relatively general framework, even though the different ingredients of the strategy have emerged… More >

  • Open Access

    ARTICLE

    On the Some Particularities of the Torsional Wave Dispersion in a Finitely Pre-Deformed Hollow Sandwich Cylinder

    Surkay D. Akbarov1,2, Tamer Kepceler1, M. Mert Egilmez1

    CMC-Computers, Materials & Continua, Vol.30, No.1, pp. 83-98, 2012, DOI:10.3970/cmc.2012.030.083

    Abstract This paper develops the investigations started in a work by Akbarov, Kepceler and Mert Egilmez (2011) and studies the some particularities of the torsional wave dispersion in a finitely pre-deformed sandwich hollow cylinder. The mentioned particularities relate to the influence of the stiffness ratio of the core and face layers' materials and the influence of the thickness ratio of these layers on the dispersion character of the wave under consideration. Moreover, the mentioned influences are studied for the various values of the parameter which characterizes the initial strains in the cylinder's layers. The mechanical relations of the materials of the… More >

  • Open Access

    ARTICLE

    Equivalence of Ratio and Residual Approaches in the Homotopy Analysis Method and Some Applications in Nonlinear Science and Engineering

    Mustafa Turkyilmazoglu1,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.120, No.1, pp. 63-81, 2019, DOI:10.32604/cmes.2019.06858

    Abstract A ratio approach based on the simple ratio test associated with the terms of homotopy series was proposed by the author in the previous publications. It was shown in the latter through various comparative physical models that the ratio approach of identifying the range of the convergence control parameter and also an optimal value for it in the homotopy analysis method is a promising alternative to the classically used h-level curves or to the minimizing the residual (squared) error. A mathematical analysis is targeted here to prove the equivalence of both the ratio approach and the traditional residual approach, especially… More >

  • Open Access

    ARTICLE

    Local and biglobal linear stability analysis of parallel

    Sanjay Mittal1, Anubhav Dwivedi1

    CMES-Computer Modeling in Engineering & Sciences, Vol.113, No.2, pp. 219-237, 2017, DOI:10.3970/cmes.2017.113.229

    Abstract Linear Stability Analysis (LSA) of parallel shear flows, v ia local and global approaches, is presented. The local analysis is carried out by solving the Orr-Sommerfeld (OS) equation using a spectral-collocation method based on Chebyshev polynomials. A stabilized finite element formulation is employed to carry out the global analysis using the linearized disturbance equations in primitive variables. The local and global analysis are compared. As per the Squires theorem, the two-dimensional disturbance has the largest growth rate. Therefore, only two-dimensional disturbances are considered. By its very nature, the local analysis assumes the disturbance field to be spatially periodic in the… More >

  • Open Access

    ARTICLE

    Approximation of Unit-Hypercubic Infinite Noncooperative Game Via Dimension-Dependent Samplings and Reshaping the Player’s Payoffs into Line Array for the Finite Game Simplification

    Vadim V. Romanuke1

    CMES-Computer Modeling in Engineering & Sciences, Vol.108, No.2, pp. 113-134, 2015, DOI:10.3970/cmes.2015.108.113

    Abstract The problem of solving infinite noncooperative games approximately is considered. The game may either have solution or have no solution. The existing solution may be unknown as well. Therefore, an approach of obtaining the approximate solution of the infinite noncooperative game on the unit hypercube is suggested. The unit-hypercubic game isomorphism to compact infinite noncooperative games allows to disseminate the approximation approach on a pretty wide class of noncooperative games. The approximation intention is in converting the infinite game into a finite one, whose solution methods are easier rather than solving infinite games. The conversion starts with sampling the players’… More >

  • Open Access

    ARTICLE

    On the Axisymmetric Time-harmonic Lamb’s Problem for a System Comprising a Half-space and a Covering Layer with Finite Initial Strains

    S.D. Akbarov1,2

    CMES-Computer Modeling in Engineering & Sciences, Vol.95, No.3, pp. 173-205, 2013, DOI:10.3970/cmes.2013.095.173

    Abstract By employing the Three-dimensional Linearized Theory of Elastic Waves in Initially Stressed Bodies (TLTEWISB) the time-harmonic Lamb’s problem for a system comprising a finite pre-strained half-space and finite pre-strained covering layer made of incompressible materials is examined for the case where the material of the covering layer is stiffer than that of the half-space material. It is assumed that on the upper free face plane of the covering layer the point-located time-harmonic force acts. The elasticity relations of the materials are described through Treloar’s potential. The corresponding boundary-value problem is solved by employing the Hankel integral transformation. The corresponding inverse… More >

  • Open Access

    ARTICLE

    Boundary Knot Method: An Overview and Some Novel Approaches

    J.Y. Zhang1, F.Z. Wang2,3

    CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.2, pp. 141-154, 2012, DOI:10.3970/cmes.2012.088.141

    Abstract The boundary knot method (BKM) is a kind of boundary-type meshless method, only boundary points are needed in the solution process. Since the BKM is mathematically simple and easy to implement, it is superior in dealing with Helmholtz problems with high wavenumbers and high dimensional problems. In this paper, we give an overview of the traditional BKM with collocation approach and provide three novel approaches for the BKM, as far as they are relevant for the other boundary-type techniques. The promising research directions are expected from an improved BKM aspect. More >

  • Open Access

    ARTICLE

    Some Fundamental Properties of Lattice Boltzmann Equation for Two Phase Flows

    Qin Lou1, Zhaoli Guo1,2, Chuguang Zheng1

    CMES-Computer Modeling in Engineering & Sciences, Vol.76, No.3&4, pp. 175-188, 2011, DOI:10.3970/cmes.2011.076.175

    Abstract Due to the mesoscopic and kinetic nature, the lattice Boltzmann equation (LBE) method has become an efficient and powerful tool for modeling and simulating interfacial dynamics of multi-phase flows. In this work we discuss several fundamental properties of two-phase LBE models. Particularly, the effects of force discretization, spurious currents in the vicinity of interfaces, and checkerboard effects with the underlying lattices, are investigated. More >

  • Open Access

    ARTICLE

    Investigation on the Singularities of Some Singular Integrals

    Zai You Yan1, Qiang Zhang1

    CMES-Computer Modeling in Engineering & Sciences, Vol.75, No.3&4, pp. 205-222, 2011, DOI:10.3970/cmes.2011.075.205

    Abstract In a boundary element method, the treatment of all the possible singular integrals is very important for the correctness and accuracy of the solutions. Generally, the directional derivative of a weakly singular integral is computed by an integral in the sense of Cauchy principal value if the directional derivative of the weakly singular integral kernel is strongly singular or in the sense of Hadamard finite part integral if it is hypersingular. In this paper, we try to discover how the strongly singular and hypersingular integrals are generated and propose an idea to avoid the appearance of such kind of strongly… More >

  • Open Access

    ARTICLE

    Internal Point Solutions for Displacements and Stresses in 3D Anisotropic Elastic Solids Using the Boundary Element Method

    Y.C. Shiah1, C. L. Tan2, R.F. Lee1

    CMES-Computer Modeling in Engineering & Sciences, Vol.69, No.2, pp. 167-198, 2010, DOI:10.3970/cmes.2010.069.167

    Abstract In this paper, fully explicit, algebraic expressions are derived for the first and second derivatives of the Green's function for the displacements in a three dimensional anisotropic, linear elastic body. These quantities are required in the direct formulation of the boundary element method (BEM) for determining the stresses at internal points in the body. To the authors' knowledge, similar quantities have never previously been presented in the literature because of their mathematical complexity. Although the BEM is a boundary solution numerical technique, solutions for the displacements and stresses at internal points are sometimes required for some engineering applications. To this… More >

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