1. Introduction#

The aim of transient dynamic analysis is to determine the response of a structure as a function of time, given an external loading or boundary conditions as a function of time, in cases where inertia effects cannot be overlooked.

In a certain number of physical configurations, one cannot be satisfied with a modal or harmonic analysis and one must perform a transitory analysis. This is especially the case if:

  • the history of the phenomenon is important in the study,

  • if the external load is complex (earthquake, multi-component excitations, etc… ),

  • if the system is non-linear (plasticity, shocks, friction, etc…).

The transient analysis methods that can then be used fall into two main categories:

  • the so-called direct integration methods,

  • Ritz methods, which include, among other things, the recombination of modal projections.

Direct integration methods are so called because no transformation is performed on the dynamic system after discretization by finite elements. They are presented in the document [R5.05.02], algorithms for the direct integration of the DYNA_VIBRA/BASE_CALCUL =” PHYS “operator.

Ritz’s methods, on the other hand, transform the initial dynamic system by projecting it onto a subspace of the initial discretization space. The resolution is then carried out on a modified system, which, if reduced, only allows access to an approximation of the response of the real system.

Time integration algorithms on a generalized coordinate system are used to solve dynamic problems in mechanics for linear structures, with possible consideration of localized nonlinearities such as shocks, friction, and effort-displacement relationships and effort-speed relationships. Some algorithms also allow substructuring.

These algorithms are programmed in the operator DYNA_VIBRA/BASE_CALCUL =” GENE “[U4.53.21].