Critical assessment of penalty-type methods for imposition of time-dependent boundary conditions in fem formulations for elastodynamics

Abstract eng:
In a recent work the authors proposed a methodology which avoiding ad hoc procedures and applicable to both linear as well as nonlinear problems, provides a variationallyconsistent way of incorporation of time-dependent boundary conditions in problems of elastodynamics. More specifically, an integral formulation of the elastodynamic problem serves as a basis for the imposition of the corresponding constraints which are enforced via the consistent form of the penalty method, e.g., a form that complies with the norm and inner product of the functional space where the weak formulation is mathematically posed. In that paper [1] it is shown that well known and broadly implemented modelling techniques in the finite element method such as ”large mass” and ”large spring” techniques arise as limiting cases of this penalty formulation. In this work we examine the performance and the characteristics of such methods through simple since qualitative examples.

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