D. Ngo-Cong^1,2, N. Mai-Duy¹, W. Karunasena², T. Tran-Cong^1,3

CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.3, pp. 275-310, 2012, DOI:10.3970/cmes.2012.083.275

Abstract In this paper, natural convection flows in concentric and eccentric annuli are studied using a new numerical method, namely local moving least square - one dimensional integrated radial basis function networks (LMLS-1D-IRBFN). The partition of unity method is used to incorporate the moving least square (MLS) and one dimensional-integrated radial basis function (1D-IRBFN) techniques in an approach that leads to sparse system matrices and offers a high level of accuracy as in the case of 1D-IRBFN method. The present method possesses a Kronecker-Delta function property which helps impose the essential boundary condition in an exact manner. The method is first… More >

L. Dong¹, S. N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.2, pp. 183-220, 2012, DOI:10.32604/cmes.2012.083.183

Abstract In this paper, we develop T-Trefftz Voronoi Cell Finite Elements (VCF -EM-TTs) for micromechanical modeling of composite and porous materials. In addition to a homogenous matrix in each polygon-shaped element, three types of arbitrarily-shaped heterogeneities are considered in each element: an elastic inclusion, a rigid inclusion, or a void. In all of these three cases, an inter-element compatible displacement field is assumed along the element outer-boundary, and interior displacement fields in the matrix as well as in the inclusion are independently assumed as T-Trefftz trial functions. Characteristic lengths are used for each element to scale the T-Trefftz trial functions, in… More >

L. Dong¹, S. N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.81, No.1, pp. 69-118, 2011, DOI:10.3970/cmes.2011.081.069

Abstract In this paper, we explore three different ways of developing T-Trefftz finite elements of quadrilateral as well as polygonal shapes. In all of these three approaches, in addition to assuming an inter-element compatible displacement field along the element boundary, an interior displacement field for each element is independently assumed as a linear combination of T-Trefftz trial functions. In addition, a characteristic length is defined for each element to scale the T-Trefftz modes, in order to avoid solving systems of ill-conditioned equations. The differences between these three approaches are that, the compatibility between the independently assumed fields at the boundary and… More >

Yi W. Wan¹, Huan J. Keh²

CMES-Computer Modeling in Engineering & Sciences, Vol.74, No.2, pp. 109-138, 2011, DOI:10.3970/cmes.2011.074.109

Abstract The steady rotation of an axially symmetric particle about its axis of revolution normal to two plane walls at an arbitrary position between them in a viscous fluid is studied theoretically in the limit of small Reynolds number. The fluid is allowed to slip at the surface of the particle. A method of distribution of a set of spherical singularities along the axis of revolution inside a prolate particle or on the fundamental disk within an oblate particle is used to find the general solution for the fluid velocity distribution that satisfies the boundary conditions at the confining walls and… More >

Ju’e Yang¹, Dehao Yu²

CMES-Computer Modeling in Engineering & Sciences, Vol.73, No.3, pp. 311-330, 2011, DOI:10.3970/cmes.2011.073.311

Abstract In this paper, we introduce a domain decomposition method with non-matching grids for a certain nonlinear interface problem in unbounded domains. To solve this problem, we discuss a new coupling of finite element method(FE) and natural boundary element(NBE). We first derive the optimal energy error estimate of finite element approximation to the coupled FEM-NBEM problem. Then we use a dual basis multipier on the interface to provide the numerical analysis with non-matching grids.Finally, we give some numerical examples further to confirm our theoretical results. More >

D.-A. An-Vo¹, N. Mai-Duy¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.72, No.4, pp. 299-336, 2011, DOI:10.3970/cmes.2011.072.299

Abstract This paper presents a new control-volume discretisation method, based on Cartesian grids and integrated-radial-basis-function elements (IRBFEs), for the solution of second-order elliptic problems in one and two dimensions. The governing equation is discretised by means of the control-volume formulation and the division of the problem domain into non-overlapping control volumes is based on a Cartesian grid. Salient features of the present method include (i) an element is defined by two adjacent nodes on a grid line, (ii) the IRBF approximations on each element are constructed using only two RBF centres (a smallest RBF set) associated with the two nodes of… More >

J. Sladek¹, V. Sladek¹, Ch. Zhang², M. Wünsche²

CMES-Computer Modeling in Engineering & Sciences, Vol.68, No.2, pp. 185-220, 2010, DOI:10.3970/cmes.2010.068.185

Abstract A meshless method based on the local Petrov-Galerkin approach is proposed to solve initial-boundary value crack problems of piezoelectric solids with nonlinear electrical boundary conditions on crack faces. Homogeneous and continuously varying material properties of the piezoelectric solid are considered. Stationary governing equations for electrical fields and the elastodynamic equations with an inertial term for mechanical 2-D fields are considered. Nodal points are spread on the analyzed domain, and each node is surrounded by a small circle for simplicity. The spatial variation of displacements and electric potential are approximated by the Moving Least-Squares (MLS) scheme. After performing the spatial integrations,… More >

D. C. C. Lam¹, L-H Keung¹, P. Tong²

CMES-Computer Modeling in Engineering & Sciences, Vol.66, No.1, pp. 73-100, 2010, DOI:10.3970/cmes.2010.066.073

Abstract Additional molecular rotations in long chained macromolecules lead to additional size dependence. In this investigation, we developed the higher order viscoelasticity framework and conducted experiments to determine the higher order material length scale parameters needed to describe the higher order viscoelastic behavior in the new framework. In the first part of the investigation of high order deformation behavior of macromolecular solids, the higher-order viscoelasticity theories for Maxwell and Kelvin-Voigt materials, and models of higher-order viscoelastic beam deflection creep are developed in this study. We conducted creep bending experiments with epoxy beams to show that the creep deflection behavior followed the… More >

Huan J. Keh¹, Yu C. Chang²

CMES-Computer Modeling in Engineering & Sciences, Vol.62, No.3, pp. 225-254, 2010, DOI:10.3970/cmes.2010.062.225

Abstract A theoretical study of the Stokes flow caused by a rigid particle of revolution translating axisymmetrically perpendicular to two parallel plane walls at an arbitrary position between them in a viscous fluid, which may slip at the particle surface, is presented. A method of distribution of a set of spherical singularities along the axis of revolution within a prolate particle or on the fundamental plane within an oblate particle is used to find the general solution of the fluid velocity field that satisfies the boundary conditions at the plane walls and at infinity. The slip condition on the particle surface… More >

Shih-Wei Yang¹, Yung-Ming Wang¹, Chih-Ping Wu^1,2, Hsuan-Teh Hu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.60, No.1, pp. 1-40, 2010, DOI:10.3970/cmes.2010.060.001

Abstract A differential reproducing kernel (DRK) approximation-based collocation method is developed for solving ordinary and partial differential equations governing the one- and two-dimensional problems of elastic bodies, respectively. In the conventional reproducing kernel (RK) approximation, the shape functions for the derivatives of RK approximants are determined by directly differentiating the RK approximants, and this is very time-consuming, especially for the calculations of their higher-order derivatives. Contrary to the previous differentiation manipulation, we construct a set of differential reproducing conditions to determine the shape functions for the derivatives of RK approximants. A meshless collocation method based on the present DRK approximation is… More >