| Contents |
| Advanced composites such as carbon fibre reinforced plastics have become one of the most promising materials to build light-weight structures, for instance in aerospace engineering. In the field, these structures are subject to fluid-structure interaction
with material fatigue and damage. Material inspection by piezoelectric induced ultrasonic waves is a relatively new and an intelligent technique for non-destructive evaluation of such structures. For the phenomenological understanding of wave propagation in composite materials and the design of structural health monitoring systems the ability to solve numerically the elastic vector-valued wave equation in three space dimensions,
\begin{equation}
\rho \, \partial_t^2 \boldsymbol u - \nabla \cdot \boldsymbol \sigma(\boldsymbol u) =
\boldsymbol f\,,\qquad \boldsymbol \sigma = \boldsymbol C(\boldsymbol x) \boldsymbol
\epsilon \,, \quad \boldsymbol \epsilon =
\left(\nabla \boldsymbol u + (\nabla \boldsymbol u)^\top\right)/2\,,
\end{equation}
for $\boldsymbol u: \Omega \times [0,T] \mapsto \mathbb{R}^3$, with $\Omega \subset \mathbb{R}^3$, is particularly important from the point of view of physical realism. In this contribution we propose and analyze higher order variational space-time Galerkin methods for the numerical approximation of solutions to (1). Continuous and discontinuous variational time discretization schemes that are at least A-stable are studied. Discontinuous Galerkin finite element methods are used for the spatial approximation. The numerical analysis of these methods as well as implementational issues are addressed. Their stability properties and their potential to predict complex wave propagation phenomena are illustrated by numerical experiments. Realistic external loads are computed from solving a fluid-structure interaction problem that is considered further. |
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