C.M.T. Tien¹, N. Thai-Quang¹, N. Mai-Duy¹, C.-D. Tran¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.105, No.4, pp. 301-340, 2015, DOI:10.3970/cmes.2015.105.301

Abstract In this study, we present a numerical discretisation scheme, based on a direct fully coupled approach and compact integrated radial basis function (CIRBF) approximations, to simulate viscous flows in regular/irregular domains. The governing equations are taken in the primitive form where the velocity and pressure fields are solved in a direct fully coupled approach. Compact local approximations, based on integrated radial basis functions, over 3-node stencils are introduced into the direct fully coupled approach to represent the field variables. The present scheme is verified through the solutions of several problems including Poisson equations, Taylor-Green vortices More >

Foad Nazari¹, Mohammad Hossein Abolbashari^1,2, Seyed Mahmoud Hosseini³

CMES-Computer Modeling in Engineering & Sciences, Vol.105, No.4, pp. 271-299, 2015, DOI:10.3970/cmes.2015.105.271

Abstract Present study is concerned with three dimensional natural frequency analysis of functionally graded sandwich rectangular plates using Meshless Local Petrov-Galerkin (MLPG) method and Artificial Neural Networks (ANNs).The plate consists of two homogeneous face sheets and a power-law FGM core. Natural frequencies of the plate are obtained by 3D MLPG method and are verified with available references. Convergence study of the first four natural frequencies for different node numbers is the next step. Also, effects of two parameters of “FG core to plate thickness ratio” and “volume fraction index” on natural frequencies of plate are investigated. More >

W. Chen^1,2, C. J. Liu¹, Y. Gu^2,3

CMES-Computer Modeling in Engineering & Sciences, Vol.105, No.4, pp. 251-270, 2015, DOI:10.3970/cmes.2015.105.251

Abstract The singular boundary method (SBM) is a recently-developed meshless boundary collocation method. This method overcomes the well-known fictitious boundary issue associated with the method of fundamental solutions (MFS) while remaining the merits of the later of being truly meshless, integral-free, and easy-to-program. Similar to the MFS, this method, however, produces dense and unsymmetrical coefficient matrix, which although much smaller in size compared with domain discretization methods, requires O(N²) operations in the iterative solution of the resulting algebraic system of equations. To remedy this bottleneck problem for its application to large-scale problems, this paper makes the first More >

S. Saha Ray¹

CMES-Computer Modeling in Engineering & Sciences, Vol.105, No.3, pp. 231-249, 2015, DOI:10.3970/cmes.2015.105.231

Abstract In the present article, a relatively very new technique viz. Coupled Fractional Reduced Differential Transform, has been executed to attain the approximate numerical solution of the predator-prey dynamical system. The fractional derivatives are defined in the Caputo sense. Utilizing the present method we can solve many linear and nonlinear coupled fractional differential equations. The results thus obtained are compared with those of other available methods. Numerical solutions are presented graphically to show the simplicity and authenticity of the method. More >

R. Shamsoddini, N. Aminizadeh1, M. Sefid

CMES-Computer Modeling in Engineering & Sciences, Vol.105, No.3, pp. 209-230, 2015, DOI:10.3970/cmes.2015.105.209

Abstract In this study, an improved weakly compressible Smoothed Particle Hydrodynamics method is introduced and applied for investigation of the non- Newtonian power-law fluid flow which is induced by motion of a square cylinder. The method is based on a predictor-corrector scheme and pressure velocity coupling to overcome the non-physical fluctuations of WCSPH. The numerical method is also supported by the corrective tensors and shifting algorithm. The results are validated against the well known test cases and benchmark data. The square motion is tested in various Reynolds numbers for various power law indices. The results show More >

B. Pekmen^1,2, M. Tezer-Sezgin^2,3

CMES-Computer Modeling in Engineering & Sciences, Vol.105, No.3, pp. 183-207, 2015, DOI:10.3970/cmes.2015.105.183

Abstract This study proposes the dual reciprocity boundary element (DRBEM) solution for full magnetohydrodynamics (MHD) equations in a lid-driven square cavity. MHD equations are coupled with the heat transfer equation by means of the Boussinesq approximation. Induced magnetic field is also taken into consideration. The governing equations in terms of stream function, temperature, induced magnetic field components, and vorticity are solved employing DRBEM in space together with the implicit backward Euler formula for the time derivatives. The use of DRBEM with linear boundary elements which is a boundary discretization method enables one to obtain small sized… More >

Farzad Ebrahimi^1,2, Erfan Salari¹

CMES-Computer Modeling in Engineering & Sciences, Vol.105, No.2, pp. 151-181, 2015, DOI:10.3970/cmes.2015.105.151

Abstract In this paper, a semi-analytical method is presented for free vibration and buckling analysis of functionally graded (FG) size-dependent nanobeams based on the physical neutral axis position. It is the first time that a semi-analytical differential transform method (DTM) solution is developed for the FG nanobeams vibration and buckling analysis. Material properties of FG nanobeam are supposed to vary continuously along the thickness according to the power-law form. The physical neutral axis position for mentioned FG nanobeams is determined. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. The… More >

Marcin Maździarz¹, Marcin Gajewski²

CMES-Computer Modeling in Engineering & Sciences, Vol.105, No.2, pp. 123-150, 2015, DOI:10.3970/cmes.2015.105.123

Abstract In this paper, the choice and parametrisation of finite deformation polyconvex isotropic hyperelastic models to describe the behaviour of a class of defect-free monocrystalline metal materials at the molecular level is examined. The article discusses some physical, mathematical and numerical demands which in our opinion should be fulfilled by elasticity models to be useful. A set of molecular numerical tests for aluminium and tungsten providing data for the fitting of a hyperelastic model was performed, and an algorithm for parametrisation is discussed. The proposed models with optimised parameters are superior to those used in non-linear More >

K. N. Grivas¹, M. G. Vavva¹, E. J. Sellountos², D. I. Fotiadis³, D. Polyzos^1,4

CMES-Computer Modeling in Engineering & Sciences, Vol.105, No.2, pp. 87-122, 2015, DOI:10.3970/cmes.2015.105.087

Abstract A simple Local Boundary Integral Equation (LBIE) method for solving the Fisher nonlinear transient diffusion equation in two dimensions (2D) is reported. The method utilizes, for its meshless implementation, randomly distributed nodal points in the interior domain and nodal points corresponding to a Boundary Element Method (BEM) mesh, at the global boundary. The interpolation of the interior and boundary potentials is accomplished using a Local Radial Basis Functions (LRBF) scheme. At the nodes of global boundary the potentials and their fluxes are treated as independent variables. On the local boundaries, potential fluxes are avoided by More >

Yiyu Lu¹, Chenpeng Song^1,2, Yunzhong Jia¹, Binwei Xia¹, Zhaolong Ge¹, Jiren Tang¹, Qian Li¹

CMES-Computer Modeling in Engineering & Sciences, Vol.105, No.1, pp. 69-86, 2015, DOI:10.3970/cmes.2015.105.069

Abstract In underground coal mines, hydrofracture can cause the increase of breathability in the fractured coal bed. When the hydrofracture crack propagates to the interface between the coal bed and the roof-floor stratum, the crack may enter roof-floor lithology, thus posing a limit on the scope of breathability increase and making it difficult to support the roof and floor board for subsequent coal mining. In this work, a two-dimensional model of coal rock bed that contains hydrofracture crack was constructed. Then an investigation that combines the fracture mechanics and the system of flow and solid in… More >