3. Transition from a quasistatic calculation to a transitory calculation#
Far from being limited to replacing the term STAT_NON_LINE by DYNA_NON_LINE in a command file (as well as defining densities, at minima…), the transition from the quasi-static to the transitory must be accompanied by a certain number of essential precautions, otherwise the quality of the digital solution obtained will greatly degrade the quality of the digital solution obtained.
These adaptations, described in detail in the U2.06.13 documentation, relate to:
the regularization of boundary conditions in time,
the definition of initial conditions that do not introduce numerical oscillations.
In addition to these general aspects, the user should pay attention to other more specific adaptations.
Definition of densities:
from a physical point of view, of course, it is necessary to define density at every point of the model. If the model includes discrete elements, a discrete mass must be attached to them. The assembled mass operator must be invertible. Artifacts that are sometimes used almost statically, such as stiffness in areas of the model (anchors, etc.) with materials having very large Young’s moduli (or very large point stiffness), should be handled with care. In fact, these very steep areas will dynamically generate high-frequency disturbances. Moreover, with an explicit time pattern, these very steep areas may cause the value of the critical time step to drop (cf. R5.05.05).
Definition of mesh sizes and time steps:
as a prerequisite for the transitory calculation, it is strongly recommended to conduct a modal calculation (with CALC_MODES) to obtain modal information that will make it possible to qualify the quality of the model in dynamics and to adjust certain parameters. Since the objective is not to go into the details of modal analysis, we can nevertheless recall a few rules.
We are looking for low frequency solutions, so only the first modes are relevant. Their good representation can give information on the mesh sizes to be used, in addition to the considerations already taken into account for the previous quasistatic calculations. In general, about ten meshes per smallest wavelength is sufficient.
Modal analysis will also make it possible to verify that the model is free of problems such as undefined contributions to inertia or stiffness.
Finally, modal analysis is essential for the use of modal damping in DYNA_NON_LINE or for adjusting Rayleigh damping, as we will see in the following.
Definition of depreciation:
the user will also have to ask himself the question of the amortization intrinsic to the model he wants to use.
In DYNA_NON_LINE, apart from discrete elements, global damping such as Rayleigh or modal can be introduced. Since one seeks to simulate slow changes, one may be tempted to use higher damping values than for classical dynamic calculations. However, a compromise remains to be found, on a case-by-case basis, between an insufficiently damped problem (which will present oscillations) and an excessively damped problem (critical or even over-critical damping).
We therefore recommend starting by implementing « realistic » amortization (therefore with a value identical to what is encountered in transitory dynamics). Then, if this amortization is considered insufficient, to increase it gradually.
On various applications [bib1], it has been observed that Rayleigh type damping, adjusted to an equivalent modal damping of the order of 20%, or even 30%, was suitable.