Ahmad Shirzadi¹, Vladimir Sladek², Jan Sladek³

CMES-Computer Modeling in Engineering & Sciences, Vol.95, No.4, pp. 259-282, 2013, DOI:10.3970/cmes.2013.095.259

Abstract This paper is concerned with the development of a numerical approach based on the Meshless Local Petrov-Galerkin (MLPG) method for the approximate solutions of the two dimensional nonlinear reaction-diffusion Brusselator systems. The method uses finite differences for discretizing the time variable and the moving least squares (MLS) approximation for field variables. The application of the weak formulation with the Heaviside type test functions supported on local subdomains (around the nodes used in MLS approximation) to semi-discretized partial differential equations yields the finite-volume local weak formulation. A predictor-corrector scheme is used to handle the nonlinearity of the problem within each time… More >

Yixian Du^1,2,3,4, De Chen¹, Xiaobo Xiang¹, Qihua Tian¹, Yi Zhang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.94, No.1, pp. 53-75, 2013, DOI:10.3970/cmes.2013.094.053

Abstract Topological design of continuum structures usually involves numerical instabilities, such as checkerboards and mesh-dependency, which degenerate the manufacturability, the efficiency and the robustness of the optimal design. This paper will propose a new topology optimization method to suppress numerical instabilities occurred in the topology optimization of continua, according to the principle of error amplifier and feedback control in the control system. The design variables associated with topological design are updated based on the Cellular Automata (CA) theory. A couple of typical numerical examples are used to demonstrate the effectiveness of the proposed method in effectively suppressing numerical instabilities occurred in… More >

Xiaokui Yue¹, Yong Xu², Jianping Yuan¹

CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.4, pp. 277-291, 2013, DOI:10.3970/cmes.2013.093.277

Abstract In this paper, a stochastic averaging method is derived for a class of non-linear stochastic systems under parametrical Poisson white noise excitation, which may be used to model the beam-beam interaction models in particle accelerators. The averaged Generalized Fokker-Planck equation is derived and the approximate stationary solution of the averaged Generalized Fokker-Planck equation is solved by using perturbation method. The present method applied in this paper can reduce the dimensions of stochastic ODE from 2n to n, which simplify the complex stochastic ODE, and then the analytical stationary solutions can be obtained. An example is employed to demonstrate the procedure… More >

K.Y. Volokh^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.92, No.1, pp. 87-101, 2013, DOI:10.3970/cmes.2013.092.087

Abstract In the laminar mode interactions among molecules generate friction between layers of water that slide with respect to each other. This friction triggers the shear stress, which is traditionally presumed to be linearly proportional to the velocity gradient. The proportionality coefficient characterizes the viscosity of water. Remarkably, the standard Navier-Stokes model surmises that materials never fail – the transition to turbulence can only be triggered by some kinematic instability of the flow. This premise is probably the reason why the Navier-Stokes theory fails to explain the so-called subcritical transition to turbulence with the help of the linear instability analysis. When… More >

Baohua Yu¹, Chuanliang Yan¹, Deli Gao^1,2, Jinxiang Li³

CMES-Computer Modeling in Engineering & Sciences, Vol.89, No.1, pp. 57-78, 2012, DOI:10.3970/cmes.2012.089.057

Abstract Shale is easy to hydrate and often causes a collapse of the borehole during drilling, especially in drilling extended-reach wells (ERW). In order to solve the problem of collapse of the shale, the changinges in the mechanical properties of shale, as affected by hydration and water absorption, are studied in this paper, through experiments. The relationships between the mechanical properties of shale and the water content are established. The borehole-stability models, which couple chemistry and mechanics are established, by considering the anisotropy of swelling, based on the experimental results. The stability of shale in the borehole is analyzed to obtain… More >

P. Redou¹, L. Gaubert¹, G. Desmeulles¹, P-A. Béal², C. Le Gal², V. Rodin³

CMES-Computer Modeling in Engineering & Sciences, Vol.70, No.1, pp. 11-40, 2010, DOI:10.3970/cmes.2010.070.011

Abstract Multi Interaction Systems, used in the context of Virtual Reality, are dedicated to real-time interactive simulations. They open the way to the in virtuo experimentation, especially useful in the domain of biochemical kinetics. To this purpose, chaotic and asynchronous scheduling of autonomous processes is based upon desynchronization of phenomena involved in the system. It permits interactivity, especially the capability to add or remove phenomena in the course of a simulation. It provides methods of resolution of ordinary differential systems and partial derivative equations. Proofs of convergence for these methods have been established, but the problem of absolute stability, although it… More >

M.V. Menshykova¹, I.A. Guz, O.V. Menshykov

CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.3, pp. 239-260, 2009, DOI:10.3970/cmes.2009.051.239

Abstract The present work is devoted to the investigation of the internal instability in laminated materials. The paper is concerned with the development of a unified computational procedure for numerical realisation of the method as applied to various constitutive equations of the layers, different loading schemes (uniaxial or biaxial loading) and different precritical conditions (large or small precritical deformations). It contains many examples of critical stresses/strains calculations for particular composites as well as analysis of different buckling modes. More >

S.-Y. Leu¹, J.T. Chen²

CMES-Computer Modeling in Engineering & Sciences, Vol.14, No.2, pp. 129-140, 2006, DOI:10.3970/cmes.2006.014.129

Abstract Plastic limit angular velocity of rotating hollow cylinders made of the von Mises materials with nonlinear isotropic hardening is investigated numerically and analytically in the paper. The paper applies sequential limit analysis to deal with the rotating problems involving hardening material property and weakening behavior resulted from the widening deformation. By sequential limit analysis, the paper treats the plasticity problems as a sequence of limit analysis problems stated in the upper bound formulation. Rigorous upper bounds are acquired iteratively through a computational optimization procedure with the angular velocity factor as the objective function. Especially, rigorous validation was conducted by numerical… More >

Xianwu Ling¹, S.N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.13, No.3, pp. 219-228, 2006, DOI:10.3970/cmes.2006.013.219

Abstract In this paper, two matrix algebraic tools are provided for studying the solution-stabilities of inverse heat conduction problems. The propagations of the computed temperature errors, as caused by a noise in temperature measurement, are presented. The spectral norm analysis reflects the effect of the computational time steps, the sensor locations and the number of future temperatures on the computed error levels. The Frobenius norm analysis manifests the dynamic propagations of the computed errors. As an application of the norm analysis, we propose a method for the best positioning of the thermocouples. More >

A. N. Guz, V. A. Dekret¹

CMES-Computer Modeling in Engineering & Sciences, Vol.13, No.3, pp. 165-170, 2006, DOI:10.3970/cmes.2006.013.165

Abstract Stability problem of composite material reinforced by two parallel short fibers is solved. The problem is formulated with application of equations of linearized three-dimensional theory of stability. The composite is modeled as piecewise-homogeneous medium. The influence of geometrical and mechanical parameters of the material on critical strain is investigated. More >