CMES-Vol. 12, No. 2, 2006

Open Access

ARTICLE

Preserving Constraints of Differential Equations by Numerical Methods Based on Integrating Factors
Chein-Shan Liu¹
CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.2, pp. 83-108, 2006, DOI:10.3970/cmes.2006.012.083
Abstract The system we consider consists of two parts: a purely algebraic system describing the manifold of constraints and a differential part describing the dynamics on this manifold. For the constrained dynamical problem in its engineering application, it is utmost important to developing numerical methods that can preserve the constraints. We embed the nonlinear dynamical system with dimensions n and with k constraints into a mathematically equivalent n + k-dimensional nonlinear system, which including k integrating factors. Each subsystem of the k independent sets constitutes a Lie type system of X^˙_i = A_iX_i with A_i ∈ so(n_i,1) and n₁ +···+n_k = n.… More >

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ARTICLE

Analysis of Circular Torsion Bar with Circular Holes Using Null-field Approach
Jeng-Tzong Chen¹, Wen-Cheng Shen², Po-Yuan Chen²
CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.2, pp. 109-119, 2006, DOI:10.3970/cmes.2006.012.109
Abstract In this paper, we derive the null-field integral equation for a circular bar weakened by circular cavities with arbitrary radii and positions under torque. To fully capture the circular geometries, separate forms of fundamental solution in the polar coordinate and Fourier series for boundary densities are adopted. The solution is formulated in a manner of a semi-analytical form since error purely attributes to the truncation of Fourier series. Torsion problems are revisited to demonstrate the validity of our method. Torsional rigidities for different number of holes are also discussed. More >

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A Meshless Spatial Coupling Scheme for Large-scale Fluid-structure-interaction Problems
R. Ahrem¹, A. Beckert², H. Wendland³
CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.2, pp. 121-136, 2006, DOI:10.3970/cmes.2006.012.121
Abstract We present a new efficient scheme for loose coupling in fluid-structure-interaction problems as they typically appear in the context of aircraft design. This coupling scheme is based upon a multivariate scattered data interpolation approach, based on radial basis functions and partition of unity methods. It allows us to couple arbitrary meshes on fluid and structure side. It conserves virtual work and forces. It is designed for large scale problems and allows the coupling of entire aircraft meshes. More >

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The Optimal Radius of the Support of Radial Weights Used in Moving Least Squares Approximation
Y.F. Nie^1,2, S.N. Atluri², C.W. Zuo¹
CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.2, pp. 137-148, 2006, DOI:10.3970/cmes.2006.012.137
Abstract Owing to the meshless and local characteristics, moving least squares (MLS) methods have been used extensively to approximate the unknown function of partial differential equation initial boundary value problem. In this paper, based on matrix analysis, a sufficient and necessary condition for the existence of inverse of coefficient matrix used in MLS methods is developed firstly. Then in the light of approximate theory, a practical mathematics model is posed to obtain the optimal radius of support of radial weights used in MLS methods. As an example, while uniform distributed particles and the 4^th order spline weight More >

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Spectral Element Approach for Forward Models of 3D Layered Pavement
Chun-Ying Wu^1,3, Xue-Yan Liu², A. Scarpas², Xiu-Run Ge³
CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.2, pp. 149-158, 2006, DOI:10.3970/cmes.2006.012.149
Abstract For the spectral analysis of the three-dimensional multi-layered pavement, 3D layer spectral element method is presented to solve the problems of bounded layer system subjected to a transient load pulse. In spectral element, each layer is treated as one spectral element. The wave propagation inside each layer element is achieved by the superposition of the incident wave and the reflection wave. Fast Fourier transformation is used to transform FWD datum from time domain to frequency domain. The accuracy and efficiency of 3D layer spectral element approach were verified by analyzing the Falling weight deflectometer(FWD) testing More >

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