CMES-Vol. 6, No. 6, 2004

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A New Implementation of the Meshless Finite Volume Method, Through the MLPG "Mixed'' Approach
S. N. Atluri¹, Z. D. Han¹, A. M. Rajendran²
CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.6, pp. 491-514, 2004, DOI:10.3970/cmes.2004.006.491
Abstract The Meshless Finite Volume Method (MFVM) is developed for solving elasto-static problems, through a new Meshless Local Petrov-Galerkin (MLPG) ``Mixed'' approach. In this MLPG mixed approach, both the strains as well as displacements are interpolated, at randomly distributed points in the domain, through local meshless interpolation schemes such as the moving least squares(MLS) or radial basis functions(RBF). The nodal values of strains are expressed in terms of the independently interpolated nodal values of displacements, by simply enforcing the strain-displacement relationships directly by collocation at the nodal points. The MLPG local weak form is then written… More >

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Computation of Energy Release Rates for Kinking Cracks based on Virtual Crack Closure Technique
De Xie¹, Anthony M. Waas^1,2, Khaled W. Shahwan³, Jessica A. Schroeder⁴, Raymond G. Boeman⁵
CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.6, pp. 515-524, 2004, DOI:10.3970/cmes.2004.006.515
Abstract A numerical method based on the virtual crack closure technique (VCCT) [Rybicki and Kanninen (1977)] and in conjunction with the finite element (FE) method is presented to compute strain energy release rates for cracks that kink. The method partitions the strain energy release rate and provides an efficient means to compute values of the mode I (G_I) and mode II (G_II) energy release rate at the tip of a kinking crack. The solution procedure is shown to be computationally efficient and operationally simple, involving only the nodal forces and displacements near the crack tip. Example problems More >

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Numerical Treatment of Domain Integrals without Internal Cells in Three-Dimensional BIEM Formulations
Yoshihiro Ochiai¹, Vladimir Sladek²
CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.6, pp. 525-536, 2004, DOI:10.3970/cmes.2004.006.525
Abstract The conventional boundary element method (BEM) uses internal cells for the domain integralsCwhen solving nonlinear problems or problems with domain effects. This paper is concerned with conversion of the domain integral into boundary ones and some non-integral terms in a three-dimensional BIEM, which does not require the use of internal cells. This method uses arbitrary internal points instead of internal cells. The method is based on a three-dimensional interpolation method in this paper by using a polyharmonic function with volume distribution. In view of this interpolation method, the three-dimensional numerical integration is replaced by boundary More >

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Aerodynamic Design of Turbomachinery Cascades Using an Enhanced Time-Marching Finite Volume Method
J. C. Páscoa¹, A. C. Mendes¹, L. M. C. Gato², R. Elder³
CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.6, pp. 537-546, 2004, DOI:10.3970/cmes.2004.006.537
Abstract The paper presents an aerodynamic design method for turbomachinery cascades of blades. The prescribed conditions are the aerodynamic blade load and the blade thickness distributions. An iterative procedure was implemented, based on the solution of the Euler equations, to seek the blade geometry that provides the specified design conditions. A central finite-volume explicit time-marching scheme is used to solve the Euler equations in two-dimensional flow. The numerical scheme uses an adaptive nonlinear artificial dissipation term based on the limiter theory. Starting with the results from the flow analysis through an initially guessed cascade geometry, the More >

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Phase Field: A Variational Method for Structural Topology Optimization
Michael Yu Wang^1,2, Shiwei Zhou²
CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.6, pp. 547-566, 2004, DOI:10.3970/cmes.2004.006.547
Abstract In this paper we present a variational method to address the topology optimization problem -- the phase transition method. A phase-field model is employed based on the phase-transition theory in the fields of mechanics and material sciences. The topology optimization is formulated as a continuous problem with the phase-field as design variables within a fixed reference domain. All regions are described in terms of the phase field which makes no distinction between the solid, void and their interface. The Van der Waals-Cahn-Hilliard theory is applied to define the variational topology optimization as a dynamic process… More >

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Construction of Integral Objective Function/Fitness Function of Multi-Objective/Multi-Disciplinary Optimization
Z. Q. Zhu¹, Z. Liu¹, X. L. Wang¹, R. X. Yu¹
CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.6, pp. 567-576, 2004, DOI:10.3970/cmes.2004.006.567
Abstract To extend an available mono-objective optimization method to multi-objective/multi-disciplinary optimization, the construction of a suitable integral objective function (in gradient based deterministic method-DM) or fitness function (in genetic algorithm-GA) is important. An auto-adjusting weighted object optimization (AWO) method in DM is suggested to improve the available weighted sum method (linear combined weighted object optimizationLWO method). Two formulae of fitness function in GA are suggested for two kinds of design problems. Flow field solution is obtained by solving Euler equations. Electromagnetic field solution is obtained by solving Maxwell equations. Bi-disciplinary optimization computation is carried out by More >

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