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  • Open Access

    ARTICLE

    Probability Density Transitions in the FitzHugh-Nagumo Model with Lévy Noise

    Xu Yong1,2, Feng Jing1, Xu Wei1, Gu Rencai1

    CMES-Computer Modeling in Engineering & Sciences, Vol.106, No.5, pp. 309-322, 2015, DOI:10.3970/cmes.2015.106.309

    Abstract In this paper, bifurcation analysis and numerical simulations are performed on the FitzHugh-Nagumo system in the presence of Lévy stable noise. The stationary probability density functions are obtained to examine the influences of noise intensity and stability index. Results show that under the influences of noise intensity and stability index, the dynamic of the FitzHugh-Nagumo model can be well characterized through the concept of stochastic bifurcation, consisting in qualitative changes of the stationary probability distribution. Then, the mean passage time between the resting and action state is investigated as functions of noise intensity and stability index of the external signal… More >

  • Open Access

    ARTICLE

    Analysis of Symmetry Breaking Bifurcation in Duffing System with Random Parameter

    Ying Zhang1, Lin Du1, Xiaole Yue1, Qun Han1, Tong Fang2

    CMES-Computer Modeling in Engineering & Sciences, Vol.106, No.1, pp. 37-51, 2015, DOI:10.3970/cmes.2015.106.037

    Abstract The symmetry breaking bifurcation (SBB) phenomenon in a deterministic parameter Duffing system (DP-DS) is well known, yet the problem how would SBB phenomenon happen in a Duffing system with random parameter (RP-DS) is still open. For comparison study, the results for DP-DS are summarized at first: in short, SBB in DP-DS is just a transition of response phase trajectories from a single self-symmetric one about the origin into two mutual symmetric once, or vice versa. However, in DP-DS case, the two mutual symmetric phase trajectories are never commutable. In view of every sample of RP-DS is a DP-DS, we think… More >

  • Open Access

    ARTICLE

    An Iterative Algorithm for Solving a System of Nonlinear Algebraic Equations, F(x) = 0, Using the System of ODEs with an Optimum α in x· = λ[αF + (1−α)BTF]; Bij = ∂Fi/∂xj

    Chein-Shan Liu1, Satya N. Atluri2

    CMES-Computer Modeling in Engineering & Sciences, Vol.73, No.4, pp. 395-432, 2011, DOI:10.3970/cmes.2011.073.395

    Abstract In this paper we solve a system of nonlinear algebraic equations (NAEs) of a vector-form: F(x) = 0. Based-on an invariant manifold defined in the space of (x,t) in terms of the residual-norm of the vector F(x), we derive a system of nonlinear ordinary differential equations (ODEs) with a fictitious time-like variable t as an independent variable: x· = λ[αF + (1−α)BTF], where λ and α are scalars and Bij = ∂Fi/∂xj. From this set of nonlinear ODEs, we derive a purely iterative algorithm for finding the solution vector x, without having to invert the Jacobian (tangent stiffness matrix)… More >

  • Open Access

    ARTICLE

    Convectively Unstable Anti-Symmetric Waves in Flows Past Bluff Bodies

    Bhaskar Kumar1, Sanjay Mittal1,2

    CMES-Computer Modeling in Engineering & Sciences, Vol.53, No.2, pp. 95-122, 2009, DOI:10.3970/cmes.2009.053.095

    Abstract The steady flow past a circular cylinder is investigated. Symmetry conditions are imposed along the centerline of the flow field. The variation of the structure of the recirculation zone with the Reynolds number is studied. The effect of the location of lateral boundary on the flow is analyzed and compared with results from earlier studies. The eddy length varies linearly with Re. Three kinds of solutions, based on eddy structure, are found for different location of the lateral boundary. Global linear stability analysis has been carried out in a translating frame to determine the convective modes for flow past a… More >

  • Open Access

    ARTICLE

    A Rate-Dependent Damage/Decohesion Model for Simulating Glass Fragmentation under Impact using the Material Point Method

    LumingShen1

    CMES-Computer Modeling in Engineering & Sciences, Vol.49, No.1, pp. 23-46, 2009, DOI:10.3970/cmes.2009.049.023

    Abstract A bifurcation-based simulation procedure is proposed in this paper to explore the transition from localization to decohesion involved in the glass fragmentation under impact loading. In the proposed procedure, the onset and orientation of discontinuous failure of glass is identified from the bifurcation analysis based on a rate-dependent tensile damage model. The material point method, which does not involve fixed mesh connectivity, is employed to accommodate the multi-scale discontinuities associated with the fragmentation of glass using a simple interface treatment. A parametric study has been conducted to demonstrate the effects of specimen size and impact velocity on the evolution of… More >

  • Open Access

    ARTICLE

    A boundary element formulation for incremental nonlinear elastic deformation of compressible solids

    Sergia Colli1, Massimiliano Gei1, Davide Bigoni1,2

    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 >

  • Open Access

    ARTICLE

    Masonry Walls under Shear Test: a CM Modeling

    E. Ferretti1, E. Casadio, A. Di Leo1

    CMES-Computer Modeling in Engineering & Sciences, Vol.30, No.3, pp. 163-190, 2008, DOI:10.3970/cmes.2008.030.163

    Abstract In this study, the Cell Method (CM) is applied in order to investigate the failure mechanisms of masonry walls under shear force. The direction of propagation is computed step-wise by the code, and the domain is updated by means of a propagation technique of intra-element nodal relaxation with re-meshing. The crack extension condition is studied in the Mohr/Coulomb plane, using the criterion of Leon. The main advantage of using the CM for numerical analyses of masonry is that the mortar, the bricks and the interfaces between mortar and bricks can be modeled without any need to use homogenization techniques, simply… More >

  • Open Access

    ARTICLE

    A Coupled Thermo-Mechanical Model for Simulating the Material Failure Evolution Due to Localized Heating

    Z. Chen1,2, Y. Gan1, J.K. Chen2

    CMES-Computer Modeling in Engineering & Sciences, Vol.26, No.2, pp. 123-138, 2008, DOI:10.3970/cmes.2008.026.123

    Abstract A coupled thermo-mechanical constitutive model with decohesion is proposed to simulate the material failure evolution due to localized heating. A discontinuous bifurcation analysis is performed based on a thermoviscoplasticity relation to identify the transition from continuous to discontinuous failure modes as well as the orientation of the discontinuous failure. The thermo-mechanical model is then implemented within the framework of the Material Point Method (MPM) so that the different gradient and divergence operators in the governing differential equations could be discretized in a single computational domain and that continuous remeshing is not required with the evolution of failure. The proposed model-based… More >

  • Open Access

    ARTICLE

    Generation-Phase Simulation of Dynamic Crack Bifurcation Phenomenon Using Moving Finite Element Method Based on Delaunay Automatic Triangulation

    T. Nishioka1, J. Furutuka1, S. Tchouikov1, T. Fujimoto1

    CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.1, pp. 129-146, 2002, DOI:10.3970/cmes.2002.003.129

    Abstract The governing condition of dynamic crack bifurcation phenomena had not been fully elucidated until our recent experimental studies. We found from the experimental results that the energy flux per unit time into a propagating crack tip or into a fracture process zone governs the crack bifurcation. Regarding the numerical simulation of dynamic crack bifurcation, to the authors' knowledge, no accurate simulations have been carried out, due to several unresolved difficulties. In order to overcome the difficulties, for the analysis of dynamic crack bifurcation, we developed a moving finite element method based on Delaunay automatic triangulation. Using the moving finite element… More >

  • Open Access

    ARTICLE

    Nonlinear Analysis of Pin-Jointed Assemblies with Buckling and Unilateral Members

    K.Yu. Volokh1

    CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.3, pp. 389-400, 2001, DOI:10.3970/cmes.2001.002.389

    Abstract A computational framework is described for modeling pin-jointed structures comprising unilateral cable members and slender struts. The deep postbuckling behavior of struts is considered by means of 'elastica' analytical approximation. Prestressing is allowed. The proposed approach is incorporated into equilibrium path following procedures and illustrated in numerical examples. More >

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