.. _V2.03.007:

**v2.03.007** SDLS07 - Eigenmodes of a thin spherical envelope
=====================================================================

**Summary:**

This test from guide VPCS makes it possible to validate the algorithms of the CALC_MODES eigenvalue search operator with the stiffness and mass matrices corresponding to the following models:


1. three-dimensional shells: finite elements DKT (mesh size of a 1/8 sphere),


2. axisymmetric :math:`\mathrm{2D}` finite elements TRIA6 and QUAD8 (mesh of a section),


3. three-dimensional shells: axisymmetric isoparametric finite elements SEG3 (linear mesh of the section),


4. three-dimensional shells COQUE_3D: finite element MEC3QU9H (1/8 sphere mesh),


5. 3D shells COQUE_3D: finite element MEC3TR7H.

The results obtained are compared with the analytical solution (HAYEK) and show differences of less than:


* :math:`\text{0,45\%}` for axisymmetric continuous medium elements,


* :math:`\text{0,20\%}` for DKT shell elements,


* :math:`\text{0,17\%}` for isoparametric axisymmetric shell elements,


* :math:`\text{0,17\%}` for COQUE_3D elements.


.. toctree::
    :hidden:

    self

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

    Probl_me_de_r_f_rence
    Solution_de_r_f_rence
    Mod_lisation_A
    Mod_lisation_B
    Mod_lisation_C
    Mod_lisation_D
    Mod_lisation_E
    Synth_se_des_r_sultats