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 when inertia effects cannot be overlooked.

In a certain number of physical configurations, one cannot do without a transitory analysis by content with a modal or harmonic analysis:

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

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

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

The methods of transient dynamic analysis that can then be used are divided into two main categories:

• the so-called direct integration methods,

• Ritz methods including, among others, modal projection recombination.

Direct integration methods are so called because no transformation is performed on the dynamic system after discretization into finite elements.

We will present the direct integration algorithms used to solve a dynamic mechanical problem for linear structures. These algorithms are used in the operator DYNA_VIBRA/BASE_CALCUL =” PHYS “

Ritz’s methods, on the contrary, transform the initial dynamic system, often a projection onto a subspace of the initial discretization space. Dynamic resolution is then performed on a modified system, which only allows access to an approximation of the response of the initial system. They are presented in another document [R5.06.04].