A weighted finite element mass redistribution method for dynamic contact problems

Farshid Dabaghi (1) , Pavel Krejci (2) , Adrien Petrov (1) , Jérôme Pousin (1) , Yves Renard (1)

1 MMCS - Modélisation mathématique, calcul scientifique
2 Mathematical Institute [Praha] - Academy of Sciences

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.

Mots clés: unilateral contact; variational inequality; energy conservation; numerical solution; mass redistribution method

Domaines: Analyse numérique [math.NA]; Mécanique des solides [physics.class-ph]; Mécanique des structures [physics.class-ph]

Farshid Dabaghi, Pavel Krejci, Adrien Petrov, Jérôme Pousin, Yves Renard. A weighted finite element mass redistribution method for dynamic contact problems. Journal of Computational and Applied Mathematics, 2019, 345, pp.338-356. ⟨10.1016/j.cam.2018.06.030⟩. ⟨hal-01237748⟩