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Conservative discretization of contact/impact problems for nearly rigid bodies. (English) Zbl 1029.74044
Summary: We propose a discretization scheme for contact/impact problems related to modeling of gears. The problem is first discretized in time, and then a variational formulation for the resulting one-step problem is developed. A finite element discretization completes the discretization process. The scheme is a reinterpretation of general Simo-Laursen-Chavla algorithm in the context of rigid body motion superimposed with small elastic deformation; it conserves precisely the linear momentum and total energy, and approximately the angular momentum. The discretization method is illustrated with two numerical examples: standard one-dimensional impact problem for an elastic rod, and a two-dimensional model problem for an elastic wheel bouncing witin a constraining box.

74S05 Finite element methods applied to problems in solid mechanics
74M15 Contact in solid mechanics
74M20 Impact in solid mechanics
2Dhp90; HP90
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