T.-T. Hoang-Trieu¹, N. Mai-Duy¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.2, pp. 171-204, 2012, DOI:10.3970/cmes.2012.084.171

Abstract In this paper, new compact local stencils based on integrated radial basis functions (IRBFs) for solving fourth-order ordinary differential equations (ODEs) and partial differential equations (PDEs) are presented. Five types of compact stencils - 3-node and 5-node for 1D problems and 5×5-node, 13-node and 3×3 -node for 2D problems - are implemented. In the case of 3-node stencil and 3×3-node stencil, nodal values of the first derivative(s) of the field variable are treated as additional unknowns (i.e. 2 unknowns per node for 3-node stencil and 3 unknowns per node for 3×3-node stencil). The integration constants arising from the construction of… More >

P. L. Bishay¹, S.N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.1, pp. 41-98, 2012, DOI:10.3970/cmes.2012.084.041

Abstract Higher-order two-dimensional as well as low and higher-order three-dimensional new Hybrid/Mixed (H/M) finite elements based on independently assumed displacement, and judiciously chosen strain fields, denoted by HMFEM-2, are developed here for applications in macro-mechanics. The idea of these new H/M finite elements is based on collocating the components of the independent strain field, with those derived from the independently assumed displacement fields at judiciously and cleverly chosen collocation points inside the element. This is unlike the other techniques used in older H/M finite elements where a two-field variational principle was used in order to enforce both equilibrium and compatibility conditions… More >

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 >

Zhen Luo^1,2, Nong Zhang^1,3, Yu Wang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.1, pp. 73-96, 2012, DOI:10.3970/cmes.2012.083.073

Abstract This paper aims to present a physically meaningful level set method for shape and topology optimization of structures. Compared to the conventional level set method which represents the design boundary as the zero level set, in this study the boundary is embedded into non-zero constant level sets of the level set function, to implicitly implement shape fidelity and topology changes in time via the propagation of the discrete level set function. A point-wise nodal density field, non-negative and value-bounded, is used to parameterize the level set function via the compactly supported radial basis functions (CSRBFs) at a uniformly defined set… More >

V. Kozulić¹, B. Gotovac¹

CMES-Computer Modeling in Engineering & Sciences, Vol.80, No.3&4, pp. 251-274, 2011, DOI:10.3970/cmes.2011.080.251

Abstract The numerical model for the elasto-plastic analysis of prismatic bars subjected to torsion is developed. The functions implemented in this model are Fup basis functions which belong to the class of atomic functions. The collocation method is used to form a system of equations in which the differential equation of the problem is satisfied in collocation points of closed domain, while boundary conditions are satisfied exactly at the domain boundary. The propagation of plastic zones in the cross-section is monitored by applying the incremental-iterative procedure until failure. An approximate solution of arbitrary accuracy is attained by hierarchically increasing the number… More >

N. Mai-Duy¹, T. Tran-Cong¹, N. Phan-Thien²

CMES-Computer Modeling in Engineering & Sciences, Vol.79, No.3&4, pp. 223-236, 2011, DOI:10.3970/cmes.2011.079.223

Abstract This paper presents a new numerical technique for solving the evolution equations in molecular dynamics (MD). The variation of the MD system is represented by radial-basis-function (RBF) equations which are constructed using integrated multiquadric basis functions and point collocation. The proposed technique requires the evaluation of forces once per time step. Several examples are given to demonstrate the attractiveness of the present implementation. More >

N.A. Dumont¹, E.Y. Mamani¹

CMES-Computer Modeling in Engineering & Sciences, Vol.78, No.2, pp. 109-150, 2011, DOI:10.3970/cmes.2011.078.109

Abstract A particular implementation of the hybrid boundary element method is presented for the two-dimensional analysis of potential and elasticity problems, which, although general in concept, is suited for fracture mechanics applications. Generalized Westergaard stress functions, as proposed by Tada, Ernst and Paris in 1993, are used as the problem's fundamental solution. The proposed formulation leads to displacement-based concepts that resemble those presented by Crouch and Starfield, although in a variational framework that leads to matrix equations with clear mechanical meanings. Problems of general topology, such as in the case of unbounded and multiply-connected domains, may be modeled. The formulation, which… More >

Y.C. Shiah¹, C. L. Tan²

CMES-Computer Modeling in Engineering & Sciences, Vol.78, No.2, pp. 95-108, 2011, DOI:10.3970/cmes.2011.078.095

Abstract By differentiating the Green function of Ting and Lee (1997) for 3D general anisotropic elastotatics in a spherical coordinate system as an intermediate step, and then using the chain rule, derivatives of up to the second order of this fundamental solution are obtained in exact, explicit, algebraic forms. No tensors of order higher than two are present in these derivatives, thereby allowing these quantities to be numerically evaluated quite expeditiously. These derivatives are required for the computation of the internal point displacements and stresses via Somigliana's identity in BEM analysis. Some examples are presented to demonstrate their successful implementation to… More >

K. Jayabal¹, A. Menzel^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.73, No.2, pp. 183-208, 2011, DOI:10.3970/cmes.2011.073.183

Abstract Naturally evolving Voronoi discretisation of two-dimensional plane domains renders representative microstructures that turn out to be useful for the modelling and simulation of polycrystalline materials. Hybrid finite element approaches are employed on such polygonal discretisations to solve, for instance, mechanical and electromechanical problems within a finite element context. In view of solving mechanical problems, varying order of polynomial functions are suggested in the literature to sufficiently approximate stresses within the polygonal finite elements. These are, in addition to the order of the approximation functions for the displacements, characterised by the number of edges in the polygonal elements. It appears, as… More >

Annamaria Mazzia¹, Flavio Sartoretto²

CMES-Computer Modeling in Engineering & Sciences, Vol.68, No.1, pp. 95-112, 2010, DOI:10.3970/cmes.2010.068.095

Abstract Meshless methods for the solution of Partial Differential Equations receive nowadays increasing attention. Many meshless strategies have been proposed. The majority of meshless variational methods one can find in the literature, use Radial Basis Functions (RBF) as generators of suitable trial and test spaces. One of the main problems encountered when exploiting RBF is performing numerical integrations over circles (when 2D problems are attacked, spheres for 3D ones). We exploit Tensor Product Functions (TPF) as the test function space. This strategy allows one to consider rectangular integration domains, which are much easier to manage. This paper numerically analyzes the effectiveness… More >