Open Access
ARTICLE
M. Azreg-Aïnou1
CMES-Computer Modeling in Engineering & Sciences, Vol.42, No.1, pp. 1-18, 2009, DOI:10.3970/cmes.2009.042.001
Abstract Adomian polynomials (AP's) are expressed in terms of new objects called reduced polynomials (RP's). These new objects, which carry two subscripts, are independent of the form of the nonlinear operator. Apart from the well-known two properties of AP's, curiously enough no further properties are discussed in the literature. We derive and discuss in full detail the properties of the RP's and AP's. We focus on the case where the nonlinear operator depends on one variable and construct the most general analytical expressions of the RP's for small values of the difference of their subscripts. It is shown that each RP… More >
Open Access
ARTICLE
Juan Zheng1,2,3, Shuyao Long1,2, Yuanbo Xiong1,2, Guangyao Li1
CMES-Computer Modeling in Engineering & Sciences, Vol.42, No.1, pp. 19-34, 2009, DOI:10.3970/cmes.2009.042.019
Abstract In this paper, the finite volume meshless local Petrov-Galerkin method (FVMLPG) is applied to carry out a topology optimization design for the continuum structures. In FVMLPG method, the finite volume method is combined with the meshless local Petrov-Galekin method, and both strains as well as displacements are independently interpolated, at randomly distributed points in a local domain, using the moving least squares (MLS) approximation. The nodal values of strains are expressed in terms of the independently interpolated nodal values of displacements, by simple enforcing the strain-displacement relationships directly. Considering the relative density of nodes as design variable, and the minimization… More >
Open Access
ARTICLE
G. Haasemann1, M. Kästner2, V. Ulbricht3
CMES-Computer Modeling in Engineering & Sciences, Vol.42, No.1, pp. 35-58, 2009, DOI:10.3970/cmes.2009.042.035
Abstract The purpose of this paper is the presentation of a new efficient modelling strategy based on the combination of Binary Model and Extended Finite Element Method (X-FEM). It is applied to represent the internal architecture of textile reinforced composites where the resin-saturated fabric is characterised by a complex geometry. Homogenisation methods are used to compute the effective elastic material properties. Thereby, the discrete formulation of periodic boundary conditions is adapted regarding additional degrees of freedom used by finite elements which are based on the X-FEM. Finally, the results in terms of effective material properties reveal a good agreement with parameters… More >
Open Access
ARTICLE
Rencheng Song1,2, Wen Chen2,3
CMES-Computer Modeling in Engineering & Sciences, Vol.42, No.1, pp. 59-70, 2009, DOI:10.3970/cmes.2009.042.059
Abstract The regularized meshless method (RMM) is a novel boundary-type meshless method but by now has mainly been tested successfully to the regular domain problems in reports. This note makes a further investigation on its solution of irregular domain problems. We find that the method fails to produce satisfactory results for some benchmark problems. The reason is due to the inaccurate calculation of the diagonal elements of the numerical discretization matrix in the original RMM, which have strong effect on the resulting solution accuracy. To overcome this severe drawback, this study introduces the weighted diagonal element approach. Our numerical experiments demonstrate… More >
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