A weighted finite element mass redistribution method for dynamic contact problems
For researchers in computational mechanics, this provides an improved numerical method for wave equations with unilateral boundary conditions, though it is an incremental improvement over existing mass redistribution techniques.
The paper proposes a weighted finite element mass redistribution method for dynamic contact problems, proving convergence and error estimates. A new unconditionally stable and lightly dissipative scheme is introduced to reduce energy oscillations after impact.
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 are 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, an new unconditionally stable and a very lightly dissipative scheme is proposed.