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  • Open Access

    ARTICLE

    The Computations of Large Rotation Through an Index Two Nilpotent Equation

    Chein-Shan Liu1

    CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.3, pp. 157-176, 2006, DOI:10.3970/cmes.2006.016.157

    Abstract To characterize largely deformed spin-free reference configuration of materials, we have to construct an orthogonal transformation tensor Q relative to the fixed frame, such that the tensorial equation Q˙ = WQ holds for a given spin history W. This paper addresses some interesting issues about this equation. The Euler's angles representation, and the (modified) Rodrigues parameters representation of the rotation group SO(3) unavoidably suffer certain singularity, and at the same time the governing equations are nonlinear three-dimensional ODEs. A decomposition Q = FQ1 is first derived here, which is amenable to a simpler treatment of Q1 than Q, and… More >

  • Open Access

    ARTICLE

    Three-Dimensional Dynamic Fracture Analysis Using the Material Point Method

    Y. J. Guo1, J. A. Nairn2

    CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.3, pp. 141-156, 2006, DOI:10.3970/cmes.2006.016.141

    Abstract This paper describes algorithms for three-dimensional dynamic stress and fracture analysis using the material point method (MPM). By allowing dual velocity fields at background grid nodes, the method provides exact numerical implementation of explicit cracks in a predominantly meshless method. Crack contact schemes were included for automatically preventing crack surfaces from interpenetration. Crack-tip parameters, dynamic$J$-integral vector and mode I, II, and III stress intensity factors, were calculated from the dynamic stress solution. Comparisons to finite difference method (FDM), finite element method (FEM), and boundary element method (BEM), as well as to static theories showed that More >

  • Open Access

    ARTICLE

    A Fast Space-Time BEM Method for 3D Elastodynamics

    J. X. Zhou1, T. Koziara1, T. G. Davies1

    CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.2, pp. 131-140, 2006, DOI:10.3970/cmes.2006.016.131

    Abstract The classical BEM approach for elastodynamics can produce poor results when high gradients are generated by impulses. High gradient areas evolve over time and their locations are unknown a priori, so they usually can not be captured by uniform meshes. In this paper, we propose a novel method which interpolates both spatial and temporal domains. A direct space-time discretization scheme is used to capture the wave fronts accurately and to forestall generation of spurious oscillations there. Some numerical examples are given to demonstrate the power and scope of the method. More >

  • Open Access

    ARTICLE

    A Meshfree Thin Shell for Arbitrary Evolving Cracks Based on An Extrinsic Basis

    Timon Rabczuk1, Pedro Areias2

    CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.2, pp. 115-130, 2006, DOI:10.3970/cmes.2006.016.115

    Abstract This paper proposes a meshfree method for arbitrary evolving cracks in thin shells. The approach is an improvement of the method proposed by Rabczuk T., Areias P.M.A., Belytschko T. (A meshfree thin shell for large deformation, finite strain and arbitrary evolving cracks, International Journal for Numerical Methods in Engineering). In the above cited paper, a shell was developed based on an intrinsic basis of third order completeness. Third order completeness was necessary to remove membrane locking. This resulted in the use of very large domains of influence that made the method computationally expensive. If the More >

  • Open Access

    ARTICLE

    Investigations on the Accuracy and Condition Number for the Method of Fundamental Solutions

    C.C. Tsai1, Y.C. Lin2, D.L. Young2,3, S.N. Atluri4

    CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.2, pp. 103-114, 2006, DOI:10.3970/cmes.2006.016.103

    Abstract In the applications of the method of fundamental solutions, locations of sources are treated either as variables or a priori known constants. In which, the former results in a nonlinear optimization problem and the other has to face the problem of locating sources. Theoretically, farther sources results in worse conditioning and better accuracy. In this paper, a practical procedure is provided to locate the sources for various time-independent operators, including Laplacian, Helmholtz operator, modified Helmholtz operator, and biharmonic operator. Wherein, the procedure is developed through systematic numerical experiments for relations among the accuracy, condition number, and More >

  • Open Access

    ARTICLE

    3D Multi-Material Structural Topology Optimization with the Generalized Cahn-Hilliard Equations

    Shiwei Zhou1, Michael Yu Wang2

    CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.2, pp. 83-102, 2006, DOI:10.3970/cmes.2006.016.083

    Abstract This paper describes a self-mass-conservative Cahn-Hilliard (C-H) model with elastic strain energy (mean compliance) for the optimization of multi-material structure topology. The total free energy of the generalized C-H system can be represented as a Lyapunov functional so that the elastic strain energy, as a part of the total free energy, decreases gradually to attain optimal material distribution. The interface energy relating to phase gradient in the total free energy plays an important role in regularizing the original ill-posed problem by restricting the structure's boundaries. On the other hand, interface coalescence and break-up due to More >

  • Open Access

    ARTICLE

    Distributed Finite Element Normalized Approximate Inverse Preconditioning

    G.A. Gravvanis1, K.M. Giannoutakis1

    CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.2, pp. 69-82, 2006, DOI:10.3970/cmes.2006.016.069

    Abstract A new class of normalized explicit optimized approximate inverse finite element matrix techniques, based on normalized finite element approximate factorization procedures, for solving sparse linear systems resulting from the finite element discretization of partial differential equations in three space variables are introduced. A new parallel normalized explicit preconditioned conjugate gradient square method in conjunction with normalized approximate inverse finite element matrix techniques for solving efficiently sparse finite element linear systems on distributed memory systems is also presented along with theoretical estimates on speedups and efficiency. The performance on a distributed memory machine, using Message Passing More >

  • Open Access

    ARTICLE

    Meshless Local Petrov-Galerkin Method for Linear Coupled Thermoelastic Analysis

    J. Sladek1, V. Sladek1, Ch. Zhang2, C.L. Tan3

    CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.1, pp. 57-68, 2006, DOI:10.3970/cmes.2006.016.057

    Abstract The Meshless Local Petrov-Galerkin (MLPG) method for linear transient coupled thermoelastic analysis is presented. Orthotropic material properties are considered here. A Heaviside step function as the test functions is applied in the weak-form to derive local integral equations for solving two-dimensional (2-D) problems. In transient coupled thermoelasticity an inertial term appears in the equations of motion. The second governing equation derived from the energy balance in coupled thermoelasticity has a diffusive character. To eliminate the time-dependence in these equations, the Laplace-transform technique is applied to both of them. Local integral equations are written on small More >

  • Open Access

    ARTICLE

    Multiscale Simulation of Nanoindentation Using the Generalized Interpolation Material Point (GIMP) Method, Dislocation Dynamics (DD) and Molecular Dynamics (MD)

    Jin Ma, Yang Liu, Hongbing Lu, Ranga Komanduri1

    CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.1, pp. 41-56, 2006, DOI:10.3970/cmes.2006.016.041

    Abstract A multiscale simulation technique coupling three scales, namely, the molecular dynamics (MD) at the atomistic scale, the discrete dislocations at the meso scale and the generalized interpolation material point (GIMP) method at the continuum scale is presented. Discrete dislocations are first coupled with GIMP using the principle of superposition (van der Giessen and Needleman (1995)). A detection band seeded in the MD region is used to pass the dislocations to and from the MD simulations (Shilkrot, Miller and Curtin (2004)). A common domain decomposition scheme for each of the three scales was implemented for parallel More >

  • Open Access

    ARTICLE

    Regularized Meshless Method for Solving Acoustic Eigenproblem with Multiply-Connected Domain

    K.H. Chen1, J.T. Chen2, J.H. Kao3

    CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.1, pp. 27-40, 2006, DOI:10.3970/cmes.2006.016.027

    Abstract In this paper, we employ the regularized meshless method (RMM) to search for eigenfrequency of two-dimension acoustics with multiply-connected domain. The solution is represented by using the double layer potentials. The source points can be located on the physical boundary not alike method of fundamental solutions (MFS) after using the proposed technique to regularize the singularity and hypersingularity of the kernel functions. The troublesome singularity in the MFS methods is desingularized and the diagonal terms of influence matrices are determined by employing the subtracting and adding-back technique. Spurious eigenvalues are filtered out by using singular More >

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