David Stevens¹, Henry Power^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.55, No.2, pp. 111-146, 2010, DOI:10.3970/cmes.2010.055.111

Abstract Problems involving nonlinear time-dependent heat conduction in materials which have temperature-dependent thermal properties are solved with a novel meshless numerical solution technique using multiquadric radial basis functions (RBFs). Unlike traditional RBF collocation methods, the local Hermitian interpolation (LHI) method examined here can be scaled to arbitrarily large problems without numerical ill-conditioning or computational cost issues, due to the presence of small overlapping interpolation systems which grow in number but not in size as the global dataset grows. The flexibility of the full-domain multiquadric collocation method to directly interpolate arbitrary boundary conditions is maintained, via the local interpolations. The Kirchhoff transformation… More >

Chih-Fung Ho¹, Cheng Chang¹, Kuen-Hau Lin¹, Chao-An Lin^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.44, No.2, pp. 137-156, 2009, DOI:10.3970/cmes.2009.044.137

Abstract Consistent formulations of 2D and 3D pressure and velocity boundary conditions along both the stationary and non-stationary plane wall and corner for lattice Boltzmann simulations are proposed. The unknown distribution functions are made function of local known distribution functions and correctors, where the correctors at the boundary nodes are obtained directly from the definitions of density and momentum. This boundary condition can be easily implemented on the wall and corner boundary using the same formulation. Discrete macroscopic equation is also derived for steady fully developed channel flow to assess the effect of the boundary condition on the solutions, where the… More >

J. Sladek¹, V. Sladek¹, P. Solek²

CMES-Computer Modeling in Engineering & Sciences, Vol.43, No.3, pp. 223-252, 2009, DOI:10.3970/cmes.2009.043.223

Abstract A meshless method based on the local Petrov-Galerkin approach is proposed for solution of static and elastodynamic problems in 3-D continuously non-homogeneous anisotropic bodies. Functionally graded materials (FGM) are multi-phase materials with the phase volume fractions varying gradually in space, in a pre-determined profile. The Heaviside step function is used as the test functions in the local weak form resulting into the derived local integral equations (LIEs). For transient elastodynamic problems either the Laplace transform or the time difference techniques are applied. Nodal points are randomly distributed in the 3D analyzed domain and each node is surrounded by a spherical… More >

C. L. Tan¹, Y.C. Shiah², C.W. Lin²

CMES-Computer Modeling in Engineering & Sciences, Vol.41, No.3, pp. 195-214, 2009, DOI:10.3970/cmes.2009.041.195

Abstract The explicit, closed-form expressions of the Green's functions for generally anisotropic elastic solids in three-dimensions that have been derived using Stroh's formalism are employed in a formulation of the boundary element method (BEM). Unlike several other existing schemes, the evaluation of these fundamental solutions does not require further numerical integration in the BEM algorithm; they have surprisingly not been implemented previously. Three numerical examples are presented to demonstrate the veracity of the implementation and the general applicability of the BEM for the 3D elastic stress analysis of generally anisotropic solids. The results are compared with known solutions in the literature… More >

D. L. Young^1,3, K. H. Chen², T. Y. Liu³, L. H. Shen³, C. S. Wu³

CMES-Computer Modeling in Engineering & Sciences, Vol.40, No.3, pp. 225-270, 2009, DOI:10.3970/cmes.2009.040.225

Abstract In this article, a hypersingular meshless method (HMM) is extended to solve 3D potential problems for arbitrary domains after a 2D model was successfully developed (Young et al. 2005a). The solutions are represented by a distribution of the double layer potentials instead of the single layer potentials as generally used in the conventional method of fundamental solutions (MFS). By using the desingularization technique to regularize the singularity and hypersingularity of the double layer potentials, the source points can be located exactly on the real boundary to avoid the sensitivity of locating fictitious boundary for putting the singularity outside the computational… More >

W. Attaporn¹, H. Koguchi²

CMES-Computer Modeling in Engineering & Sciences, Vol.39, No.3, pp. 237-262, 2009, DOI:10.3970/cmes.2009.039.237

Abstract In the present study, a stress singularity field along free edges meeting at a corner in a three-dimensional joint structure is investigated. The order of stress singularity is determined using an eigen analysis based on a finite element method. Intensities of stress singularity not only at the corner but also along the free edge of interface are determined directly without any post-processing by a new FEM formulation referred to as a three-dimensional enriched FEM. Result in the present analysis is also compared with that in another numerical method. It was slightly larger than the intensity of stress singularity, which was… More >

Marco La Mantia¹, Peter Dabnichki^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.33, No.2, pp. 131-154, 2008, DOI:10.3970/cmes.2008.033.131

Abstract A potential flow based boundary element method was devised to obtain the hydrodynamic forces acting on oscillating wings. A new formulation of the unsteady Kutta condition, postulating a finite pressure difference at the trailing edge of the flapping wing and proposed earlier by the authors, is implemented in the numerical procedure. A comparison with published experimental data (Read et al., 2003) is carried out and the three-dimensional computational results showed good agreement, especially if compared with a similar two-dimensional numerical approach (La Mantia and Dabnichki, 2008) and the potential analytical model of Garrick (1936). The need of considering the differences… More >

J. Sladek¹, V. Sladek¹, C.L. Tan², S.N. Atluri³

CMES-Computer Modeling in Engineering & Sciences, Vol.32, No.3, pp. 161-174, 2008, DOI:10.3970/cmes.2008.032.161

Abstract A meshless method based on the local Petrov-Galerkin approach is proposed for the solution of steady-state and transient heat conduction problems in a continuously non-homogeneous anisotropic medium. The Laplace transform is used to treat the time dependence of the variables for transient problems. The analyzed domain is covered by small subdomains with a simple geometry. A weak formulation for the set of governing equations is transformed into local integral equations on local subdomains by using a unit test function. Nodal points are randomly distributed in the 3D analyzed domain and each node is surrounded by a spherical subdomain to which… More >

A. Owatsiriwong¹, B. Phansri¹, K.H. Park^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.31, No.1, pp. 37-60, 2008, DOI:10.3970/cmes.2008.031.037

Abstract This study deals with the particular integral formulation for two (2D) and three (3D) dimensional elastoplastic analyses. The elastostatic equation is used for the complementary solution. The particular integrals for displacement, stress and traction rates are derived by introducing the concept of global shape function to approximate an initial stress rate term of the inhomogeneous equation. The Newton-Raphson algorithm for the plastic multiplier is used to solve the system equation. The developed program is integrated with the pre- and post-processor. The collapse analyses of the smooth flexible strip, square and circular footings are given by comparing the numerical results of… More >

Shih-Kai Chien¹, Tzu-Hsiang Yen¹, Yue-Tzu Yang¹, Chao-Kuang Chen^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.29, No.3, pp. 163-174, 2008, DOI:10.3970/cmes.2008.029.163

Abstract Conventional proton exchange membrane fuel cells (PEMFCs) have a straight gas flow serpentine channel, and hence the reactant gases are transferred to the catalyst layers as a result of diffusion alone. Since the diffusion process is inherently slow, the electrical performance of such PEMFCs is inevitably limited. In an attempt to improve the PEMFC performance, this study replaces the straight channel with containing different type of obstacles and conducts a series of lattice Boltzmann method simulations to investigate the flow field phenomena induced in a viscous liquid as it flows along the serpentine channel at Reynolds numbers ranging from Re=5~25.… More >