Zhuo-Jia Fu¹, Wen Chen^1,2, Jeng-Tzong Chen³, Wen-Zhen Qu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.5, pp. 417-443, 2014, DOI:10.3970/cmes.2014.099.417

Abstract This study investigates the singular boundary method (SBM) with three regularization approaches for solving 2D and 3D exterior wave problems. The singular boundary method is a recent meshless boundary collocation method, which introduces the concept of source intensity factors to eliminate the singularity of the fundamental solutions. Recently, three approaches, the inverse interpolation technique (IIT), the semi-analytical technique with boundary IIT (SAT1) and the semi-analytical technique with integral mean value (SAT2), have been proposed to determine the source intensity factors for removing the singularities of Helmholtz fundamental solutions at origin. This study compares numerical accuracy… More >

Chein-Shan Liu ¹

CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.5, pp. 371-391, 2014, DOI:10.3970/cmes.2014.099.371

Abstract We recover an unknown initial temperature for a nonlinear heat conduction equation u_t(x,t) = u_xx(x,t) + H(x,t,u,u_x), under the Cauchy boundary conditions specified on the left-boundary. The method in the present paper transforms the Cauchy problem into an inverse heat source problem to find F(x) in T_t(x,t) = T_xx(x,t) + H + F(x). By using the GL(N,R) Lie-group differential algebraic equations (LGDAE) algorithm to integrate the numerical method of lines discretized equations from sideways heat equation, we can fast recover the initial temperature and two boundary conditions on the right-boundary. The accuracy and efficiency are confirmed by comparing the More >

Ş. Emrah Amrahov¹, N. A. Gasilov², A. G. Fatullayev²

CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.5, pp. 351-369, 2014, DOI:10.3970/cmes.2014.099.351

Abstract In this paper, we present a new approach to a time-optimal control problem with uncertainties. The dynamics of the controlled object, expressed by a linear system of differential equations, is assumed to be crisp, while the initial and final phase states are fuzzy sets. We interpret the problem as a set of crisp problems. We introduce a new notion of fuzzy optimal time and transform its calculation to two classical time-optimal control problems with initial and final sets. We examine the proposed approach on an example which is a problem of fuzzy control of mathematical More >

S.Yu. Reutskiy¹

CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.4, pp. 327-349, 2014, DOI:10.3970/cmes.2014.099.327

Abstract The paper presents a new meshless numerical method for solving 2D and 3D boundary value problems (BVPs) with elliptic PDEs of general form. The coefficients of the PDEs including the main operator part are spatially dependent functions. The key idea of the method is the use of the basis functions which satisfy the homogeneous boundary conditions of the problem. This allows us to seek an approximate solution in the form which satisfies the boundary conditions of the initial problem with any choice of the free parameters. As a result we separate approximation of the boundary More >

Y. T. Wu¹, Y. F. Nie², Z. H. Yang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.4, pp. 297-325, 2014, DOI:10.3970/cmes.2014.099.297

Abstract Four representative multiscale methods, namely asymptotic homogenization method (AHM), heterogeneous multiscale method (HMM), variational multiscale (VMS) method and multiscale finite element method (MsFEM), for elliptic problems with multiscale coefficients are surveyed. According to the features they possess, these methods are divided into two categories. AHM and HMM belong to the up–down framework. The feature of the framework is that the macroscopic solution is solved first with the help of effective information computed in local domains, and then the multiscale solution is resolved in local domains using the macroscopic solution when necessary. VMS method andMsFEM fall More >

J. Sladek^1,2, V. Sladek¹, E. Pan³, D.L. Young⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.4, pp. 273-296, 2014, DOI:10.3970/cmes.2014.099.273

Abstract This paper presents a dynamic analysis of an anti-plane crack in functionally graded piezoelectric semiconductors. General boundary conditions and sample geometry are allowed in the proposed formulation. The coupled governing partial differential equations (PDEs) for shear stresses, electric displacement field and current are satisfied in a local weak-form on small fictitious subdomains. The derived local integral equations involve one order lower derivatives than the original PDEs. All field quantities are approximated by the moving least-squares (MLS) scheme. After performing spatial integrations, we obtain a system of ordinary differential equations for the involved nodal unknowns. It More >

F.L.S. Bussamra¹, E.Lucena Neto¹, W.M. Ponciano¹

CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.3, pp. 255-272, 2014, DOI:10.3970/cmes.2014.099.255

Abstract Hybrid-Trefftz stress finite elements have been applied with success to the analysis of linear and non-linear problems in structural mechanics. Two independent fields are approximated: stresses within the elements and displacements on their boundary. The stress field satisfies the Trefftz constraint a priori, i.e., it is extracted from the Navier equation solution. This type of element has provided remarkable improvement in stress predictions compared to the standard displacement-based finite elements. In this work, solution of stress concentration problems is carried out by hexahedral hybrid-Trefftz stress element models. Stress concentration factors and stress intensity factors are then More >

Yong-Lin Pi¹, Mark Andrew Bradford¹

CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.3, pp. 233-253, 2014, DOI:10.3970/cmes.2014.099.233

Abstract Creep and shrinkage of the concrete core of a concrete-filled steel tubular (CFST) arch under sustained loading are inevitable, and cause a long-term change of the equilibrium configuration of the CFST arch. As the equilibrium configuration changes continuously, the long-term radial and axial displacements of the CFST arch, stress distributions as well as the internal forces in the steel tube and the concrete core change substantially with time. Creep and shrinkage of the concrete core are related to a number of its material parameters such as its creep coefficient, aging coefficient, and shrinkage strain. The… More >

Damian Sokolowski¹, Marcin Kamiński², Michal Strakowski¹

CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.3, pp. 209-231, 2014, DOI:10.3970/cmes.2014.099.209

Abstract The main issue in this paper is to present stochastic analysis of the steel plate girder with the corrugated web subjected to Gaussian random fluctuations in its web thickness. Such an analysis is carried out using the Stochastic Finite Element Method based on the generalized stochastic perturbation technique and discretization of structure with the quadrilateral 4-noded shell finite elements. It is numerically implemented using the FEM system ABAQUS and the symbolic algebra system MAPLE, where all the probabilistic procedures are programmed. We compare the perturbation-based results with these obtained from traditional Monte-Carlo simulation and, separately, More >

Nadjib Ghiti¹

CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.3, pp. 195-208, 2014, DOI:10.3970/cmes.2014.099.195

Abstract This paper presents a large eddy simulation of three dimensional vertically impinging jet on a horizontal plate. The air impinging jet was simulated using the perturbed method based on a high vortex number in the jet inlet for different ranges of Reynolds number Re= 6000, 8000, 10000, 12000, 14000 and for the same distance between the jet and the impinging plate. The effect of the Reynolds number of the air jet impinging on a horizontal plate was studied; the study showed that the vorticity magnitude is increased with the increasing of the Reynolds number. The More >