Journal
SIAM JOURNAL ON NUMERICAL ANALYSIS
Volume 49, Issue 5, Pages 2039-2056Publisher
SIAM PUBLICATIONS
DOI: 10.1137/100804711
Keywords
finite elements; time-integration scheme; elastodynamics; unilateral contact; Coulomb friction; differential inclusion; modified mass method
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The aim of the present work is to analyze the modified mass method for the dynamic Signorini problem with Coulomb friction. We prove that the space semidiscrete problem is equivalent to an upper semicontinuous one-sided Lipschitz differential inclusion and is, therefore, well-posed. We derive an energy balance. Next, considering an implicit time-integration scheme, we prove that, under a CFL-type condition on the discretization parameters, the fully discrete problem is well-posed. For a fixed discretization in space, we also prove that the fully discrete solutions converge to the space semidiscrete solution when the time step tends to zero.
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