Shueei-Muh Lin¹

CMES-Computer Modeling in Engineering & Sciences, Vol.52, No.1, pp. 105-124, 2009, DOI:10.3970/cmes.2009.052.105

Abstract In this study, the mathematical model of a non-constant rotating beam is established. It is an in-plane moving mass problem. Due to the effect of non-constant rotation, this model is composed of a governing differential equation with time-dependent coefficients and forcing term and three homogenous boundary conditions and one non-homogeneous boundary condition with time-dependent coefficients and forcing term. It is basically different to the system with constant rotation speed [Lin, 2008] and the linear moving beam system [Lin, 2009]. Obviously, a moving mass problem with time-dependent coefficients and forcing term is very complicated. A new solution method is here developed… More >

P.R. Venkatesh¹, B.Chandrasekhar² , M.M.Benal³

CMES-Computer Modeling in Engineering & Sciences, Vol.52, No.1, pp. 83-104, 2009, DOI:10.3970/cmes.2009.052.083

Abstract In this work, node based basis functions are used to solve the acoustic scattering from plain thin bodies like plates, discs; and intersecting thin bodies like fins on a cylinder. Node based basis functions are defined on the vertices of triangles generated by triangular patch modeling, and these functions are used to define the unknown source distribution. Also the same functions are used as testing functions in the method of moment's solution. Three kinds of nodes were treated for defining the basis functions, namely, boundary node, non-boundary node and non boundary intersecting node. Also, three kinds of bodies were considered… More >

Z. C. Li², T. T. Lu³, H. T. Huang⁴, A. H.-D. Cheng⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.52, No.1, pp. 39-82, 2009, DOI:10.3970/cmes.2009.052.039

Abstract For Laplace's equation and other homogeneous elliptic equations, when the particular and fundamental solutions can be found, we may choose their linear combination as the admissible functions, and obtain the expansion coefficients by satisfying the boundary conditions only. This is known as the Trefftz method (TM) (or boundary approximation methods). Since the TM is a meshless method, it has drawn great attention of researchers in recent years, and Inter. Workshops of TM and MFS (i.e., the method of fundamental solutions). A number of efficient algorithms, such the collocation algorithms, Lagrange multiplier methods, etc., have been developed in computation. However, there… More >

Chih-Ping Wu^1,2, Jian-Sin Wang², Yung-Ming Wang²

CMES-Computer Modeling in Engineering & Sciences, Vol.52, No.1, pp. 1-38, 2009, DOI:10.3970/cmes.2009.052.001

Abstract A meshless collocation method based on the differential reproducing kernel (DRK) interpolation is developed for the three-dimensional (3D) coupled analysis of simply-supported, functionally graded (FG) piezoelectric hollow cylinders. The material properties of FG hollow cylinders are regarded as heterogeneous through the thickness coordinate, and then specified to obey an exponent-law dependent on this. In the present formulation, the shape function for the reproducing kernel (RK) interpolation function at each sampling node is separated into a primitive function possessing Kronecker delta properties and an enrichment function constituting reproducing conditions. By means of this DRK interpolation, the essential boundary conditions can be… More >

Chih-Wen Chang¹, Chein-Shan Liu²

CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.3, pp. 261-276, 2009, DOI:10.3970/cmes.2009.051.261

Abstract The backward advection-dispersion equation (ADE) for identifying the groundwater pollution source identification problems (GPSIPs) is numerically solved by employing a fictitious time integration method (FTIM). The backward ADE is renowned as ill-posed because the solution does not continuously count on the data. We transform the original parabolic equation into another parabolic type evolution equation by introducing a fictitious time coordinate, and adding a viscous damping coefficient to enhance the stability of numerical integration of the discretized equations by employing a group preserving scheme. When several numerical examples are amenable, we find that the FTIM is applicable to retrieve all past… More >

M.V. Menshykova¹, I.A. Guz, O.V. Menshykov

CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.3, pp. 239-260, 2009, DOI:10.3970/cmes.2009.051.239

Abstract The present work is devoted to the investigation of the internal instability in laminated materials. The paper is concerned with the development of a unified computational procedure for numerical realisation of the method as applied to various constitutive equations of the layers, different loading schemes (uniaxial or biaxial loading) and different precritical conditions (large or small precritical deformations). It contains many examples of critical stresses/strains calculations for particular composites as well as analysis of different buckling modes. More >

N. Mai-Duy¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.3, pp. 213-238, 2009, DOI:10.3970/cmes.2009.051.213

Abstract This paper reports a new numerical scheme based on Cartesian grids and local integrated radial-basis-function networks (IRBFNs) for the solution of second-order elliptic differential problems defined on two-dimensional regular and irregular domains. At each grid point, only neighbouring nodes are activated to construct the IRBFN approximations. Local IRBFNs are introduced into two different schemes for discretisation of partial differential equations, namely point collocation and control-volume (CV)/subregion-collocation. Linear (e.g. heat flow) and nonlinear (e.g. lid-driven triangular-cavity fluid flow) problems are considered. Numerical results indicate that the local IRBFN CV scheme outperforms the local IRBFN point-collocation scheme regarding accuracy. Moreover, the former… More >

Chan T.L.^1,2, Xie M.L.^1,3, Cheung C.S.¹

CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.3, pp. 191-212, 2009, DOI:10.3970/cmes.2009.051.191

Abstract An efficient Petrov-Galerkin Chebyshev spectral method coupled with the Taylor-series expansion method of moments (TEMOM) was developed to simulate the effect of coherent structures on particle coagulation in the exhaust pipe. The Petrov-Galerkin Chebyshev spectral method was presented in detail focusing on the analyticity of solenoidal vector field used for the approximation of the flow. It satisfies the pole condition exactly at the origin, and can be used to expand the vector functions efficiently by using the solenoidal condition. This developed TEMOM method has no prior requirement for the particle size distribution (PSD). It is much simpler than the method… More >

D.N. Srinath¹, Sanjay Mittal¹, Veera Manek²

CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.2, pp. 169-190, 2009, DOI:10.3970/cmes.2009.051.169

Abstract A continuous adjoint method is formulated and implemented for the multi-point shape optimization of airfoils at low Re. The airfoil shape is parametrized with a non-uniform rational B-Spline (NURBS). Optimization studies are carried out for two different objective functions. The first involves an inverse function on the lift coefficient over a range of Re. The objective is to determine a shape that results in a lift coefficient of 0.4 at three values of Re: 10, 100 and 500. The second objective involves a direct function on the lift coefficient over a range of angles of attack,a. The lift coefficient is… More >

E. Mesquita¹, J.Labaki ¹ and L.O.S.Ferreira¹

CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.2, pp. 143-168, 2009, DOI:10.3970/cmes.2009.051.143

Abstract There is a growing trend towards solving problems of computational mechanics by parallelization strategies. The traditional approach is to implement the parallelization procedures on CPUs based on the MPI or OpenMP paradigms. Recent efforts have been made to implement computational tasks on general-purpose programmable graphics hardware (GPGPU). The GPU is specially well-suited to address problems that can be formulated in form of data-parallel computations with high arithmetic intensity. This work addresses the implementation of the Longman's integration method on graphics hardware. A serial implementation of Longman's method was rewritten under the SIMD (Single Input Multiple Data) parallel programming paradigm. The… More >