Grid dispersion analysis of plane square biquadratic serendipity finite elements in transient elastodynamics

0395253 - ÚT 2014 RIV GB eng J - Journal Article
Kolman, Radek - Plešek, Jiří - Okrouhlík, Miloslav - Gabriel, Dušan
Grid dispersion analysis of plane square biquadratic serendipity finite elements in transient elastodynamics.
International Journal for Numerical Methods in Engineering. Roč. 96, č. 1 (2013), s. 1-28. ISSN 0029-5981. E-ISSN 1097-0207
R&D Projects: GA ČR GPP101/10/P376; GA ČR(CZ) GAP101/11/0288; GA ČR GA101/09/1630; GA ČR(CZ) GAP101/12/2315
Institutional support: RVO:61388998
Keywords : wave propagation * dispersion properties * biquadratic serendipity finite elements
Subject RIV: BI - Acoustics
Impact factor: 1.961, year: 2013
http://onlinelibrary.wiley.com/doi/10.1002/nme.4539/abstract

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.
Permanent Link: http://hdl.handle.net/11104/0223902