Applications of Variationally Consistent Selective Mass Scaling in Explicit Dynamics

Abstract eng:
The aim of Selective Mass Scaling (SMS) in context of non-linear structural mechanics is to increase the critical time-step for explicit time integration without substantial loss in accuracy in the lower modes. The Conventional Mass Scaling (CMS) adds artificial mass only to diagonal terms of the lumped mass matrix and thus preserves diagonal format of mass matrix. It is usually applied in little number of small or stiff elements, like spot-welds in car crash, whose high eigenfrequencies limit time-step. However, translational and rotational inertia of the structure increases, which may cause non-physical phenomena. SMS technique adds artificial terms both to diagonal and non-diagonal terms, which results in non-diagonal mass matrix, but at least allows preservation of translational mass. Thus SMS can be used uniformly in domain with less non-physical artifacts. The previous works on SMS rely on algebraically constructed mass scaling matrices or stiffness proportional mass scaling. These approaches provide very small choice of mass scaling templates and they lack rigorous variational formulation. The goal of this paper is to develop variational basis for SMS with consistent discretization of inertial term and to assess efficiency of the proposed approach.

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