Numerical approximations of a one dimensional elastodynamic contact problem based on mass redistribution method

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

1 ICJ - Institut Camille Jordan

This paper focuses on a one-dimensional elastodynamic contact problem and aims to give some new numerical results. Under appropriate regularity assumptions on the initial data, a new proof of existence and uniqueness results is proposed. An approximation of this evolutionary problem combining the nite element method as well as the mass redistribution method that consists on a redistribution of the body mass such that there is no inertia at the contact node, is introduced. Then two benchmark problems (one being new) with their analytical solutions are presented and some possible discretizations using di erent time{ integration schemes are described. Finally, numerical experiments are reported and analyzed.

Keywords: energy conservation; Numerical solution; mass redistribution method; variational inequality; unilateral contact; energy conservation.

Domains: Numerical Analysis [math.NA]

Farshid Dabaghi, Adrien Petrov, Jérôme Pousin, Yves Renard. Numerical approximations of a one dimensional elastodynamic contact problem based on mass redistribution method. 2013. ⟨hal-00917450v1⟩