Space-Time Isogeometric Analysis for linear and non-linear elastodynamics. (1st October 2021) - Saadé, C.; Lejeunes, S.; Eyheramendy, D.; Saad, R.
Highlights: New space-time formulation with stabilization terms for elastodynamics. Continuous Galerkin form and Isogeometric Analysis space-time discretization. Small and Finite strains with compressible or nearly-incompressible behaviors. Comparisons with standard schemes for elastodynamics with time discontinuities. Abstract: In this study we investigate a stabilized space-time formulation for linear and non-linear elastodynamics. We use Isogeometric Analysis (IGA) in order to benefit from its numerical qualities. We focus on two points: the formulation of stabilized weak-forms in a linear and non-linear context and the interest of using continuous Galerkin schemes in space and time with higher order and higher continuity basis functions. We illustrate the numerical performance of these methods through typical impact or vibration problems commonly encountered in the field of the elastodynamics of solids.