S.Yu. Reutskiy¹

CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.2, pp. 115-142, 2009, DOI:10.3970/cmes.2009.051.115

Abstract In this paper a new numerical technique for problems of free vibrations of arbitrary shaped non-homogeneous membranes:∇²w + k²q(x)w = 0, x∈ Ω⊂R², B[w] = 0, x∈∂Ω is presented. Homogeneous membranes of a complex form are considered as a particular case. The method is based on mathematically modeling of physical response of a system to excitation over a range of frequencies. The response amplitudes are then used to determine the resonant frequencies. Applying the method, one gets a sequence of boundary value problems (BVPs) depending on the spectral parameter k. The eigenvalues are sought as positions of the maxima of… More >

Dongjie Liu¹, Dehao Yu²

CMES-Computer Modeling in Engineering & Sciences, Vol.37, No.3, pp. 305-330, 2008, DOI:10.3970/cmes.2008.037.305

Abstract The coupling method of natural boundary element and mixed finite element is applied to analyze the stationary Navier-Stokes equation in 2-D unbounded domains. After an artificial smooth boundary is introduced, the original nonlinear problem is reduced into an equivalent problem defined in bounded computational domain. The well-posedness of the reduced problem is proved. The finite element approximation of this problem is given, and numerical example is provided to show the feasibility and efficiency of the method. More >

R. Martin¹, D. Komatitsch^1,2, S. D. Gedney³

CMES-Computer Modeling in Engineering & Sciences, Vol.37, No.3, pp. 274-304, 2008, DOI:10.3970/cmes.2008.037.274

Abstract In the context of the numerical simulation of seismic wave propagation, the perfectly matched layer (PML) absorbing boundary condition has proven to be efficient to absorb surface waves as well as body waves with non grazing incidence. But unfortunately the classical discrete PML generates spurious modes traveling and growing along the absorbing layers in the case of waves impinging the boundary at grazing incidence. This is significant in the case of thin mesh slices, or in the case of sources located close to the absorbing boundaries or receivers located at large offset. In previous work we derived an unsplit convolutional… More >

Wei-Ming Lee¹, Jeng-Tzong Chen^2,3

CMES-Computer Modeling in Engineering & Sciences, Vol.37, No.3, pp. 243-273, 2008, DOI:10.3970/cmes.2008.037.243

Abstract In this paper, a semi-analytical approach is proposed to solve the scattering problem of flexural waves and to determine dynamic moment concentration factors (DMCFs) in an infinite thin plate with multiple circular holes. The null-field integral formulation is employed in conjunction with degenerate kernels, tensor transformation and Fourier series. In the proposed direct formulation, all dynamic kernels of plate are expanded into degenerate forms and further the rotated degenerate kernels have been derived for the general exterior problem. By uniformly collocating points on the real boundary, a linear algebraic system is constructed. The results of dynamic moment concentration factors for… More >

LiviuMarin ¹

CMES-Computer Modeling in Engineering & Sciences, Vol.37, No.3, pp. 203-242, 2008, DOI:10.3970/cmes.2008.037.203

Abstract In this paper, a meshless method for the stable solution of direct and inverse problems associated with the two-dimensional Laplace equation in the presence of boundary singularities and noisy boundary data is proposed. The governing equation and boundary conditions are discretized by the method of fundamental solutions (MFS), whilst the existence of the boundary singularity is taken into account by subtracting from the original MFS solution the corresponding singular solutions, as given by the asymptotic expansion of the solution near the singular point. However, even in the case when the boundary singularity is accounted for, the numerical solutions obtained by… More >

Hokyung Shim¹, Vinh Thuy Tran Ho^1,,Semyung Wang^1,2, Daniel A. Tortorelli³

CMES-Computer Modeling in Engineering & Sciences, Vol.37, No.2, pp. 175-202, 2008, DOI:10.3970/cmes.2008.037.175

Abstract This paper presents a topological shape optimization technique for electromagnetic problems using a level set method and radial basis functions. The proposed technique is a level set (LS) based optimization dealing with geometrical shape derivatives and topological design. The shape derivative is computed by an adjoint variable method to avoid numerous sensitivity evaluations. A level set model embedded into the scalar function of higher dimensions is propagated to represent the design boundary of a domain. The level set function interpolated into a fixed initial domain is evolved by using the Hamilton-Jacobi equation. The moving free boundaries (dynamic interfaces) represented in… More >

H. T. Wang, G. Hall, S. Y. Yu, Z. H. Yao

CMES-Computer Modeling in Engineering & Sciences, Vol.37, No.2, pp. 153-174, 2008, DOI:10.3970/cmes.2008.037.153

Abstract Graphite materials are widely used in gas-cooled nuclear reactors as both moderators and reflectors. The graphite properties change when the microstructure damage occurs due to the in-core radiation and oxidation, thereby having a strong impact on the service life of graphite. In this paper, the X-ray tomography and the boundary element method (BEM) are introduced to the microstructure modeling and numerical simulations of both the mechanical and thermal property changes of nuclear graphite due to radiolytic oxidation. The model is established by the three-dimensional X-ray scan on the isotropic nuclear graphite Gilsocarbon, which is used in the UK commercial reactors.… More >

S. Venkatesha¹, R. Rajender², C. S. Manohar³

CMES-Computer Modeling in Engineering & Sciences, Vol.37, No.2, pp. 113-152, 2008, DOI:10.3970/cmes.2008.037.113

Abstract The problem of structural damage detection based on measured frequency response functions of the structure in its damaged and undamaged states is considered. A novel procedure that is based on inverse sensitivity of the singular solutions of the system FRF matrix is proposed. The treatment of possibly ill-conditioned set of equations via regularization scheme and questions on spatial incompleteness of measurements are considered. The application of the method in dealing with systems with repeated natural frequencies and (or) packets of closely spaced modes is demonstrated. The relationship between the proposed method and the methods based on inverse sensitivity of eigensolutions… More >

Meiling Zhao¹, Yufeng Nie²

CMES-Computer Modeling in Engineering & Sciences, Vol.37, No.2, pp. 97-112, 2008, DOI:10.3970/cmes.2008.037.097

Abstract Meshless local Petrov-Galerkin (MLPG) method is successfully applied for electromagnetic field computations. The moving least square technique is used to interpolate the trial and test functions. More attention is paid to imposing the essential boundary conditions of electromagnetic equations. A new coupled meshless local Petrov-Galerkin and finite element (MLPG-FE) method is presented to enforce the essential boundary conditions. Unlike the conventional coupled technique, this approach can ensure the smooth blending of the potential variables as well as their derivatives in the transition region between the meshless and finite element domains. Then the boundary singular weight method is proposed to enforce… More >

Kuo-Ning Chiang¹, Chan-Yen Chou², Chung-Jung Wu²,Chao-Jen Huang², Ming-Chih Yew²

CMES-Computer Modeling in Engineering & Sciences, Vol.37, No.1, pp. 85-96, 2008, DOI:10.3970/cmes.2008.037.085

Abstract An atomic-level analytical solution, together with a modified Morse potential, has been developed to estimate temperature-dependent thermal expansion coefficients (CTE) and elastic characteristics of bulk metals. In this study, inter-atomic forces are considered as a set of anharmonic oscillator networks which can be described by Morse potential, while the material properties can be defined by these inter-atomic forces; when temperature increases, the vibration of the anharmonic oscillator causes the phenomenon of temperature-dependent material properties. The results of analysis showed that the original Morse potential can give a reasonable prediction of the thermal expansion coefficients and elastic constants of metals at… More >