Shuncai Li^1,2,3, Shichuang Zhuo⁴, Qiang Zhang⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.3, pp. 283-296, 2012, DOI:10.3970/cmes.2012.084.283

Abstract Based on the complex functions theory in elastic mechanics, the bending deflection formula expressed by the complex Fourier series is derived for the infinite plate with a circular opening at first, then the boundary conditions of the circular opening are expanded in Fourier Series, and the unknown coefficients of the Fourier series are determined by comparing coefficients method. By means of the convolution of the complex Fourier series and some basic formulas in the generalized functions theory, the natural boundary integral formula or the analytical deflection formulas expressed by the boundary displacement or loads are… More >

Ryuta Imai¹, Masatoshi Nakagawa²

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.3, pp. 253-282, 2012, DOI:10.3970/cmes.2012.084.253

Abstract In order to evaluate seismic response of fast breeder reactors, finite element analysis for core vibration with contact/impact is performed so far. However a full model analysis of whole core vibration requires huge calculation times and memory sizes. In this research, we propose an acceleration method of reducing the number of degrees of freedom to be solved until converged for nonlinear contact problems. Furthermore we show a sufficient condition for the algorithm to work well and discuss its efficiency and a generalization of the algorithm. In particular we carry out the full model analysis to More >

Yu Wang¹, Zhen Luo^1,2, Nong Zhang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.3, pp. 229-252, 2012, DOI:10.3970/cmes.2012.084.229

Abstract This paper proposes an alternative topology optimization method for the optimal design of continuum structures, which involves a multilevel nodal density-based approximant based on the concept of conventional SIMP (solid isotropic material with penalization) model. First, in terms of the original set of nodal densities, the Shepard function method is applied to generate a non-local nodal density field with enriched smoothness over the design domain. The new nodal density field possesses non-negative and range-bounded properties to ensure a physically meaningful approximation of topology optimization design. Second, the density variables at the nodes of finite elements… More >

Bing Li^1,2, Hongbo Dong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.3, pp. 205-228, 2012, DOI:10.3970/cmes.2012.084.205

Abstract Different from single crack identification method, the number of cracks should be firstly identified, and then the location and depth of each crack can be predicted for multiple cracks identification technology. This paper presents a multiple crack identification algorithm for rotor using wavelet finite element method. Firstly, the changes in natural frequency of a structure with various crack locations and depths are accurately obtained by means of wavelet finite element method; and then the damage coefficient method is used to determine the number and region of cracks. Finally, by finding the points of intersection of More >

T.-T. Hoang-Trieu¹, N. Mai-Duy¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.2, pp. 171-204, 2012, DOI:10.3970/cmes.2012.084.171

Abstract In this paper, new compact local stencils based on integrated radial basis functions (IRBFs) for solving fourth-order ordinary differential equations (ODEs) and partial differential equations (PDEs) are presented. Five types of compact stencils - 3-node and 5-node for 1D problems and 5×5-node, 13-node and 3×3 -node for 2D problems - are implemented. In the case of 3-node stencil and 3×3-node stencil, nodal values of the first derivative(s) of the field variable are treated as additional unknowns (i.e. 2 unknowns per node for 3-node stencil and 3 unknowns per node for 3×3-node stencil). The integration constants… More >

Wei-Chung Tien¹, Yue-Tzu Yang¹, Cha’o-Kuang Chen^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.2, pp. 155-170, 2012, DOI:10.3970/cmes.2012.084.155

Abstract In this paper, the homotopy analysis method is applied to analyze the heat transfer of the oscillating base temperature processes occurring in a convective rectangular fin with variable thermal conductivity. This method is a powerful and easy-to-use tool for non-linear problems and it provides us with a simple way to adjust and control the convergence region of solution series. Without the need of iteration, the obtained solution is in the form of an infinite power series and the results indicated that the series has high accuracy by comparing it with those generated by the complex More >

J. D. Hales¹, S. R. Novascone¹, R. L. Williamson¹, D. R. Gaston¹, M. R. Tonks¹

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.2, pp. 123-154, 2012, DOI:10.3970/cmes.2012.084.123

Abstract The equations governing solid mechanics are often solved via Newton's method. This approach can be problematic if the Jacobian determination, storage, or solution cost is high. These challenges are magnified for multiphysics applications. The Jacobian-free Newton-Krylov (JFNK) method avoids many of these difficulties through a finite difference approximation. A parallel, nonlinear solid mechanics and multiphysics application named BISON has been created that leverages JFNK. We overview JFNK, outline the capabilities of BISON, and demonstrate the effectiveness of JFNK for solid mechanics and multiphysics applications using a series of demonstration problems. We show that JFNK has More >

Zaobao Liu^1,2, Weiya Xu¹, Jianfu Shao²

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.2, pp. 99-122, 2012, DOI:10.3970/cmes.2012.084.099

Abstract In this paper, the Gauss process is proposed for application on landslide displacement analysis and prediction with dynamic crossing validation. The prediction problem using noisy observations is first introduced. Then the Gauss process method is proposed for modeling non-stationary series of landslide displacements based on its ability to model noisy data. The monitoring displacement series of the New Wolong Temple Landslide is comparatively studied with other methods as an instance to implement the strategy of the Gauss process for predicting landslide displacement. The dynamic crossing validation method is adopted to manage the displacement series so… More >

P. L. Bishay¹, S.N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.1, pp. 41-98, 2012, DOI:10.3970/cmes.2012.084.041

Abstract Higher-order two-dimensional as well as low and higher-order three-dimensional new Hybrid/Mixed (H/M) finite elements based on independently assumed displacement, and judiciously chosen strain fields, denoted by HMFEM-2, are developed here for applications in macro-mechanics. The idea of these new H/M finite elements is based on collocating the components of the independent strain field, with those derived from the independently assumed displacement fields at judiciously and cleverly chosen collocation points inside the element. This is unlike the other techniques used in older H/M finite elements where a two-field variational principle was used in order to enforce… More >

O. Baysal¹, G. Tanoglu²

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.1, pp. 27-40, 2012, DOI:10.3970/cmes.2012.084.027

Abstract In this work, an operator splitting method is proposed in order to obtain a stable numerical solution for transport equation with non-linear reaction term. We split the transport equation into a reaction part and an advection diffusion part. The former one which becomes a nonlinear ordinary differential equation can be approximated by the simple higher order integrator or solved exactly. The later one is approximated by the Streamline-Upwind Petrov-Galerkin (SUPG) method combined with the generalized Euler time integration (θ-method). Numerical results that illustrate the good performance of this method are reported. More >