.. _U2.08.04:

**u2.08.04** Instructions for buckling calculation
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**Summary:**

The objective of this documentation is to present a methodological guide for a nonlinear buckling analysis of a structure. It mainly covers two functionalities of*Code_Aster*:


* linear buckling analysis, called Euler, through CALC_MODES (with the keyword TYPE_RESU =' MODE_FLAMB '),


* the calculation of the quasistatic evolution (operator STAT_NON_LINE) of the structure which presents geometric and behavioral nonlinearities, whose instabilities are sought (option CRIT_STAB), a limit point, or even the post-critical response.

The first step is generally an Euler buckling calculation, which will make it possible to know the buckling modes and the corresponding critical loads. From the designer's point of view, knowledge of the first mode and its critical load is often sufficient in order to define a margin of operation in relation to the imposed load: the multiplying coefficient between the imposed load and the lowest critical load gives the margin of safety.

**Remarks**


* *Knowledge of the first buckling mode can also be used as an indication to optimize the management of the nonlinear incremental calculation carried out later. In fact, as the critical load approaches, it is then possible to decide to modify the control or to reduce the time step, or even to increase the number of balance verification iterations in the residue method, at each load step.*


* *The shape of the Euler buckling mode can also be used to impose an initial geometric defect on the structure, in order to ensure, among other things, that the incremental nonlinear calculation will indeed branch off this mode.*

Since Euler's analysis is by definition linear, it does not make it possible to take into account inelastic behavioral relationships, contact or the follow-on aspect of forces. It is then necessary to do a non-linear calculation, which in a semi-static way will be based on the command STAT_NON_LINE of *Code_Aster*. This is the classical incremental method per residue in equilibrium.

The particular points of its use will be discussed later, in particular the use of non-linear stability analysis with the keyword CRIT_STAB (which is also available in DYNA_NON_LINE for dynamic studies).

.. toctree::
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    self

.. toctree::
    :maxdepth: 2
    :numbered:

    Analyse_de_flambement_d_Euler
    _tude_non_lin_aire_quasi-statique_de_la_structure
    Bibliographie