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Finite Element Method

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Ted Belytschko - One of the best experts on this subject based on the ideXlab platform.

  • Moving particle Finite Element Method with global smoothness
    International Journal for Numerical Methods in Engineering, 2004
    Co-Authors: Su Hao, Kam Liu, Ted Belytschko
    Abstract:

    We describe a new version of the moving particle Finite Element Method (MPFEM) that provides solutions within a C0 Finite Element framework. The Finite Elements determine the weighting for the moving partition of unity. A concept of ‘General Shape Function’ is proposed which extends regular Finite Element shape functions to a larger domain. These are combined with Shepard functions to obtain a smooth approximation. The Moving Particle Finite Element Method combines desirable features of Finite Element and meshfree Methods. The proposed approach, in fact, can be interpreted as a ‘moving partition of unity Finite Element Method’ or ‘moving kernel Finite Element Method’. This Method possesses the robustness and efficiency of the C0 Finite Element Method while providing at least C1 continuity. Copyright © 2004 John Wiley & Sons, Ltd.

Harold S. Park - One of the best experts on this subject based on the ideXlab platform.

  • Moving particle Finite Element Method
    International Journal for Numerical Methods in Engineering, 2002
    Co-Authors: Harold S. Park
    Abstract:

    This paper presents the fundamental concepts behind the moving particle Finite Element Method, which combines salient features of Finite Element and meshfree Methods. The proposed Method alleviates certain problems that plague meshfree techniques, such as essential boundary condition enforcement and the use of a separate background mesh to integrate the weak form. The Method is illustrated via two-dimensional linear elastic problems. Numerical examples are provided to show the capability of the Method in benchmark problems. Copyright © 2001 John Wiley & Sons, Ltd.

Su Hao - One of the best experts on this subject based on the ideXlab platform.

  • Moving particle Finite Element Method with global smoothness
    International Journal for Numerical Methods in Engineering, 2004
    Co-Authors: Su Hao, Kam Liu, Ted Belytschko
    Abstract:

    We describe a new version of the moving particle Finite Element Method (MPFEM) that provides solutions within a C0 Finite Element framework. The Finite Elements determine the weighting for the moving partition of unity. A concept of ‘General Shape Function’ is proposed which extends regular Finite Element shape functions to a larger domain. These are combined with Shepard functions to obtain a smooth approximation. The Moving Particle Finite Element Method combines desirable features of Finite Element and meshfree Methods. The proposed approach, in fact, can be interpreted as a ‘moving partition of unity Finite Element Method’ or ‘moving kernel Finite Element Method’. This Method possesses the robustness and efficiency of the C0 Finite Element Method while providing at least C1 continuity. Copyright © 2004 John Wiley & Sons, Ltd.

Kam Liu - One of the best experts on this subject based on the ideXlab platform.

  • Moving particle Finite Element Method with global smoothness
    International Journal for Numerical Methods in Engineering, 2004
    Co-Authors: Su Hao, Kam Liu, Ted Belytschko
    Abstract:

    We describe a new version of the moving particle Finite Element Method (MPFEM) that provides solutions within a C0 Finite Element framework. The Finite Elements determine the weighting for the moving partition of unity. A concept of ‘General Shape Function’ is proposed which extends regular Finite Element shape functions to a larger domain. These are combined with Shepard functions to obtain a smooth approximation. The Moving Particle Finite Element Method combines desirable features of Finite Element and meshfree Methods. The proposed approach, in fact, can be interpreted as a ‘moving partition of unity Finite Element Method’ or ‘moving kernel Finite Element Method’. This Method possesses the robustness and efficiency of the C0 Finite Element Method while providing at least C1 continuity. Copyright © 2004 John Wiley & Sons, Ltd.

Yih Huang - One of the best experts on this subject based on the ideXlab platform.

  • A wavelet-based stochastic Finite Element Method of thin plate bending
    Applied Mathematical Modelling, 2007
    Co-Authors: Yih Huang
    Abstract:

    Abstract A wavelet-based stochastic Finite Element Method is presented for the bending analysis of thin plates. The wavelet scaling functions of spline wavelets are selected to construct the displacement interpolation functions of a rectangular thin plate Element and the displacement shape functions are expressed by the spline wavelets. A new wavelet-based Finite Element formulation of thin plate bending is developed by using the virtual work principle. A wavelet-based stochastic Finite Element Method that combines the proposed wavelet-based Finite Element Method with Monte Carlo Method is further formulated. With the aid of the wavelet-based stochastic Finite Element Method, the present paper can deal with the problem of thin plate response variability resulting from the spatial variability of the material properties when it is subjected to static loads of uncertain nature. Numerical examples of thin plate bending have demonstrated that the proposed wavelet-based stochastic Finite Element Method can achieve a high numerical accuracy and converges fast.