Home / Advanced Search

  • Title/Keywords

  • Author/Affliations

  • Journal

  • Article Type

  • Start Year

  • End Year

Update SearchingClear
  • Articles
  • Online
Search Results (41)
  • Open Access

    ARTICLE

    A Highly Accurate MCTM for Inverse Cauchy Problems of Laplace Equation in Arbitrary Plane Domains

    Chein-Shan Liu1

    CMES-Computer Modeling in Engineering & Sciences, Vol.35, No.2, pp. 91-112, 2008, DOI:10.3970/cmes.2008.035.091

    Abstract We consider the inverse Cauchy problems for Laplace equation in simply and doubly connected plane domains by recoverning the unknown boundary value on an inaccessible part of a noncircular contour from overspecified data. A modified Trefftz method is used directly to solve those problems with a simple collocation technique to determine unknown coefficients, which is named a modified collocation Trefftz method (MCTM). Because the condition number is small for the MCTM, we can apply it to numerically solve the inverse Cauchy problems without needing of an extra regularization, as that used in the solutions of direct problems for Laplace equation.… More >

  • Open Access

    ARTICLE

    Fast BEM Solvers for 3D Poisson-Type Equations

    Xuefei He1, Kian-Meng Lim1,2,3, Siak-Piang Lim1,2

    CMES-Computer Modeling in Engineering & Sciences, Vol.35, No.1, pp. 21-48, 2008, DOI:10.3970/cmes.2008.035.021

    Abstract The boundary element method (BEM) is known to have the advantage of reducing the dimension of problem by discretizing only the boundary of the domain. But it becomes less attractive for solving Poisson-type equations, due to the need to evaluate the domain integral which is computationally expensive. In this paper, we present the extension of a recently developed fast algorithm for Laplace equation, based on fast Fourier transform on multipoles (FFTM), to solve large scale 3D Poisson-type equations. We combined the Laplace solver with two fast methods for handling the domain integral based on fast Fourier transform (FFT). The first… More >

  • Open Access

    ARTICLE

    A Numerical Model for Elastoplastic Rough Contact

    P. Sainsot1, C. Jacq2, D. Nélias1

    CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.4, pp. 497-506, 2002, DOI:10.3970/cmes.2002.003.497

    Abstract Pressure distributions calculated in the simulation of rough contacts show high values and induce high stresses just beneath the surface. These stresses often exceed the yield strength of the material, therefore, a purely elastic contact model is restrictive. Plastic flow occurs and modifies the surface shape and consequently modifies the surface pressure.
    This paper presents a numerical model for 3D-elastoplastic rough contact. It allows the determination of real pressure and permanent surface displacement (flattening of asperities) as well as residual stresses and plastic strains useful in fatigue analysis. The material is assumed to follow the Von-Mises yield criterion with… More >

  • Open Access

    ARTICLE

    A Simple Multi-Source-Point Trefftz Method for Solving Direct/Inverse SHM Problems of Plane Elasticity in Arbitrary Multiply-Connected Domains

    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 logarithmic and negative power series… More >

  • Open Access

    ARTICLE

    T-Trefftz Voronoi Cell Finite Elements with Elastic/Rigid Inclusions or Voids for Micromechanical Analysis of Composite and Porous Materials

    L. Dong1, S. N. Atluri2

    CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.2, pp. 183-220, 2012, DOI:10.32604/cmes.2012.083.183

    Abstract In this paper, we develop T-Trefftz Voronoi Cell Finite Elements (VCF -EM-TTs) for micromechanical modeling of composite and porous materials. In addition to a homogenous matrix in each polygon-shaped element, three types of arbitrarily-shaped heterogeneities are considered in each element: an elastic inclusion, a rigid inclusion, or a void. In all of these three cases, an inter-element compatible displacement field is assumed along the element outer-boundary, and interior displacement fields in the matrix as well as in the inclusion are independently assumed as T-Trefftz trial functions. Characteristic lengths are used for each element to scale the T-Trefftz trial functions, in… More >

  • Open Access

    ARTICLE

    Development of T-Trefftz Four-Node Quadrilateral and Voronoi Cell Finite Elements for Macro- & Micromechanical Modeling of Solids

    L. Dong1, S. N. Atluri2

    CMES-Computer Modeling in Engineering & Sciences, Vol.81, No.1, pp. 69-118, 2011, DOI:10.3970/cmes.2011.081.069

    Abstract In this paper, we explore three different ways of developing T-Trefftz finite elements of quadrilateral as well as polygonal shapes. In all of these three approaches, in addition to assuming an inter-element compatible displacement field along the element boundary, an interior displacement field for each element is independently assumed as a linear combination of T-Trefftz trial functions. In addition, a characteristic length is defined for each element to scale the T-Trefftz modes, in order to avoid solving systems of ill-conditioned equations. The differences between these three approaches are that, the compatibility between the independently assumed fields at the boundary and… More >

  • Open Access

    ARTICLE

    An Efficient Trefftz-Based Method for Three-Dimensional Helmholtz Problems in Unbounded Domains

    Bart Bergen1, Bert Van Genechten1, Dirk Vandepitte1, Wim Desmet1

    CMES-Computer Modeling in Engineering & Sciences, Vol.61, No.2, pp. 155-176, 2010, DOI:10.3970/cmes.2010.061.155

    Abstract The Wave Based Method (WBM) is a numerical prediction technique for Helmholtz problems. It is an indirect Trefftz method using wave functions, which satisfy the Helmholtz equation, for the description of the dynamic variables. In this way, it avoids both the large systems and the pollution errors that jeopardize accurate element-based predictions in the mid-frequency range. The enhanced computational efficiency of the WBM as compared to the element-based methods has been proven for the analysis of both three-dimensional bounded and two-dimensional unbounded problems. This paper presents an extension of the WBM to the application of three-dimensional acoustic scattering and radiation… More >

  • Open Access

    ARTICLE

    Numerical Characterization of Porous Solids and Performance Evaluation of Theoretical Models via the Precorrected-FFT Accelerated BEM

    Z. Y. Yan1,2, J. Zhang1, W. Ye1, T.X. Yu1

    CMES-Computer Modeling in Engineering & Sciences, Vol.55, No.1, pp. 33-60, 2010, DOI:10.3970/cmes.2010.055.033

    Abstract An 3-D precorrected-FFT accelerated BEM approach for the linear elastic analysis of porous solids with randomly distributed pores of arbitrary shape and size is described in this paper. Both the upper bound and the lower bound of elastic properties of solids with spherical pores are obtained using the developed fast BEM code. Effects of porosity and pore shape on the elastic properties are investigated. The performance of several theoretical models is evaluated by comparing the theoretical predictions with the numerical results. It is found that for porous solids with spherical pores, the performances of the generalized self-consistent method and Mori-Tanaka… More >

  • Open Access

    ARTICLE

    Free Vibration Analysis of a Circular Plate with Multiple Circular Holes by Using the Multipole Trefftz Method

    Wei-Ming Lee1, Jeng-Tzong Chen2

    CMES-Computer Modeling in Engineering & Sciences, Vol.50, No.2, pp. 141-160, 2009, DOI:10.3970/cmes.2009.050.141

    Abstract This paper presents the multipole Trefftz method to derive an analytical model describing the free vibration of a circular plate with multiple circular holes. Based on the addition theorem, the solution of multipoles centered at each circle can be expressed in terms of multipoles centered at one circle, where boundary conditions are specified. In this way, a coupled infinite system of simultaneous linear algebraic equations is derived for the circular plate with multiple holes. The direct searching approach is employed in the truncated finite system to determine the natural frequencies by using the singular value decomposition (SVD). After determining the… More >

  • Open Access

    ARTICLE

    On Solving the Ill-Conditioned System Ax=b: General-Purpose Conditioners Obtained From the Boundary-Collocation Solution of the Laplace Equation, Using Trefftz Expansions With Multiple Length Scales

    Chein-Shan Liu1, Weichung Yeih2, Satya N. Atluri3

    CMES-Computer Modeling in Engineering & Sciences, Vol.44, No.3, pp. 281-312, 2009, DOI:10.3970/cmes.2009.044.281

    Abstract Here we develop a general purpose pre/post conditionerT, to solve an ill-posed system of linear equations,Ax=b. The conditionerTis obtained in the course of the solution of the Laplace equation, through a boundary-collocation Trefftz method, leading to:Ty=x, whereyis the vector of coefficients in the Trefftz expansion, andxis the boundary data at the discrete points on a unit circle. We show that the quality of the conditionerTis greatly enhanced by using multiple characteristic lengths (Multiple Length Scales) in the Trefftz expansion. We further show thatTcan be multiplicatively decomposed into a dilationTDand a rotationTR. For an odd-orderedA, we develop four conditioners based on… More >

Displaying 21-30 on page 3 of 41. Per Page