.. _V6.04.127:

**v6.04.127** SSNV127 - Cylinder in a bore with contact and friction
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**Summary:**

This problem corresponds to a semi-static analysis of a mechanical problem with contact and friction. A cylinder is compressed into a cylindrical bore with a slightly larger diameter by a concentrated force applied to its axis.

This test, called the "Klang problem", is quite widely used in the literature to validate frictional contact models and was in particular used by P. Alart and A. Curnier [:ref:`bib1 <bib1>`] to validate their finite contact and friction elements.

Three 2D models are proposed (D and H with linear elements and F with quadratic elements):

The 3D modeling tests the algorithm of the "PENALISATION" method with master-slave pairing, the penalty relates to contact and friction.

The F and H models test the "CONTINUE" method algorithm with quadratic (SEG3) and linear (SEG2) contact elements, respectively.

The results are compared to an analytical solution given by Klang [:ref:`bib2 <bib2>`].

Instead of reproducing this relatively complicated analytical solution we will use the pressure values obtained from it [:ref:`bib1 <bib1>`].


.. toctree::
    :hidden:

    self

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

    Probl_me_de_r_f_rence
    Solution_de_r_f_rence
    Mod_lisation_D
    Mod_lisation_F
    Mod_lisation_H
    Synth_se_des_r_sultats