CMES-Vol. 87, No. 4, 2012

Open Access

ARTICLE

Thin Plate Bending Analysis and Treatment of Material Discontinuities Using the Generalised RKP-FSM
M. Khezri¹, Z. Vrcelj¹, M.A. Bradford^1,2
CMES-Computer Modeling in Engineering & Sciences, Vol.87, No.4, pp. 271-306, 2012, DOI:10.3970/cmes.2012.087.271
Abstract A finite strip method (FSM) utilising the generalised reproducing kernel particle method (RKPM) [Behzadan, Shodja, and Khezri (2011)] is developed for the bending analysis of thin plates. In this innovative approach, the spline functions in the conventional spline finite strip method (SFSM) are replaced with generalised RKPM 1-D shape functions in the longitudinal direction, while the transverse cubic functions which are used in the conventional formulations are retained. Since the generalised RKPM is one of the class of meshfree methods which deal efficiently with derivative-type essential boundary conditions, its introduction in the FSM is beneficial… More >

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ARTICLE

Determination of an Unknown Heat Source Term from Boundary Data
Y. Hu¹, T. Wei^1,2
CMES-Computer Modeling in Engineering & Sciences, Vol.87, No.4, pp. 307-326, 2012, DOI:10.3970/cmes.2012.087.307
Abstract This paper employ the method of fundamental solutions for determining an unknown heat source term in a heat equation from overspecified boundary measurement data. By a function transformation, the inverse source problem is changed into an inverse initial data problem which is solved by a method of fundamental solutions. The standard Tikhonov regularization technique with the generalized cross-validation criterion for choosing the regularization parameter is adopted for solving the resulting ill-conditioned system of linear algebraic equations. The effectiveness of the algorithm is illustrated by five numerical examples in one-dimensional and two-dimensional cases. More >

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ARTICLE

Frequency Domain Analysis of Fluid-Solid Interaction Problems by Means of Iteratively Coupled Meshless Approaches
L. Godinho¹, D. Soares Jr.²
CMES-Computer Modeling in Engineering & Sciences, Vol.87, No.4, pp. 327-354, 2012, DOI:10.3970/cmes.2012.087.327
Abstract In this work, a coupling strategy between the Method of Fundamental Solutions (MFS) and the Kansa's Method (KM) for the analysis of fluid-solid interaction problems in the frequency domain is proposed. In this approach, the MFS is used to model the acoustic fluid medium, while KM accounts for the elastodynamic solid medium. The coupling between the two methods is performed iteratively, with independent discretizations being used for the two methods, without requiring matching between the boundary nodes along the solid-fluid interface. Two application examples, with single and multiple solid sub-domains, are presented, illustrating the behavior More >

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ARTICLE

A Novel Method for Solving One-, Two- and Three-Dimensional Problems with Nonlinear Equation of the Poisson Type
S.Yu. Reutskiy¹
CMES-Computer Modeling in Engineering & Sciences, Vol.87, No.4, pp. 355-386, 2012, DOI:10.3970/cmes.2012.087.355
Abstract The paper presents a new meshless numerical technique for solving nonlinear Poisson-type equation ∇²u = f (x) + F(u,x) for x ∈ R^d, d =1,2,3. We assume that the nonlinear term can be represented as a linear combination of basis functions F(u,x) = ∑_m^Mq_mφ_m. We use the basis functions φ_m of three types: the the monomials, the trigonometric functions and the multiquadric radial basis functions. For basis functions φ_m of each kind there exist particular solutions of the equation ∇²ϕ_m = φ_m in an analytic form. This permits to write the approximate solution in the form u_M = u_f +∑_m^Mq_mΦ_m, where Φ_m… More >

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