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  • Open Access


    Meshfree Solution of Q-tensor Equations of Nematostatics Using the MLPG Method

    Radek Pecher1, Steve Elston, Peter Raynes

    CMES-Computer Modeling in Engineering & Sciences, Vol.13, No.2, pp. 91-102, 2006, DOI:10.3970/cmes.2006.013.091

    Abstract Meshfree techniques for solving partial differential equations in physics and engineering are a powerful new alternative to the traditional mesh-based techniques, such as the finite difference method or the finite element method. The elimination of the domain mesh enables, among other benefits, more efficient solutions of nonlinear and multi-scale problems. One particular example of these kinds of problems is a Q-tensor based model of nematic liquid crystals involving topological defects.
    This paper presents the first application of the meshless local Petrov-Galerkin method to solving the Q-tensor equations of nematostatics. The theoretical part introduces the Landau -- de Gennes free-energy… More >

  • Open Access


    Treatment of Sharp Edges & Corners in the Acoustic Boundary Element Method under Neumann Boundary Condition

    Zai You Yan1

    CMES-Computer Modeling in Engineering & Sciences, Vol.13, No.2, pp. 81-90, 2006, DOI:10.3970/cmes.2006.013.081

    Abstract Boundary element method in acoustics for Neumann boundary condition problems including sharp edges & corners is investigated. In previous acoustic boundary element method, acoustic pressure and normal velocity are the two variables at sharp edges & corners. However, the normal velocity at sharp edges & corners is discontinuous due to the indefinite normal vector. To avoid the indefinite normal vector and the discontinuous normal velocity at sharp edges & corners, normal vector of elemental node is defined and applied in the numerical implementation. Then the normal velocity is transformed to velocity which is unique even at sharp edges & corners.… More >

  • Open Access


    Buckling of Honeycomb Sandwiches: Periodic Finite Element Considerations

    D. H. Pahr1, F.G. Rammerstorfer1

    CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.3, pp. 229-242, 2006, DOI:10.3970/cmes.2006.012.229

    Abstract Sandwich structures are efficient lightweight materials. Due to there design they exhibit very special failure modes such as global buckling, shear crimping, facesheet wrinkling, facesheet dimpling, and face/core yielding. The core of the sandwich is usually made of foams or cellular materials, e.g., honeycombs. Especially in the case of honeycomb cores the correlation between analytical buckling predictions and experiments might be poor (Ley, Lin, and Uy (1999)). The reason for this lies in the fact that analytical formulae typically assume a homogeneous core (continuous support of the facesheets). This work highlights problems of honeycomb core sandwiches in a parameter regime,… More >

  • Open Access


    Structured Mesh Refinement in Generalized Interpolation Material Point (GIMP) Method for Simulation of Dynamic Problems

    Jin Ma, Hongbing Lu, Ranga Komanduri1

    CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.3, pp. 213-228, 2006, DOI:10.3970/cmes.2006.012.213

    Abstract The generalized interpolation material point (GIMP) method, recently developed using a C1 continuous weighting function, has solved the numerical noise problem associated with material points just crossing the cell borders, so that it is suitable for simulation of relatively large deformation problems. However, this method typically uses a uniform mesh in computation when one level of material points is used, thus limiting its effectiveness in dealing with structures involving areas of high stress gradients. In this paper, a spatial refinement scheme of the structured grid for GIMP is presented for simulations with highly localized stress gradients. A uniform structured background… More >

  • Open Access


    A Group Preserving Scheme for Burgers Equation with Very Large Reynolds Number

    Chein-Shan Liu1

    CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.3, pp. 197-212, 2006, DOI:10.3970/cmes.2006.012.197

    Abstract In this paper we numerically solve the Burgers equation by semi-discretizing it at the n interior spatial grid points into a set of ordinary differential equations: u· = f(u,t), u ∈ Rn. Then, we take the dissipative behavior of Burgers equation into account by considering the magnitude ||u|| as another component; hence, an augmented quasilinear differential equations system X˙ = AX with X := (uT,||u||)T ∈ Mn+1 is derived. According to a Lie algebra property of A∈so(n,1) we thus develop a new numerical scheme with the transformation matrix G∈SOo(n,1) being an element of the proper orthochronous Lorentz group.… More >

  • Open Access


    Applications of MLPG Method in Dynamic Fracture Problems

    L. Gao1, K. Liu1,2, Y. Liu3

    CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.3, pp. 181-196, 2006, DOI:10.3970/cmes.2006.012.181

    Abstract A new numerical algorithm based on the Meshless Local Petrov-Galerkin approach is presented for analyzing the dynamic fracture problems in elastic media. To simplify the treatment of essential boundary condition, a novel modified Moving Least Square (MLS) procedure is proposed by introducing Lagrange multiplier into MLS procedure, which can perform both MLS approximation and interpolation in one approximation domain. The compact spline function is used as the test function in the local form of elasto-dynamic equations. For the feature of stress wave propagation, the coupled second-order ODEs respect to the time are solved by the explicit central difference method with… More >

  • Open Access


    Computing Prager's Kinematic Hardening Mixed-Control Equations in a Pseudo-Riemann Manifold

    Chein-Shan Liu1

    CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.3, pp. 161-180, 2006, DOI:10.3970/cmes.2006.012.161

    Abstract Materials' internal spacetime may bear certain similarities with the external spacetime of special relativity theory. Previously, it is shown that material hardening and anisotropy may cause the internal spacetime curved. In this paper we announce the third mechanism of mixed-control to cause the curvedness of internal spacetime. To tackle the mixed-control problem for a Prager kinematic hardening material, we demonstrate two new formulations. By using two-integrating factors idea we can derive two Lie type systems in the product space of Mm+1⊗Mn+1. The Lie algebra is a direct sum of so(m,1)so(n,1), and correspondingly the symmetry group is a direct product of… More >

  • Open Access


    Spectral Element Approach for Forward Models of 3D Layered Pavement

    Chun-Ying Wu1,3, Xue-Yan Liu2, A. Scarpas2, Xiu-Run Ge3

    CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.2, pp. 149-158, 2006, DOI:10.3970/cmes.2006.012.149

    Abstract For the spectral analysis of the three-dimensional multi-layered pavement, 3D layer spectral element method is presented to solve the problems of bounded layer system subjected to a transient load pulse. In spectral element, each layer is treated as one spectral element. The wave propagation inside each layer element is achieved by the superposition of the incident wave and the reflection wave. Fast Fourier transformation is used to transform FWD datum from time domain to frequency domain. The accuracy and efficiency of 3D layer spectral element approach were verified by analyzing the Falling weight deflectometer(FWD) testing model with the spectral methods… More >

  • Open Access


    The Optimal Radius of the Support of Radial Weights Used in Moving Least Squares Approximation

    Y.F. Nie1,2, S.N. Atluri2, C.W. Zuo1

    CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.2, pp. 137-148, 2006, DOI:10.3970/cmes.2006.012.137

    Abstract Owing to the meshless and local characteristics, moving least squares (MLS) methods have been used extensively to approximate the unknown function of partial differential equation initial boundary value problem. In this paper, based on matrix analysis, a sufficient and necessary condition for the existence of inverse of coefficient matrix used in MLS methods is developed firstly. Then in the light of approximate theory, a practical mathematics model is posed to obtain the optimal radius of support of radial weights used in MLS methods. As an example, while uniform distributed particles and the 4th order spline weight function are adopted in… More >

  • Open Access


    A Meshless Spatial Coupling Scheme for Large-scale Fluid-structure-interaction Problems

    R. Ahrem1, A. Beckert2, H. Wendland3

    CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.2, pp. 121-136, 2006, DOI:10.3970/cmes.2006.012.121

    Abstract We present a new efficient scheme for loose coupling in fluid-structure-interaction problems as they typically appear in the context of aircraft design. This coupling scheme is based upon a multivariate scattered data interpolation approach, based on radial basis functions and partition of unity methods. It allows us to couple arbitrary meshes on fluid and structure side. It conserves virtual work and forces. It is designed for large scale problems and allows the coupling of entire aircraft meshes. More >

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