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  • 1
    Electronic Resource
    Electronic Resource
    A Petrov-Galerkin Diffuse Element Method (PG DEM) and its comparison to EFG (1997)
    Springer
    Computational mechanics 19 (1997), S. 327-333 
    Details
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The diffuse element method (DEM) pioneered␣by B. Nayroles, G. Touzot and P. Villon is a meshless method for solving partial differential equations. The original version does not pass the patch test. Here an improved version is proposed. This version is based on a Petrov-Galerkin formulation where test functions are required to meet different conditions than trial functions and is labeled here as PG DEM. It is shown that the original DEM derivative approximation is consistent but not integrable; therefore these functions are not suitable as test functions. A set of conditions on test and trial functions is applied. It is shown that the present Petrov-Galerkin (PG DEM) formulation satisfies the patch test and the numerical results show that it exhibits accuracy and rate of convergence superior to the original DEM, while the “stiffness matrix” will be unsymmetric even for self-adjoint problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004660050181
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    A coupled finite element-element-free Galerkin method (1995)
    Springer
    Computational mechanics 17 (1995), S. 186-195 
    Details
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract A procedure is developed for coupling meshless methods such as the element-free Galerkin method with finite element methods. The coupling is developed so that continuity and consistency are preserved on the interface elements. Results are presented for both elastostatic and elastodynamic problems, including a problem with crack growth.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00364080
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    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    A coupled finite element–element-free Galerkin method (1995)
    Springer
    Computational mechanics 17 (1995), S. 186-195 
    Details
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract  A procedure is developed for coupling meshless methods such as the element-free Galerkin method with finite element methods. The coupling is developed so that continuity and consistency are preserved on the interface elements. Results are presented for both elastostatic and elastodynamic problems, including a problem with crack growth.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00364080
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    Paper (German National Licenses)
    Fulltext
  • 4
    Electronic Resource
    Electronic Resource
    EFG approximation with discontinuous derivatives (1998)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 41 (1998), S. 1215-1233 
    Details
    ISSN: 0029-5981
    Keywords: meshless ; projections ; approximation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A technique for incorporating discontinuities in derivatives into meshless methods is presented. The technique enriches the approximation by adding special shape functions that contain discontinuities in derivatives. The special shape functions have compact support which results in banded matrix equations. The technique is described in element-free Galerkin context, but is easily applicable to other meshless methods and projections. Numerical results for problems in one and two dimensions are reported. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 5
    Electronic Resource
    Electronic Resource
    On the completeness of meshfree particle methods (1998)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 43 (1998), S. 785-819 
    Details
    ISSN: 0029-5981
    Keywords: EFG ; SPH ; particle methods ; meshfree ; completeness ; consistency ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The completeness of Smooth Particle Hydrodynamics (SPH) and its modifications is investigated. Completeness, or the reproducing conditions, in Galerkin approximations play the same role as consistency in finite-difference approximations. Several techniques which restore various levels of completeness by satisfying reproducing conditions on the approximation or the derivatives of the approximation are examined. A Petrov-Galerkin formulation for a particle method is developed using approximations with corrected derivatives. It is compared to a normalized SPH formulation based on kernel approximations and a Galerkin method based on moving least-square approximations. It is shown that the major difference is that in the SPH discretization, the function which plays the role of the test function is not integrable. Numerical results show that approximations which do not satisfy the completeness and integrability conditions fail to converge for linear elastostatics, so convergence is not expected in non-linear continuum mechanics. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 6
    Electronic Resource
    Electronic Resource
    A three-dimensional explicit element-free galerkin method (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 1253-1270 
    Details
    ISSN: 0271-2091
    Keywords: meshless methods ; sloshing ; computational fluid dynamics ; impact ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The formulation and implementation of a three-dimensional meshless method, the element-free Galerkin (EFG) method, are described. The formulation is intended for dynamic problems with geometric and material non-linearities solved with explicit time integration, but some of the developments are applicable to other solution methods. The mechanical formulation is posed in the reference configuration so that the shape functions and their derivatives need to be computed only once. A method for speeding up the calculation of shape functions and their derivatives is presented. Results are presented for sloshing problems and Taylor bar impact problems, including an impact problem in which the bar impacts with an angle of obliquity. © 1997 John Wiley & Sons, Ltd.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
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