Analysis of shell structures under transient loading using adaptivity in time and space

The adaptive analysis of structures under transient loading leads to the question, which time integration scheme, finite elements or finite differences, is most favorably combined with an adaptive spatial FE discretization. In order to judge this, the properties of different discontinuous Galerkin (DG) and the standard Newmark method are investigated first, also concerning efficiency. In particular, the damping and dispersion effects are discussed in detail for various types of problems. It must be noted that the type of problem has to be carefully checked in order to apply the most appropriate and efficient time integration scheme. It is shown that e.g. for the wave propagation problems the DG method with linear approximations (DG P1-P1) has to be favored when adaptivity in space is applied. Finally, an adaptive time step modification scheme is presented and applied to various problems.