.. _R3.07.04:

**r3.07.04** Finite elements of solid shells
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**Summary:**

In order to complete the library of finite elements for flat plates [:ref:`R3.07.03 <R3.07.03>`] currently available in *Code_Aster* (DKT, DST, Q4G...), it is proposed to introduce two finite elements of a solid or three-dimensional shell [:ref:`bib1 <bib1>`]. This modeling COQUE_3D [:external:ref:`U3.12.03 <U3.12.03>`] makes it possible to perform calculations of shell structures of any shape with a better approximation of geometry and kinematics.

We will limit ourselves to the framework of linear kinematics. We therefore remain in small movements and in small deformations. No restrictions are made on the type of behavior under plane constraints.

The two elements that are introduced are the quadratic quadratic quadrangle element Heterosis with 9 nodes and its triangular equivalent with 7 nodes. The formulation of the continuous problem is done in Cartesian coordinates, which makes it possible to avoid explicit calculations of curvatures. These two elements correspond to the 3-node shell line element presented in document [:ref:`R3.07.02 <R3.07.02>`].

These two new elements are validated on existing plate test cases, and on three new shell test cases developed in the validation documentation and whose main conclusions are presented briefly here.

This note also shows in the appendix how to take into account the anisotropy of materials.

 **Table of Contents**




.. toctree::
    :hidden:

    self

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

    Introduction
    Formulation
    Principe_des_travaux_virtuels
    Discr_tisation_num_rique_de_la_formulation_variationnelle_issue_du_principe_du_travail_virtuel
    Validation
    Cha_nage_thermom_canique
    Implantation_des__l_ments_de_coque_dans_Code_Aster
    Conclusion
    Bibliographie
    Description_des_versions_du_document