O. Hassan¹, K. Morgan, J. Jones, B. Larwood, N. P. Weatherill

CMES-Computer Modeling in Engineering & Sciences, Vol.5, No.5, pp. 383-394, 2004, DOI:10.3970/cmes.2004.005.383

Abstract A numerical procedure for the simulation of 3D problems involving the scattering of electromagnetic waves is presented. As practical problems of interest in this area often involve domains of complex geometrical shape, an unstructured mesh based method is adopted. The solution algorithm employs an explicit finite element procedure for the solution of Maxwell's curl equations in the time domain using unstructured tetrahedral meshes. A PML absorbing layer is added at the artificial far field boundary that is created by the truncation of the physical domain prior to the numerical solution. The complete solution procedure is More >

J. Sorić¹, Q. Li², T. Jarak¹, S.N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.4, pp. 349-358, 2004, DOI:10.3970/cmes.2004.006.349

Abstract An efficient meshless formulation based on the Local Petrov-Galerkin approach for the analysis of shear deformable thick plates is presented. Using the kinematics of a three-dimensional continuum, the local symmetric weak form of the equilibrium equations over the cylindrical shaped local sub-domain is derived. The linear test function in the plate thickness direction is assumed. Discretization in the in-plane directions is performed by means of the moving least squares approximation. The linear interpolation over the thickness is used for the in-plane displacements, while the hierarchical quadratic interpolation is adopted for the transversal displacement in order More >

J. Sladek¹, V. Sladek¹, S.N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.3, pp. 309-318, 2004, DOI:10.3970/cmes.2004.006.309

Abstract Meshless methods based on the local Petrov-Galerkin approach are proposed for solution of steady and transient heat conduction problem in a continuously nonhomogeneous anisotropic medium. Fundamental solution of the governing partial differential equations and the Heaviside step function are used as the test functions in the local weak form. It is leading to derive local boundary integral equations which are given in the Laplace transform domain. The analyzed domain is covered by small subdomains with a simple geometry. To eliminate the number of unknowns on artificial boundaries of subdomains the modified fundamental solution and/or the More >

B. Jin^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.3, pp. 253-262, 2004, DOI:10.3970/cmes.2004.006.253

Abstract In this paper, we propose a new numerical scheme for the solution of the Laplace and biharmonic equations subjected to noisy boundary data. The equations are discretized by the method of fundamental solutions. Since the resulting matrix equation is highly ill-conditioned, a regularized solution is obtained using the truncated singular value decomposition, with the regularization parameter given by the L-curve method. Numerical experiments show that the method is stable with respect to the noise in the data, highly accurate and computationally very efficient. More >

E. Ferretti¹

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.3, pp. 227-244, 2004, DOI:10.3970/cmes.2004.006.227

Abstract Defining the crack path in brittle and non-brittle crack is not easy, due to several unknowns. If the direction of crack propagation can be computed by means of one of the existing criteria, it is not known whether this direction will remain constant during crack propagation. A crack initiation leads to an enhanced stress field at crack tip. During propagation, the enhanced tip stress field propagates into the solid, locally interacting with the pre-existing stress field. This interaction can lead to modifications of the propagation direction, depending on the domain and crack geometry. Moreover, trajectory… More >

Soon Wan Chung¹, Yoo Jin Choi¹, Seung Jo Kim¹

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.6, pp. 707-718, 2003, DOI:10.3970/cmes.2003.004.707

Abstract In this paper, an automatic finite element remeshing algorithm based on the bubble packing method is utilized for the purpose of numerical simulations of localized damage, because fine meshes are needed to represent the gradually concentrated damage. The bubble packing method introduces two parameters that easily control the remeshing criterion and the new mesh size. The refined area is determined by \textit {a posteriori} error estimation utilizing the value obtained from Superconvergent Patch Recovery. The isotropic ductile damage theory, founded on continuum damage mechanics, is used for this damage analysis. It was successfully shown in More >

N. Sukumar¹, J. E. Bolander¹

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.6, pp. 691-706, 2003, DOI:10.3970/cmes.2003.004.691

Abstract In this paper, we explore the numerical approximation of discrete differential operators on non-uniform grids. The Voronoi cell and the notion of natural neighbors are used to approximate the Laplacian and the gradient operator on irregular grids. The underlying weight measure used in the numerical computations is the {\em Laplace weight function}, which has been previously adopted in meshless Galerkin methods. We develop a difference approximation for the diffusion operator on irregular grids, and present numerical solutions for the Poisson equation. On regular grids, the discrete Laplacian is shown to reduce to the classical finite More >

Z. D. Han¹, S. N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.6, pp. 665-678, 2003, DOI:10.3970/cmes.2003.004.665

Abstract The numerical implementation of the truly Meshless Local Petrov-Galerkin (MLPG) type weak-forms of the displacement and traction boundary integral equations is presented, for solids undergoing small deformations. In the accompanying part I of this paper, the general MLPG/BIE weak-forms were presented [Atluri, Han and Shen (2003)]. The MLPG weak forms provide the most general basis for the numerical solution of the non-hyper-singular displacement and traction BIEs [given in Han, and Atluri (2003)], which are simply derived by using the gradients of the displacements of the fundamental solutions [Okada, Rajiyah, and Atluri (1989a,b)]. By employing the… More >

Jan Sladek¹, Vladimir Sladek¹, Chuanzeng Zhang²

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.6, pp. 637-648, 2003, DOI:10.3970/cmes.2003.004.637

Abstract A new computational method for solving transient elastodynamic initial-boundary value problems in continuously non-homogeneous solids, based on the meshless local Petrov-Galerkin (MLPG) method, is proposed in the present paper. The moving least squares (MLS) is used for interpolation and the modified fundamental solution as the test function. The local Petrov-Galerkin method for unsymmetric weak form in such a way is transformed to the local boundary integral equations (LBIE). The analyzed domain is divided into small subdomains, in which a weak solution is assumed to exist. Nodal points are randomly spread in the analyzed domain and More >

E. J. Sellountos¹, D. Polyzos²

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.6, pp. 619-636, 2003, DOI:10.3970/cmes.2003.004.619

Abstract A new meshless local Petrov-Galerkin (MLPG) method for solving two dimensional frequency domain elastodynamic problems is proposed. Since the method utilizes, in its weak formulation, either the elastostatic or the frequency domain elastodynamic fundamental solution as test function, it is equivalent to the local boundary integral equation (LBIE) method. Nodal points spread over the analyzed domain are considered and the moving least squares (MLS) interpolation scheme for the approximation of the interior and boundary variables is employed. Two integral equations suitable for the integral representation of the displacement fields in the local sub- domains are… More >