.. _V6.04.166:

**v6.04.166** SSNV166 — Cracked cylinder under multiple loads
===================================================================

**Summary**

The purpose of this test is to calculate the stress intensity factors along the crack bottom for a cylinder with an axisymmetric crack.

The influence of the degree of the elements and the type of the method is studied through various models.


1. Modeling :math:`A` tests :math:`\mathrm{K1}` and :math:`\mathrm{K3}` with a :math:`\mathrm{3D}` linear mesh and a classical finite element method (:math:`\mathrm{FEM}`).


2. Modeling :math:`B` tests :math:`\mathrm{K1}` and :math:`\mathrm{K3}` with a :math:`\mathrm{3D}` quadratic mesh (Barsoum elements) around the crack bottom and an :math:`\mathrm{FEM}`.


3. Modeling :math:`C` tests :math:`\mathrm{K1}` and :math:`\mathrm{K3}` with a :math:`\mathrm{3D}` linear mesh with a classical resolution but an extraction of intensity factors based on an energy calculation.

In addition, for each model, various load cases are studied:


* traction (stress in :math:`I` mode);


* twisting (stress in :math:`\mathrm{III}` mode);


* flexure (opening on one side, closing on the other) with and without taking into account contact.

Cases of traction and twisting do not involve contact.

Although symmetries exist in some cases (axisymmetry for case 1, plane symmetry for case 2) the representation is done in :math:`\mathrm{3D}` to make the test generalizable under multiple loading.


.. toctree::
    :hidden:

    self

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

    Probl_me_de_r_f_rence
    Solution_de_r_f_rence
    Mod_lisation_A___Maillage_lin_aire__formulation_classique
    Mod_lisation_B___Maillage_quadratique__formulation_classique
    Mod_lisation_C___Maillage_lin_aire__formulation_classique_et_m_thode__nerg_tique
    Synth_se_des_r_sultats