1. Introduction#

In order to have the finest possible evaluation of the response of a mechanical system to a given set of stresses, it may prove essential to take into account non-linearities and dynamic phenomena.

Usually, we can distinguish two evolutions of numerical methods to achieve this:

  • on the one hand, classical linear dynamic calculations (often on a modal basis) are called into question by the possible appearance of non-linearities (material, contact/friction or large transformations) which require the use of the operator « DYNA_NON_LINE » (the operator « DYNA_VIBRA » in transition on a modal basis only accepts local nonlinearities, for example of the shock node type),

  • on the other hand, we can ask ourselves the question of the validity and the limits of applications of nonlinear quasi‑static approaches (operator [STAT_NON_LINE]), when the evolution of the solution may be subject to transient phenomena whose time scale becomes small compared to the specific characteristics of the structure.

In the first case, the user therefore starts from a model that is relevant for linear dynamics and that must be enriched correctly in order to take into account non-linearities.

In the second case, it is a bit the opposite: the user starts from a relevant, almost static non-linear model that must be adapted to the dynamics.

This documentation will attempt to guide users who are potentially confronted with these two situations.

Given the very wide variety of problems that may be addressed, the rules proposed here are necessarily quite general and it is highly likely that case-by-case adjustments for specific problems are indispensable. It is completely illusory to think that even if all the specifications in this document are respected, non-linear calculation will take place without any surprises… Expertise work remains essential!

Prior to reading this documentation, it is strongly recommended that you have read the reference documentation for the « STAT_NON_LINE » and « DYNA_NON_LINE » operators: [R5.03.01] and [R5.05.05]. Indeed, the theoretical aspects will not be detailed here because they are already covered in these two reference documents.

This documentation is supplemented by other more specific references:

  1. [U2.06.03]: on amortization modeling,

  2. [U2.06.05]: for soil-structure interaction (linear and non-linear),

  3. [U2.06.09]: for single and multi-support in seismic calculation of equipment in particular,

  4. [U2.06.10]: on the specificities of studies such as civil engineering under seismic loading,

  5. [U2.06.11]: for the use of fluid-structure models coupled with « DYNA_NON_LINE »,

  6. [U2.04.07]: use of « DYNA_NON_LINE » to solve slowly evolving but highly non-linear problems that have difficulty converging with « STAT_NON_LINE » (see bibliography),

  7. [U2.07.04]: for the non-linear transient dynamics of a model partially reduced by dynamic condensation with « DYNA_NON_LINE »,

  8. [U2.06.32]: for modeling rotating machines.

Reading the documentation [U2.04.01], which gives advice on how to use the « STAT_NON_LINE » operator, is also highly recommended because here you will especially delve into the specificities related to dynamics. All aspects common to « STAT_NON_LINE » and « DYNA_NON_LINE » and that are detailed in the documentation [U2.04.01], such as the choice of parameters for Newton’s algorithm, remain valid in dynamics and are therefore not included here.