N.B.Petrovskaya ¹

CMES-Computer Modeling in Engineering & Sciences, Vol.32, No.2, pp. 69-84, 2008, DOI:10.3970/cmes.2008.032.069

Abstract Discontinuous weighted least--squares (DWLS) approximation is a modification of a standard weighted least-squares approach that nowadays is intensively exploited in computational aerodynamics. A DWLS method is often employed to approximate a solution function over an unstructured computational grid that results in an irregular local support for the approximation. While the properties of a weighted least-squares reconstruction are well known for regular geometries, the approximation over a non-uniform grid is not a well researched area so far. In our paper we demonstrate the difficulties related to the performance of a DWLS method on distorted grids and outline a new approach based… More >

L. Codecasa¹, R. Specogna², F. Trevisan³

CMES-Computer Modeling in Engineering & Sciences, Vol.31, No.3, pp. 129-144, 2008, DOI:10.3970/cmes.2008.031.129

Abstract In the paper we introduce a methodology to construct discrete constitutive matrices relating magnetic fluxes with magneto motive forces (reluctance matrix) and electro motive forces with currents (conductance matrix) needed for discretizing eddy current problems over hexahedral primal grids by means of the Finite Integration Technique (FIT) and the Cell Method (CM). We prove that, unlike the mass matrices of Finite Elements, the proposed matrices ensure both the stability and the consistency of the discrete equations introduced in FIT and CM. More >

Shuling Hu¹, Shengping Shen^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.30, No.2, pp. 57-64, 2008, DOI:10.3970/cmes.2008.030.057

Abstract The effects of surface energy on the interaction between two voids of equal size are investigated. The problem is solved by series expansion in bipolar coordinates. The results show that the surface energy significantly affects the stress concentration around the holes as the size of the holes shrinks to nanometers, meanwhile the interaction between the holes also influences the stress distribution around the holes, which become evident as the holes close to each other. This problem is of great importance in engineering applications. More >

Shu Li¹, S. N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.30, No.1, pp. 37-56, 2008, DOI:10.3970/cmes.2008.030.037

Abstract In this paper, a method based on a combination of an optimization of directions of orthotropy, along with topology optimization, is applied to continuum orthotropic solids with the objective of minimizing their compliance. The spatial discretization algorithm is the so called Meshless Local Petrov-Galerkin (MLPG) "mixed collocation'' method for the design domain, and the material-orthotropy orientation angles and the nodal volume fractions are used as the design variables in material optimization and topology optimization, respectively. Filtering after each iteration diminishes the checkerboard effect in the topology optimization problem. The example results are provided to illustrate the effects of the orthotropic… More >

J. Sladek¹, V. Sladek¹, Ch. Zhang², P. Solek³

CMES-Computer Modeling in Engineering & Sciences, Vol.22, No.3, pp. 217-234, 2007, DOI:10.3970/cmes.2007.022.217

Abstract A meshless method based on the local Petrov-Galerkin approach is proposed for the solution of boundary value problems for coupled thermo-electro-mechanical fields. Transient dynamic governing equations are considered here. To eliminate the time-dependence in these equations, the Laplace-transform technique is applied. Material properties of piezoelectric materials are influenced by a thermal field. It is leading to an induced nonhomogeneity and the governing equations are more complicated than in a homogeneous counterpart. Two-dimensional analyzed domain is subdivided into small circular subdomains surrounding nodes randomly spread over the whole domain. A unit step function is used as the test functions in the… More >

R. Criado¹, J.E. Ortiz¹, V. Mantič¹, L.J. Gray^1,2, F. París¹

CMES-Computer Modeling in Engineering & Sciences, Vol.22, No.2, pp. 151-164, 2007, DOI:10.3970/cmes.2007.022.151

Abstract A numerical implementation of the Somigliana identity in displacements for the solution of 3D elastic problems in exponentially graded isotropic solids is presented. An expression for the fundamental solution in displacements, U_jl, was deduced by Martin et al. (Proc. R. Soc. Lond. A, 458, pp. 1931--1947, 2002). This expression was recently corrected and implemented in a Galerkin indirect 3D BEM code by Criado et al. (Int. J. Numer. Meth. Engng., 2008). Starting from this expression of U_jl, a new expression for the fundamental solution in tractions T_jl has been deduced in the present work. These quite complex expressions of the… More >

J. Sladek¹, V. Sladek¹, Ch. Zhang², P. Solek³, L. Starek³

CMES-Computer Modeling in Engineering & Sciences, Vol.19, No.3, pp. 247-262, 2007, DOI:10.3970/cmes.2007.019.247

Abstract A meshless method based on the local Petrov-Galerkin approach is proposed for crack analysis in two-dimensional (2-D) and three-dimensional (3-D) axisymmetric piezoelectric solids with continuously varying material properties. Axial symmetry of geometry and boundary conditions reduces the original 3-d boundary value problem into a 2-d problem. Stationary problems are considered in this paper. The axial cross section is discretized into small circular subdomains surrounding nodes randomly spread over the analyzed domain. A unit step function is used as the test functions in the local weak-form. Then, the derived local integral equations (LBIEs) involve only contour-integrals on the surfaces of subdomains.… More >

S. Chen^1,2, Y. Liu^1,3, B.C. Khoo⁴, X.J. Fan⁵, J.T. Fan⁶

CMES-Computer Modeling in Engineering & Sciences, Vol.19, No.3, pp. 181-196, 2007, DOI:10.3970/cmes.2007.019.181

Abstract The mesoscopic simulation for fluids flow in a square microchannel is investigated using dissipative particle dynamics. The velocity distribution for single fluid in a square channel is compared with the solutions of CFD solver, which is found to be in good agreement with each other. The no-slip boundary condition could be well held for the repulsive coefficient ranged from 9.68 to 18.0. For the same range of repulsive coefficient, various wettabilities could be obtained by changing the repulsive coefficient for binary immiscible fluids, in which the immiscible fluids are achieved by increasing the repulsive force between species. The typical motion… More >

J. Perko¹, B. Šarler²

CMES-Computer Modeling in Engineering & Sciences, Vol.19, No.1, pp. 55-68, 2007, DOI:10.3970/cmes.2007.019.055

Abstract This work introduces a procedure for automated determination of weight function free parameters in moving least squares (MLS) based meshless methods for non-uniform grids. The meshless method used in present work is Diffuse Approximate Method (DAM). The DAM is structured in 2D with the one or two parameter Gaussian weigh function, 6 polynomial basis and 9 noded domain of influence. The procedure consists of three main elements. The first is definition of the reference quality function which measures the difference between the MLS approximation on non-uniform and hypothetic uniform node arrangements. The second is the construction of the object function… More >

J.A. Sanz, M. Solis, J. Dominguez¹

CMES-Computer Modeling in Engineering & Sciences, Vol.17, No.3, pp. 215-230, 2007, DOI:10.3970/cmes.2007.017.215

Abstract A general mixed boundary element formulation for three-dimensional piezoelectric fracture mechanics problems is presented in this paper. The numerical procedure is based on the extended displacement and traction integral equations for external and crack boundaries, respectively. Integrals with strongly singular and hypersingular kernels appearing in the formulation are analytically transformed into weakly singular and regular integrals. Quadratic boundary elements and quarter-point boundary elements are implemented in a direct way in a computer code. Electric and stress intensity factors are directly computed from nodal values at quarter-point elements. Crack problems in 3D piezoelectric bounded and unbounded solids are solved. The obtained… More >