CMES-Vol. 9, No. 2, 2005

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Vibrations of Cracked Euler-Bernoulli Beams using Meshless Local Petrov-Galerkin (MLPG) Method
U. Andreaus^1,3, R.C. Batra², M. Porfiri^{2, 3}
CMES-Computer Modeling in Engineering & Sciences, Vol.9, No.2, pp. 111-132, 2005, DOI:10.3970/cmes.2005.009.111
Abstract Structural health monitoring techniques based on vibration data have received increasing attention in recent years. Since the measured modal characteristics and the transient motion of a beam exhibit low sensitivity to damage, numerical techniques for accurately computing vibration characteristics are needed. Here we use a Meshless Local Petrov-Galerkin (MLPG) method to analyze vibrations of a beam with multiple cracks. The trial and the test functions are constructed using the Generalized Moving Least Squares (GMLS) approximation. The smoothness of the GMLS basis functions requires the use of special techniques to account for the slope discontinuities at More >

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Finite Element Approaches to Non-classical Heat Conduction in Solids
S. Bargmann, P. Steinmann¹
CMES-Computer Modeling in Engineering & Sciences, Vol.9, No.2, pp. 133-150, 2005, DOI:10.3970/cmes.2005.009.133
Abstract The present contribution is concerned with the modeling and computation of non-classical heat conduction. In the 90s Green and Naghdi presented a new theory which is fully consistent. We suggest a solution method based on finite elements for the spatial as well as for the temporal discretization. A numerical example is compared to existing experimental results in order to illustrate the performance of the method. More >

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A Combination of Group Preserving Scheme and Runge-Kutta Method for the Integration of Landau-Lifshitz Equation
Chein-Shan Liu, Yu-Ling Ku
CMES-Computer Modeling in Engineering & Sciences, Vol.9, No.2, pp. 151-178, 2005, DOI:10.3970/cmes.2005.009.151
Abstract In this paper we are concerned with the integration of a semi-discretized version of the Landau-Lifshitz equation, which is fundamental to describe the magnetization dynamics in micro/nano-scale magnetic systems. The resulting ordinary differential equations at the interior grid points are numerically integrated by a combination of the group preserving scheme derived by Liu (2004a) and the fourth-order Runge-Kutta method, abbreviated as GPS-RK4. The new method not only conserves the magnetization magnitude and has the fourth-order accuracy, but also preserves the Lyapunov property of the Landau-Lifshitz equation, namely the free energy is decreasing with time. In More >

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3-D Modeling of a composite material reinforced with multiple thickly coated particles using the infinite element method
D.S. Liu^1,2 , C.Y. Chen² , D.Y. Chiou³
CMES-Computer Modeling in Engineering & Sciences, Vol.9, No.2, pp. 179-192, 2005, DOI:10.3970/cmes.2005.009.179
Abstract A three-dimensional heterogeneous infinite element method (HIEM) for modeling inclusions with interphases in composite materials is presented. This special element is formulated based on the conventional finite element method (FEM) using the similarity stiffness property and matrix condensation operations. An HIE-FE coupling scheme is also developed and implemented using the commercial software ABAQUS to conduct the elastostatic analysis. The proposed approach was validated first to study heterogeneous material containing one spherical inclusion. The displacement and stress variations around the inclusion vicinity are verified against conventional FEM. The proposed approach was next applied to analyze the effective More >

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MLPG Method Based on Rankine Source Solution for Simulating Nonlinear Water Waves
Q.W. Ma¹
CMES-Computer Modeling in Engineering & Sciences, Vol.9, No.2, pp. 193-210, 2005, DOI:10.3970/cmes.2005.009.193
Abstract Recently, the MLPG (Meshless Local Petrov-Galerkin Method) method has been successfully extended to simulating nonlinear water waves [Ma, (2005)]. In that paper, the author employed the Heaviside step function as the test function to formulate the weak form over local sub-domains, acquiring an expression in terms of pressure gradient. In this paper, the solution for Rankine sources is taken as the test function and the local weak form is expressed in term of pressure rather than pressure gradient. Apart from not including pressure gradient, velocity gradient is also eliminated from the weak form. In addition, More >

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Numerical Simulations of Unstable Flow through a Spherical Bulge in a 90-degree Asymmetrical Bend
J.M.M. Sousa¹
CMES-Computer Modeling in Engineering & Sciences, Vol.9, No.2, pp. 211-220, 2005, DOI:10.3970/cmes.2005.009.211
Abstract Time-dependent numerical simulations of the flow through a spherical bulge in a 90-degree asymmetrical bend have been performed for Reynolds numbers in the range 100-400. The present results have demonstrated that the flow reaches asymptotically steady, symmetrical solutions for Reynolds numbers up to 300, whereas a value of 400 for this parameter leads to unsteadiness. The computed flow behavior at this higher Reynolds number has shown to be characterized by an intermittent transition between small-amplitude, irregular oscillations and large-amplitude bursts occurring at a low frequency. In addition, the unsteady flow was asymmetrical and exhibited swirl More >

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