.. _R3.07.05:

**r3.07.05** Solid shell elements in geometric nonlinear
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**Summary:**

In this document, we present the theoretical formulation and the numerical implementation of a finite element of a volume shell for geometric nonlinear analyses. This approach should make it possible to take into account large displacements and large rotations of thin structures, whose characteristic thickness-to-length ratio is less than :math:`1\mathrm{/}10`. Care should be taken to ensure that these rotations remain less than :math:`2\pi`.

This formulation is based on a 3D continuous medium approach, degenerated by the introduction of shell kinematics into plane stresses in the weak form of equilibrium. The measure of the deformations that we use is that of Green-Lagrange, energetically combined with Piola-Kirchhoff constraints of the second kind. The equilibrium formulation is therefore total Lagrangian.

The entirely nonlinear geometric problem is examined first. The case of linear buckling is treated as a borderline case of the first approach.




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    self

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

    Introduction
    Formulation
    Principe_du_travail_virtuel
    Discr_tisation_num_rique_de_la_formulation_variationnelle_issue_du_principe_du_travail_virtuel
    Rigidit__autour_de_la_transform_e_de_la_normale
    Flambement_lin_aire
    Implantation_des__l_ments_de_coque_dans_Code_Aster
    Conclusion
    Bibliographie
    Description_des_versions_du_document