Dan Xie¹, Min Xu²

CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.5, pp. 377-409, 2013, DOI:10.3970/cmes.2013.093.377

Abstract We apply a simple proper orthogonal decomposition (POD) method to compute the nonlinear oscillations of a degenerate two-dimensional fluttering plate undergoing supersonic flow. First, the von Karman’s large deflection theory and quasi-steady aerodynamic theory are employed in constructing the governing equations of the simply supported plate. Then, the governing equations are solved by both the Galerkin method and the POD method. The Galerkin method is accurate but sometimes computationally expensive, since the number of degrees of freedom (dofs) required is relatively large provided that nonlinearity is strong. The POD method can be used to capture… More >

K. Kakuda¹, T. Nagashima¹, Y. Hayashi¹, S. Obara¹, J. Toyotani¹, S. Miura², N. Katsurada³, S. Higuchi³, S. Matsuda³

CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.5, pp. 363-376, 2013, DOI:10.3970/cmes.2013.093.363

Abstract The application of a GPU-based particle method to three-dimensional incompressible viscous fluid flow problems is presented. The particle approach is based on the MPS (Moving Particle Semi-implicit) scheme using logarithmic weighting function to stabilize the spurious oscillatory solutions for solving the Poisson equation with respect to the pressure fields by using GPU-based SCG (Scaled Conjugate Gradient) method. Numerical results demonstrate the workability and the validity of the present approach through the dam-breaking flow problem and flow behavior in a liquid ring pump with rotating impeller blades. More >

G. P. Nikishkov¹

CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.5, pp. 335-361, 2013, DOI:10.3970/cmes.2013.093.335

Abstract Accuracy of the quarter-point and transition elements is investigated on one- and two-dimensional problems with inverse square-root singularity. It is demonstrated that most coefficients of the stiffness matrix of the quarter-point element are unbounded. However, numerical integration produces finite values of these coefficients. Influence of several parameters on the error in determining the stress intensity factor is studied. Solution accuracy can be improved using special distribution of element sizes and increasing the element integration order in the radial direction. More >

Tai C. Lee¹, Huan J. Keh²

CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.5, pp. 317-333, 2013, DOI:10.3970/cmes.2013.093.317

Abstract A theoretical study of the thermocapillary migration of a fluid sphere located at an arbitrary position inside a spherical cavity is presented in the quasisteady limit of small Reynolds and Marangoni numbers. The applied temperature gradient is perpendicular to the line through the drop and cavity centers. The general solutions to the energy and momentum equations governing the system are constructed from the superposition of their fundamental solutions in the spherical coordinates originating from the two centers, and the boundary conditions are satisfied by a multipole collocation method. Results for the thermocapillary migration velocity of… More >

Bing Li^1,2, Zhengjia He¹

CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.4, pp. 293-316, 2013, DOI:10.3970/cmes.2013.093.293

Abstract The vibration-based crack identification problem insists of finding a measured vibration parameter from a complete crack-detection-database constructed by numerical simulation. It is one of the classical optimization problems. Many intelligence methods, such as neural network (NN), genetic algorithm (GA), determinant transformation (DT), and frequency contour (FC) etc., have been extensively employed as optimization tools to achieve this task. The aim of this paper is to propose a benchmark problem to compare these extensive-used optimization methods in terms of crack identification precision and computational time. The merit and demerits for each method are discussed. The results More >

Xiaokui Yue¹, Yong Xu², Jianping Yuan¹

CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.4, pp. 277-291, 2013, DOI:10.3970/cmes.2013.093.277

Abstract In this paper, a stochastic averaging method is derived for a class of non-linear stochastic systems under parametrical Poisson white noise excitation, which may be used to model the beam-beam interaction models in particle accelerators. The averaged Generalized Fokker-Planck equation is derived and the approximate stationary solution of the averaged Generalized Fokker-Planck equation is solved by using perturbation method. The present method applied in this paper can reduce the dimensions of stochastic ODE from 2n to n, which simplify the complex stochastic ODE, and then the analytical stationary solutions can be obtained. An example is More >

C. F. Loeffler¹, R. G. Peixoto²

CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.4, pp. 253-276, 2013, DOI:10.3970/cmes.2013.093.253

Abstract Here is presented a formal deduction for the Dual Reciprocity hypersingular boundary integral equation for application to two dimensional potential problems. The theoretical and numerical derivations are presented in detail, and some simple test problems are included to verify the accuracy of the proposed formulation. Due to its simplicity, Poisson’s Equation is used as a basis for the mathematical formulations and operational procedures related to the body force term, but the methodology can easily be extended to other more elaborate classes of potential problems. Poles are inserted internally to improve the interpolation within the domain, More >

Wen-Ping Wu^1,2, Zong-Zhuan Yao³

CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.4, pp. 235-252, 2013, DOI:10.3970/cmes.2013.093.235

Abstract The internal microstructure evolution and atomic stress distribution around the crack tip of a pre-cracked single crystal nickel with unequal sample sizes are studied by molecular dynamics (MD) simulation. The simulated results indicate that the crack propagation dynamics and stress distributions around the crack tip are strongly dependent on the microstructure evolution caused by the change of sample size. Unequal sample sizes induce various atomic configurations around the crack tip during the crack propagation. When atomic configuration is invariable around the crack tip, the crack grows rapidly along the crack path, the stress concentration occurs… More >

C. K. Chen¹

CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.3, pp. 221-234, 2013, DOI:10.3970/cmes.2013.093.221

Abstract By extending Bückner’s superposition principle and alternating iteration method, this presentation studies the dual holes interactions. A newly developed numerical scheme is embedded in the conventional Gauss-Legendre quadrature routine for evaluating the boundary integral holding stress singularities. This developed scheme can avoid numerical singularity and facilitate the achieved stress field to be exact as that of analytical solution; however the chosen Gaussian integration points must enter a large quantity. This presentation uses an infinite plate with a centered hole strained by remote axial loading as a testing example, and the numerical results are capable of More >

Ji-Chuan Liu¹, Quan-Guo Zhang²

CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.3, pp. 203-220, 2013, DOI:10.3970/cmes.2013.093.203

Abstract In this paper, we propose an algorithm to solve a Cauchy problem of the Laplace equation in doubly connected domains for 2D and 3D cases in which the Cauchy data are given on the outer boundary. We want to seek a solution in the form of the single-layer potential and discrete it by parametrization to yield an ill-conditioned system of algebraic equations. Then we apply the Tikhonov regularization method to solve this ill-posed problem and obtain a stable numerical solution. Based on the regularization parameter chosen suitably by GCV criterion, the proposed method can get More >