About: Grid dispersion analysis of plane square biquadratic serendipity finite elements in transient elastodynamics     Goto   Sponge   NotDistinct   Permalink

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  • The spatial discretisation of a continuum by the FEM introduces dispersion errors to the numerical solution of stress wave propagation. When the propagating phenomena are modelled by the FEM, the speed of a single harmonic wave depends on its frequency. With higher order finite elements, there are optical modes in the spectrum resulting in spurious oscillations of stress and velocity distributions near the sharp wavefronts. For reliable numerical solutions by the FEM, the dispersion errors should be analysed and determined. The dispersion properties of a plane square biquadratic serendipity finite element are examined and compared with a bilinear one. Dispersion analysis is carried out for the consistent and lumped mass matrices. A dispersive improved’ lumped mass matrix for biquadratic serendipity elements is proposed. The paper closes with the recommendation of a choice of permissible dimensionless wavelengths for bilinear and biquadratic serendipity finite element meshes.
  • The spatial discretisation of a continuum by the FEM introduces dispersion errors to the numerical solution of stress wave propagation. When the propagating phenomena are modelled by the FEM, the speed of a single harmonic wave depends on its frequency. With higher order finite elements, there are optical modes in the spectrum resulting in spurious oscillations of stress and velocity distributions near the sharp wavefronts. For reliable numerical solutions by the FEM, the dispersion errors should be analysed and determined. The dispersion properties of a plane square biquadratic serendipity finite element are examined and compared with a bilinear one. Dispersion analysis is carried out for the consistent and lumped mass matrices. A dispersive improved’ lumped mass matrix for biquadratic serendipity elements is proposed. The paper closes with the recommendation of a choice of permissible dimensionless wavelengths for bilinear and biquadratic serendipity finite element meshes. (en)
Title
  • Grid dispersion analysis of plane square biquadratic serendipity finite elements in transient elastodynamics
  • Grid dispersion analysis of plane square biquadratic serendipity finite elements in transient elastodynamics (en)
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  • Grid dispersion analysis of plane square biquadratic serendipity finite elements in transient elastodynamics
  • Grid dispersion analysis of plane square biquadratic serendipity finite elements in transient elastodynamics (en)
skos:notation
  • RIV/61388998:_____/13:00395253!RIV14-GA0-61388998
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  • I, P(GA101/09/1630), P(GAP101/11/0288), P(GAP101/12/2315), P(GPP101/10/P376)
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  • 1
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  • 76893
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  • RIV/61388998:_____/13:00395253
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  • wave propagation; dispersion properties; biquadratic serendipity finite elements (en)
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  • GB - Spojené království Velké Británie a Severního Irska
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  • [83A0053B7757]
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  • International Journal for Numerical Methods in Engineering
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  • 96
http://linked.open...iv/tvurceVysledku
  • Kolman, Radek
  • Plešek, Jiří
  • Gabriel, Dušan
  • Okrouhlík, Miloslav
http://linked.open...ain/vavai/riv/wos
  • 000323887400001
issn
  • 0029-5981
number of pages
http://bibframe.org/vocab/doi
  • 10.1002/nme.4539
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