U. Hanoglu¹, B. Šarler^1,2,3

CMES-Computer Modeling in Engineering & Sciences, Vol.109-110, No.5, pp. 447-479, 2015, DOI:10.3970/cmes.2015.109.447

Abstract The aim of this paper is to demonstrate the use of the novel Local Radial Basis Function Collocation Method (LRBFCM) [Šarler and Vertnik (2006)] in an industrial coupled thermo-mechanical problem of hot shape rolling of steel. The physical concept of such a large deformation problem is based on a two dimensional traveling slice model [Glowacki (2005)], which assumes deformation and heat flow only in the perpendicular direction to rolling. The solution is performed based on strong formulation. Elliptic Node Generation (ENG) is applied to reposition the nodes over a slice when necessary in order to sustain stability throughout the simulation.… More >

H.Q. Nguyen¹, C.-D. Tran¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.109-110, No.4, pp. 361-403, 2015, DOI:10.3970/cmes.2015.109.361

Abstract In this paper, an Integrated Radial Basis Function (IRBF)-based multiscale method is used to simulate the rheological properties of dilute fibre suspensions. For the approach, a fusion of the IRBF computation scheme, the Discrete Adaptive Viscoelastic Stress Splitting (DAVSS) technique and the Fibre Configuration Field has been developed to investigate the evolution of the flow and the fibre configurations through two separate computational processes. Indeed, the flow conservation equations, which are expressed in vorticity-stream function formulation, are solved using IRBF-based numerical schemes while the evolution of fibre configuration fields governed by the Jeffery’s equation is captured using the principle of… More >

V. Panchore¹, R. Ganguli², S. N. Omkar³

CMES-Computer Modeling in Engineering & Sciences, Vol.108, No.4, pp. 215-237, 2015, DOI:10.3970/cmes.2015.108.215

Abstract A rotating Timoshenko beam free vibration problem is solved using the meshless local Petrov-Galerkin method. A locking-free shape function formulation is introduced with an improved radial basis function interpolation and the governing differential equations of the Timoshenko beam are used instead of the alternative formulation used by Cho and Atluri (2001). The locking-free approximation overcomes the problem of ill conditioning associated with the normal approximation. The radial basis functions satisfy the Kronercker delta property and make it easier to apply the essential boundary conditions. The mass matrix and the stiffness matrix are derived for the meshless local Petrov-Galerkin method. Results… More >

H.Q. Nguyen¹, C.-D. Tran¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.105, No.5, pp. 399-439, 2015, DOI:10.3970/cmes.2015.105.399

Abstract In this paper, dynamic behaviours of dilute polymer solutions of various bead-spring chain models in shear flow are studied using a coarse-grained method based on the Integrated Radial Basis Function Networks (IRBFNs) and stochastic technique. The velocity field governed by the macroscopic conservation equations is determined by the IRBFN-based method, whereas the evolution of configurations of polymer chains governed by the diffusion stochastic differential equations are captured by the Brownian Configuration Field (BCF) approach. The system of micro-macro equations is closed by the Kramers’ expression, which allows for the determination of the polymer stresses in terms of BCF configurations. In… 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 using the Laplacian companion solution.… More >

V. Panchore¹, R. Ganguli², S. N. Omkar³

CMES-Computer Modeling in Engineering & Sciences, Vol.104, No.5, pp. 353-373, 2015, DOI:10.3970/cmes.2015.104.353

Abstract Free vibration problem of a rotating Euler-Bernoulli beam is solved with a truly meshless local Petrov-Galerkin method. Radial basis function and summation of two radial basis functions are used for interpolation. Radial basis function satisfies the Kronecker delta property and makes it simpler to apply the essential boundary conditions. Interpolation with summation of two radial basis functions increases the node carrying capacity within the sub-domain of the trial function and higher natural frequencies can be computed by selecting the complete domain as a sub-domain of the trial function. The mass and stiffness matrices are derived and numerical results for frequencies… More >

S.Yu. Reutskiy¹

CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.4, pp. 327-349, 2014, DOI:10.3970/cmes.2014.099.327

Abstract The paper presents a new meshless numerical method for solving 2D and 3D boundary value problems (BVPs) with elliptic PDEs of general form. The coefficients of the PDEs including the main operator part are spatially dependent functions. The key idea of the method is the use of the basis functions which satisfy the homogeneous boundary conditions of the problem. This allows us to seek an approximate solution in the form which satisfies the boundary conditions of the initial problem with any choice of the free parameters. As a result we separate approximation of the boundary conditions and approximation of the… More >

M. Dehghan¹, M. Abbaszadeh², A. Mohebbi³

CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.5, pp. 399-444, 2014, DOI:10.3970/cmes.2014.100.399

Abstract In this paper three numerical techniques are proposed for solving the system of N-coupled nonlinear Schrödinger (CNLS) equations. Firstly, we obtain a time discrete scheme by approximating the first-order time derivative via the forward finite difference formula, then for obtaining a full discretization scheme, we use the Kansa’s approach to approximate the spatial derivatives via radial basis functions (RBFs) collocation methodology. We introduce the moving least squares (MLS) approximation and radial point interpolation method (RPIM) with their shape functions, separately. It should be noted that the shape functions of RPIM unlike the shape functions of the MLS approximation have kronecker… More >

N. Pham-Sy¹, C.-D. Tran¹, N. Mai-Duy¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.5, pp. 363-397, 2014, DOI:10.3970/cmes.2014.100.363

Abstract In this paper, a high performance computing method based on the Integrated Radial Basis Function (IRBF), Control Volume (CV) and Domain Decomposition technique for solving Partial Differential Equations is presented. The goal is to develop an efficient parallel algorithm based on the Compact Local IRBF method using the CV approach, especially for problems with non-rectangular domain. The results showed that the goal is achieved as the computational efficiency is quite significant. For the case of square lid driven cavity problem with Renoylds number 100, super-linear speed-up is also achieved. The parallel algorithm is implemented in the Matlab environment using Parallel… More >

Soleiman Ghouhestani¹, Farzad Shahabian¹, Seyed Mahmoud Hosseini^2,3

CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.4, pp. 295-321, 2014, DOI:10.3970/cmes.2014.100.295

Abstract In this paper, the meshless local Petrov-Galerkin (MLPG) method is exploited for dynamic analysis of functionally graded nanocomposite cylindrical layered structure reinforced by carbon nanotube subjected to mechanical shock loading. The carbon nanotubes (CNTs) are distributed across radial direction on thickness of cylinder, which can be simulated by linear and nonlinear volume fraction. Free vibration and elastic wave propagation are studied for various value of volume fraction exponent at various time intervals. The layered cylinder is assumed to be under axisymmetric and plane strain conditions. Four types of CNTs distributions including uniform and three kinds of functionally graded distributions along… More >