An explicit time scheme with local time stepping for one-dimensional wave and impact problems in layered and functionally graded materials

0483805 - ÚT 2018 RIV GR eng C - Konferenční příspěvek (zahraniční konf.)
Kolman, Radek - Cho, S.S. - Park, K.C. - Gonzalez, J.G.
An explicit time scheme with local time stepping for one-dimensional wave and impact problems in layered and functionally graded materials.
COMPDYN 2017. 6th International conference on computational methods in structural dynamics and earthquake engineering. Proceedings. Athens: National Technical University of Athens, 2017 - (Papadrakakis, M.; Fragiadakis, M.), s. 1297-1303. ISBN 978-618-82844-1-8.
[COMPDYN 2017 /6./. Rhodes (GR), 15.06.2017-17.06.2017]
Grant CEP: GA MŠMT(CZ) EF15_003/0000493; GA ČR(CZ) GA16-03823S; GA ČR GA17-12925S
Grant ostatní: AV ČR(CZ) ETA-15-03
Program: Bilaterální spolupráce
Institucionální podpora: RVO:61388998
Klíčová slova: wave propagation * heterogeneous and graded materials * explicit time integration * finite element method * local time stepping * spurious oscillations
Obor OECD: Acoustics
https://2017.compdyn.org/

The standard explicit time scheme (e.g. the central difference method) in finite element analysis is not able to keep accuracy of stress distribution through meshes with different local Courant numbers for each finite element. Therefore in this paper, we suggest and test a two-time step explicit scheme with local time stepping for direct time integration in finite element analysis of wave propagation in heterogeneous solids. The nominated two-time step scheme with the diagonal mass matrix is based on the modification of the central difference method with pullback interpolation and local time stepping. It means that we integrate stress
situation on each finite element with local stable time step size. With local time stepping, it is possible to track more accurately a movement of wavefronts for finite element meshes with different local Courant numbers. We present numerical examples of one-dimensional wave propagation in layered and graded elastic bars under shock loading. Based on numerical tests, the presented time scheme is able to eliminate spurious oscillations in stress distribution in numerical modelling of shock wave propagation in heterogeneous materials.

Trvalý link: http://hdl.handle.net/11104/0279205