N. Mai-Duy¹, A. Khennane², T. Tran-Cong³

CMC-Computers, Materials & Continua, Vol.5, No.1, pp. 63-78, 2007, DOI:10.3970/cmc.2007.005.063

Abstract This paper reports a meshless method, which is based on radial-basis-function networks (RBFNs), for the static analysis of moderately-thick laminated composite plates using the first-order shear deformation theory. Integrated RBFNs are employed to represent the field variables, and the governing equations are discretized by means of point collocation. The use of integration rather than conventional differentiation to construct the RBF approximations significantly stabilizes the solution and enhances the quality of approximation. The proposed method is verified through the solution of rectangular and non-rectangular composite plates. Numerical results obtained show that the method achieves a very high degree of accuracy and… More >

Vladimir Sladek¹, Jan Sladek¹, Chuanzeng Zhang²

CMC-Computers, Materials & Continua, Vol.4, No.3, pp. 177-188, 2006, DOI:10.3970/cmc.2006.004.177

Abstract This paper concerns the stability, convergence of accuracy and cost efficiency of four various formulations for solution of boundary value problems in non-homogeneous elastic solids with functionally graded Young's modulus. The meshless point interpolation method is employed with using various basis functions. The interaction among the elastic continuum constituents is considered in the discretized formulation either by collocation of the governing equations or by integral satisfaction of the force equilibrium on local sub-domains. The exact benchmark solutions are used in numerical tests. More >

Rooh ul Amin¹, Irum Inayat², Li Aijun¹, Shahaboddin Shamshirband^3,4,*, Timon Rabczuk⁵

CMC-Computers, Materials & Continua, Vol.57, No.3, pp. 365-388, 2018, DOI:10.32604/cmc.2018.03757

Abstract A bio-inspired global finite time control using global fast-terminal sliding mode controller and radial basis function network is presented in this article, to address the attitude tracking control problem of the three degree-of-freedom four-rotor hover system. The proposed controller provides convergence of system states in a pre-determined finite time and estimates the unmodeled dynamics of the four-rotor system. Dynamic model of the four-rotor system is derived with Newton’s force equations. The unknown dynamics of four-rotor systems are estimated using Radial basis function. The bio-inspired global fast terminal sliding mode controller is proposed to provide chattering free finite time error convergence… More >

K. Mramor¹, R. Vertnik^2,3, B. Šarler^1,3,4,5

CMC-Computers, Materials & Continua, Vol.36, No.1, pp. 1-21, 2013, DOI:10.3970/cmc.2013.036.001

Abstract This paper explores the application of Local Radial Basis Function Collocation Method (LRBFCM) [Šarler and Vertnik (2006)] for solution of Newtonian incompressible 2D fluid flow for a lid driven cavity problem [Ghia, Ghia, and Shin (1982)] in primitive variables. The involved velocity and pressure fields are represented on overlapping five-noded sub-domains through collocation by using Radial Basis Functions (RBF). The required first and second derivatives of the fields are calculated from the respective derivatives of the RBF’s. The momentum equation is solved through explicit time stepping. The method is alternatively structured with multiquadrics and inverse multiquadrics RBF’s. In addition, two… More >

L.H. Kuo¹, M.H. Gu², D.L. Young³, C.Y. Lin³

CMC-Computers, Materials & Continua, Vol.33, No.3, pp. 213-228, 2013, DOI:10.3970/cmc.2013.033.213

Abstract Coupled with the Houbolt method, a third order finite difference time marching scheme, the method of approximate particular solutions (MAPS) has been applied to solve wave equations. Radial basis function has played an important role in the solution process of the MAPS. To show the effectiveness of the MAPS, we compare the results with the well known Kansa's method, timemarching method of fundamental solutions (TMMFS), and traditional finite element methods. To validate the effectiveness and easiness of the MAPS, four numerical examples which including regular, smooth irregular, and non-smooth domains are given. More >

Gregor Kosec¹, Miha Založnik², Božidar Šarler¹, Hervé Combeau²

CMC-Computers, Materials & Continua, Vol.22, No.2, pp. 169-196, 2011, DOI:10.3970/cmc.2011.022.169

Abstract The simulation of macrosegregation as a consequence of solidification of a binary Al-4.5%Cu alloy in a 2-dimensional rectangular enclosure is tackled in the present paper. Coupled volume-averaged governing equations for mass, energy, momentum and species transfer are considered. The phase properties are resolved from the Lever solidification rule, the mushy zone is modeled by the Darcy law and the liquid phase is assumed to behave like an incompressible Newtonian fluid. Double diffusive effects in the melt are modeled by the thermal and solutal Boussinesq hypothesis. The physical model is solved by the novel Local Radial Basis Function Collocation Method (LRBFCM).… More >

A. La Rocca¹, H. Power¹, V. La Rocca², M. Morale²

CMC-Computers, Materials & Continua, Vol.2, No.4, pp. 239-250, 2005, DOI:10.3970/cmc.2005.002.239

Abstract This work presents a meshless numerical scheme for the solution of time dependent non linear heat transfer problems in terms of a radial basis function Hermite collocation approach. The proposed scheme is applied to foodstuff's samples during freezing process; evaluation of the time evolution of the temperature profile along the sample, as well as at the core, is carried out. The moving phase-change zone is identified in the domain and plotted at several timesteps. The robustness of the proposed scheme is tested by a comparison of the obtained numerical results with those found using a Finite Volume Method and with… More >

Y. C. Hon¹, L. Ling², K. M. Liew³

CMC-Computers, Materials & Continua, Vol.2, No.1, pp. 39-50, 2005, DOI:10.3970/cmc.2005.002.039

Abstract In this paper we investigate a thermal driven Micro-Electrical-Mechanical system which was originally designed for inkjet printer to precisely deliver small ink droplets onto paper. In the model, a tiny free-ended beam of metal bends and projects ink onto paper. The model is solved by using the recently developed radial basis functions method. We establish the accuracy of the proposed approach by comparing the numerical results with reported experimental data. Numerical simulations indicate that a light (low composite mass) beam is more stable as it does not oscillate much. A soft (low rigidity) beam results in a higher rate of… More >