Enforcement of essential boundary conditions in meshless approximations using finite elements

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Abstract

A technique for easily treating essential boundary conditions for approximations which are not interpolants, such as moving least-square approximations in the element-free Galerkin method, is presented. The technique employs a string of elements along the essential boundaries and combines the finite element shape functions with the approximation. In the resulting approximation, essential boundary conditions can be treated exactly as in finite elements. It is shown that the resulting approximation can exactly reproduce linear polynomials so that it satisfies the patch test. Numerical studies show that the method retains the high rate of convergence associated with moving least-square approximations.

References (14)

  • T. Belytschko et al.

    A variationally couple finite element boundary element method

    Comput. Struct.

    (1989)
  • Y.Y. Lu et al.

    A new implementation of the element free Galerkin method

    Comput. Methods Appl. Mech. Engrg.

    (1994)
  • T. Belytschko et al.

    Element-free Galerkin methods

    Int. J. Numer. Methods Engrg.

    (1994)
  • R.H. Gallagher

    Finite Element Anslysis: Fundamentals

    (1974)
  • R.A. Gingold et al.

    Smoothed particle hydrodynamics: Theory and application to non-spherical stars

    Mon. Not. Roy. Astron. Soc.

    (1977)
  • P. Lancaster et al.

    Surfaces generated by moving least-squares methods

    Math. Comput.

    (1981)
  • W.K. Liu et al.

    Reproducing kernel particle methods for structural dynamics

    Int. J. Numer. Methods Engrg.

    (1995)
There are more references available in the full text version of this article.

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Research Assistant.

2

Walter P. Murphy Professor.

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