A weighted finite element mass redistribution method for dynamic contact problems

0491866 - MÚ 2019 RIV NL eng J - Článek v odborném periodiku
Dabaghi, F. - Krejčí, Pavel - Petrov, A. - Pousin, J. - Renard, Y.
A weighted finite element mass redistribution method for dynamic contact problems.
Journal of Computational and Applied Mathematics. Roč. 345, January (2019), s. 338-356. ISSN 0377-0427. E-ISSN 1879-1778
Grant CEP: GA ČR(CZ) GA15-12227S
Grant ostatní: AV ČR(CZ) CNRS - F-13-14-01
Program: Bilaterální spolupráce
Institucionální podpora: RVO:67985840
Klíčová slova: mass redistribution method * unilateral contact
Obor OECD: Applied mathematics
Impakt faktor: 2.037, rok: 2019
https://www.sciencedirect.com/science/article/pii/S0377042718303820

This paper deals with a one-dimensional wave equation being subjected to a unilateral boundary condition. An approximation of this problem combining the finite element and mass redistribution methods is proposed. The mass redistribution method is based on a redistribution of the body mass such that there is no inertia at the contact node and the mass of the contact node is redistributed on the other nodes. The convergence as well as an error estimate in time is proved. The analytical solution associated with a benchmark problem is introduced and it is compared to approximate solutions for different choices of mass redistribution. However some oscillations for the energy associated with approximate solutions obtained for the second order schemes can be observed after the impact. To overcome this difficulty, a new unconditionally stable and a very lightly dissipative scheme is proposed.
Trvalý link: http://hdl.handle.net/11104/0285474