CMES-Vol. 66, No. 1, 2010

Open Access

ARTICLE

Unified Isoparametric 3D LagrangeFinite Elements
Marcin Maździarz¹
CMES-Computer Modeling in Engineering & Sciences, Vol.66, No.1, pp. 1-24, 2010, DOI:10.3970/cmes.2010.066.001
Abstract The paper presents unified approach to 3D isoparametric Lagrange brick, tetra, and prism finite elements. All shape functions, linear, quadratic and cubic, are depicted in one Cartesian orthogonal coordinate system x,y,z regardless of the type of element. This allows one to use a single transformation rule to calculate global derivatives and a second for integration. Proper numerical Gauss quadratures for these isoparametric elements in a unified approach are presented additionally. More >

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A Moving IRBFN-Based Galerkin Meshless Method
Phong B.H. Le¹, Timon Rabczuk², Nam Mai-Duy¹, Thanh Tran-Cong¹
CMES-Computer Modeling in Engineering & Sciences, Vol.66, No.1, pp. 25-52, 2010, DOI:10.3970/cmes.2010.066.025
Abstract A novel meshless method based on Radial Basis Function networks (RBFN) and variational principle (global weak form) is presented in this paper. In this method, the global integrated RBFN is localized and coupled with the moving least square method via the partition of unity concept. As a result, the system matrix is symmetric, sparse and banded. The trial and test functions satisfy the Kronecker-delta property, i.e. Φ_i(x_j) = δ_ij. Therefore, the essential boundary conditions are imposed in strong form as in the FEMs. Moreover, the proposed method is applicable to scattered nodes and arbitrary domains. The method is examined with… More >

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An Analysis of Backward Heat Conduction Problems Using the Time Evolution Method of Fundamental Solutions
C.H. Tsai¹, D.L. Young², J. Kolibal³
CMES-Computer Modeling in Engineering & Sciences, Vol.66, No.1, pp. 53-72, 2010, DOI:10.3970/cmes.2010.066.053
Abstract The time evolution method of fundamental solutions (MFS) is proposed to solve backward heat conduction problems (BHCPs). The time evolution MFS belongs to one of the mesh-free numerical methods and is essentially composed of a sequence of diffusion fundamental solutions which exactly satisfy the heat conduction equations. Through correct treatment of temporal evolution, the resulting system of the time evolution MFS is smaller, and effectively decreases the possibility of ill-conditioning induced by such strongly ill-posed problems. Both one-dimensional and two-dimensional BHCPs are examined in this study, and the numerical results demonstrate the accuracy and stability of the MFS, especially for… More >

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Size-Dependent Behavior of Macromolecular solids II: Higher-Order Viscoelastic Theory and Experiments
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 >

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