J. P. Xu¹, Y. Q. Liu^1,2, S. Q. Li³, S. C. Wu⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.3, pp. 201-216, 2008, DOI:10.3970/cmes.2008.038.201

Abstract For the first time, a special-purpose finite element simulation system CoinForm is developed to analyze the embossing process of commemorative coin, in which one-point reduced integration approach is used in solid element finite element dynamic explicit program. Viscous damping hourglass control algorithm can effectively suppress the spurious modes activated by reduced integration and the computational effort is saved about 93% compared with other method that evaluate anti-hourglass force using stabilization matrix. The embossing process of commemorative coin is then simulated and compared with results from the DEFORM 3D software, which verify the excellent performance of present CoinForm system. According to… More >

Briti Sundar Deb¹, Srinivasan Natesan²

CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.2, pp. 179-200, 2008, DOI:10.3970/cmes.2008.038.179

Abstract This paper presents an almost second--order uniformly convergent Richardson extrapolation method for convection- dominated coupled system of boundary value problems. First, we solve the system by using the classical finite difference scheme on the layer resolving Shishkin mesh, and then we construct the Richardson approximation solution using the solutions obtained on N and 2N mesh intervals. Second-order parameter--uniform error estimate is derived. The proposed method is applied to a test example for verification of the theoretical results for the case ε ≤ N⁻¹. More >

C. Zheng¹, S. C. Wu^2,3,4, X.H.Tang¹, J. H. Zhang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.2, pp. 149-178, 2008, DOI:10.3970/cmes.2008.038.149

Abstract A novel meshfree poly-cell Galerkin method is developed for problems of elasticity and fracture. To improve accuracy, a poly-cell support is proposed to ensure the alignment of shape function support and the integration domain. By orthonormalizing basis functions, the improved moving least-square is formulated soundly, in which frequent matrix inversions are avoided. The Nitsche's method is introduced to treat the essential boundary conditions. It is found that computed solutions are more accurate than those obtained using the circle support used in standard MLS. Furthermore, numerical results present the superconvergent property, compared with the theoretical values in both displacement and energy… More >

P. Huang^1,2, X. Zhang^1,3, S. Ma¹, H.K. Wang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.2, pp. 119-148, 2008, DOI:10.3970/cmes.2008.038.119

Abstract The material point method (MPM) is an extension of particle-in-cell method to solid mechanics. A parallel MPM code is developed using FORTRAN 95 and OpenMP in this study, which is designed primarily for solving impact dynamic problems. Two parallel methods, the array expansion method and the domain decomposition method, are presented to avoid data races in the nodal update stage. In the array expansion method, two-dimensional auxiliary arrays are created for nodal variables. After updating grid nodes in all threads, the auxiliary arrays are assembled to establish the global nodal array. In the domain decomposition method, the background grid is… More >

M. Patrício¹, R. Mattheij², G. de With³

CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.2, pp. 89-118, 2008, DOI:10.3970/cmes.2008.038.089

Abstract The behaviour of composite materials with periodically distributed constituents is considered. Mathematically, this can be described by a boundary value problem with highly oscillatory coefficient functions. An algorithm is proposed to handle the case when the underlying periodicity is locally disturbed. This procedure is constructed using fundamental concepts from homogenisation theory and domain decomposition techniques. Applications to layered materials are considered. More >

Zhi-Zhong Yan^1,2, Yue-Sheng Wang^1,3, Chuanzeng Zhang²

CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.1, pp. 59-88, 2008, DOI:10.3970/cmes.2008.038.059

Abstract In this paper, a numerical method based on the wavelet theory is developed for calculating band structures of 2D phononic crystals consisting of general anisotropic materials. After systematical consideration of the appropriate choice of wavelets, two types of wavelets, the Haar wavelet and Biorthogonal wavelet, are selected. Combined with the supercell technique, the developed method can be then applied to compute the band structures of phononic crystals with point or line defects. We illustrate the advantages of the method both mathematically and numerically. Particularly some representative numerical examples are presented for various material combinations (solid-solid, solid-fluid and fluid-fluid) with complex… More >

J.J. Benito¹, F. Ureňa², L. Gavete³, B. Alonso³

CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.1, pp. 39-58, 2008, DOI:10.3970/cmes.2008.038.039

Abstract One of the most universal and effective methods, in wide use today, for solving equations of mathematical physics approximately is the finite difference method (FDM). The Generalized finite difference method (GFDM) is evolved fron classical (FDM), which can be applied over general or irregular clouds of points.
This paper starts by showing the GFDM. In this paper, this meshless method is used for solving second-order partial (pde's) with constant coefficients in any type of domain. The method gives the values of derivatives in the nodes using the direct application of the formulae in differences obtained.
The following points describe… More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.1, pp. 25-38, 2008, DOI:10.3970/cmes.2008.038.025

Abstract In this paper a complex matrix operator and a complex field are used to express the Maxwell equations, of which the complex field embraces all field variables and the matrix operator embraces the time and space differential operators. By left applying the operator on the complex field one can get all the four Maxwell equations, which are usually expressed by the vector form. The new formulation matches the Lorenz gauge condition, and its mathematical advantage is that it can incorporate the Maxwell equations into a single equation. The introduction of four-potential is possible only under the Lorenz gauge. In terms… More >

Sirajul Haq¹, Siraj-ul-Islam², Arshed Ali³

CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.1, pp. 1-24, 2008, DOI:10.3970/cmes.2008.038.001

Abstract In this paper we propose a meshfree technique for the numerical solution of the modified equal width wave (MEW) equation. Combination of collocation method using the radial basis functions (RBFs) with first order accurate forward difference approximation is employed for obtaining meshfree solution of the problem. Different types of RBFs are used for this purpose. Performance of the proposed method is successfully tested in terms of various error norms. In the case of non-availability of exact solution, performance of the new method is compared with the results obtained from the existing methods. Propagation of a solitary wave, interaction of two… More >

D. H. Pahr¹, H.J. Böhm¹

CMES-Computer Modeling in Engineering & Sciences, Vol.34, No.2, pp. 117-136, 2008, DOI:10.3970/cmes.2008.034.117

Abstract The combination of heterogeneous volume elements and numerical analysis schemes such as the Finite Element method provides a powerful and well proven tool for studying the mechanical behavior of composite materials. Periodicity boundary conditions (PBC), homogeneous displacement boundary conditions (KUBC) and homogeneous traction boundary conditions (SUBC) have been widely used in such studies. Recently Pahr and Zysset (2008) proposed a special set of mixed uniform boundary conditions (MUBC) for evaluating the macroscopic elasticity tensor of human trabecular bone. These boundary conditions are not restricted to periodic phase geometries, but were found to give the same predictions as PBC for the… More >