Roman Chapko¹, B. Tomas Johansson²

CMES-Computer Modeling in Engineering & Sciences, Vol.85, No.2, pp. 105-128, 2012, DOI:10.3970/cmes.2012.085.105

Abstract We consider a Cauchy problem for the Laplace equation in a 3-dimen -sional semi-infinite domain that contains a bounded inclusion. The canonical situation is the upper half-space in I\tmspace -.1667em R3 containing a bounded smooth domain. The function value of the solution is specified throughout the plane bounding the upper half-space, and the normal derivative is given only on a finite portion of this plane. The aim is to reconstruct the solution on the surface of the bounded inclusion. This is a generalisation of the situation in Chapko and Johansson (2008) to three-dimensions and with… More >

L. Dong¹, S. N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.85, No.1, pp. 1-44, 2012, DOI:10.3970/cmes.2012.085.001

Abstract In this paper, a generalized Trefftz method in plane elasticity is developed, for solving problems in an arbitrary multiply connected domain. Firstly, the relations between Trefftz basis functions from different source points are discussed, by using the binomial theorem and the logarithmic binomial theorem. Based on these theorems, we clearly explain the relation between the T-Trefftz and the F-Trefftz methods, and why the traditional T-Trefftz method, which uses only one source point, cannot successfully solve problems in a multiply connected domain with genus larger than 1. Thereafter, a generalized Trefftz method is proposed, which uses… More >

Chein-Shan Liu¹, Satya N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.6, pp. 575-602, 2012, DOI:10.3970/cmes.2012.084.575

Abstract An iterative algorithm based on the concept of best descent vector u in x^· = λu is proposed to solve a system of nonlinear algebraic equations (NAEs): F(x) = 0. In terms of the residual vector F and a monotonically increasing positive function Q(t) of a time-like variable t, we define a future cone in the Minkowski space, wherein the discrete dynamics of the proposed algorithm evolves. A new method to approximate the best descent vector is developed, and we find a critical value of the weighting parameter α_c in the best descent vector u = α_cF + B^TF, where B = ∂F/∂x is the More >

Hong-Hua Dai^1,2, Matt Schnoor², Satya N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.5, pp. 459-498, 2012, DOI:10.3970/cmes.2012.084.459

Abstract In this study, the harmonic and 1/3 subharmonic oscillations of a single degree of freedom Duffing oscillator with large nonlinearity and large damping are investigated by using a simple point collocation method applied in the time domain over a period of the periodic solution. The relationship between the proposed collocation method and the high dimensional harmonic balance method (HDHB), proposed earlier by Thomas, Dowell, and Hall (2002), is explored. We demonstrate that the HDHB is not a kind of "harmonic balance method" but essentially a cumbersome version of the collocation method. In using the collocation method,… 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 >

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 >

Dan Ma, Xianbiao Mao, Chong Li, Feng Du

CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.6, pp. 561-574, 2012, DOI:10.3970/cmes.2012.083.561

Abstract Water resisting key strata (WRKS) is one of the most important structures in green coal mining engineering, which has the functions of water-preserved mining and disaster prevention of water inrush, while elastic WRKS is treated as one of the problems for elastic plates in this paper. The existing literatures on elastic plates have largely restricted to different engineering but minority in coal mining engineering. Based on the mechanical models of clamped circular plate with sub-uniform load and simply supported by a concentrated force for elastic WRKS, using the boundary integral equations which is obtained by More >

Li Shan, Ning Cui, Ming Cheng, Kaixin Liu

CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.4, pp. 353-384, 2012, DOI:10.3970/cmes.2012.083.353

Abstract In the present paper, a combined scheme of discrete element method (DEM) and meshless method for numerical simulation of impact problems is proposed. Based on the basic principle of continuum mechanics, an axisymmetric DEM framework is established for modeling the elastoplastic behavior of solid materials. Failure criteria are introduced to model the transformation from a continuum to a discontinuum. The friction force between contact elements is also considered after the failure appears. So our scheme can calculate not only the behavior of continuum and discontinuum, but also the transformation process from a continuum to a More >

D. Ngo-Cong^1,2, N. Mai-Duy¹, W. Karunasena², T. Tran-Cong^1,3

CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.3, pp. 311-352, 2012, DOI:10.3970/cmes.2012.083.311

Abstract In this study, local moving least square - one dimensional integrated radial basis function network (LMLS-1D-IRBFN) method is presented and demonstrated with the solution of time-dependent problems such as Burgers' equation, unsteady flow past a square cylinder in a horizontal channel and unsteady flow past a circular cylinder. The present method makes use of the partition of unity concept to combine the moving least square (MLS) and one-dimensional integrated radial basis function network (1D-IRBFN) techniques in a new approach. This approach offers the same order of accuracy as its global counterpart, the 1D-IRBFN method, while More >

M.R. Myers¹, A.B. Jorge², D.E. Yuhas³, D.G. Walker¹

CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.3, pp. 221-248, 2012, DOI:10.3970/cmes.2012.083.221

Abstract An adaptive extended Kalman filter is developed and investigated for a transient heat transfer problem in which a high heat flux spot source is applied on one side of a thin plate and ultrasonic pulse time of flight is measured between spatially separated transducers on the opposite side of the plate. The novel approach is based on the uncertainty in the state model covariance and leverages trends in the extended Kalman filter covariance to drive changes to the state model covariance during convergence. This work is an integral part of an effort to develop a… More >