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Some energy conservative schemes for vibro-impacts of a beam on rigid obstacles. (English) Zbl 1451.74209
Summary: Caused by the problem of unilateral contact during vibrations of satellite solar arrays, the aim of this paper is to better understand such a phenomenon. Therefore, it is studied here a simplified model composed by a beam moving between rigid obstacles. Our purpose is to describe and compare some families of fully discretized approximations and their properties, in the case of non-penetration Signorini’s conditions. For this, starting from the works of Dumont and Paoli, we adapt to our beam model the singular dynamic method introduced by Renard. A particular emphasis is given in the use of a restitution coefficient in the impact law. Finally, various numerical results are presented and energy conservation capabilities of the schemes are investigated.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74H15 Numerical approximation of solutions of dynamical problems in solid mechanics
74H45 Vibrations in dynamical problems in solid mechanics
35L85 Unilateral problems for linear hyperbolic equations and variational inequalities with linear hyperbolic operators
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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