Temporal-spatial dispersion and stability analysis of finite element method in explicit elastodynamics

0458121 - ÚT 2017 RIV GB eng J - Journal Article
Kolman, Radek - Plešek, Jiří - Červ, Jan - Okrouhlík, Miloslav - Pařík, Petr
Temporal-spatial dispersion and stability analysis of finite element method in explicit elastodynamics.
International Journal for Numerical Methods in Engineering. Roč. 106, č. 2 (2016), s. 113-128. ISSN 0029-5981. E-ISSN 1097-0207
R&D Projects: GA ČR(CZ) GAP101/11/0288; GA ČR(CZ) GAP101/12/2315; GA TA ČR(CZ) TH01010772
Institutional support: RVO:61388998
Keywords : bilinear and biquadratic serendipity finite elements * finite element method * stability analysis * temporal and spatial dispersion * wave propagation
Subject RIV: BI - Acoustics
Impact factor: 2.162, year: 2016
http://onlinelibrary.wiley.com/doi/10.1002/nme.5010/full

This work presents the temporal-spatial (full) dispersion and stability analysis of plane square linear and biquadratic serendipity finite elements in explicit numerical solution of transient elastodynamic problems. Here, the central difference method, as an explicit time integrator, is exploited. The paper complements and extends the previous work on spatial/grid dispersion analysis of plane square biquadratic serendipity finite elements. We report on a computational strategy for temporal-spatial dispersion relationships, where eigenfrequencies from grid/spatial dispersion analysis are adjusted to comply with the time integration method. Besides that, an ‘optimal’ lumped mass matrix for the studied finite element types is proposed and investigated. Based on the temporal-spatial dispersion and stability analysis, relationships suggesting the ‘proper’ choice of mesh size and time step size from knowledge of the loading spectrum are presented
Permanent Link: http://hdl.handle.net/11104/0258655