Analyse numérique d'un modèle de coques de koiter discrétisé en base cartésienne par éléments finis DKT

This paper describes and studies a variational formulation of a Kotier thin shell model in which the unknown displacement field is expressed and approximated in a fixed cartesian basis. More precisely, the proposed method approximates each Cartesian component of the displacement field by DKT (Discrete Kirchhoff Triangles) finite elements. Using a functional framework proposed by Blouza and Le Dret, and appropriate inverse inequalities, we prove that the corresponding discrete formulation is consistent and that its solution converge in 0(h) towards the unique solution of the continuous problem. Compared to more standard approaches written in a local basis, the approximation in a Cartesian basis is simpler and requires less regularity on the configuration φ of the shell surface or on the underlying mesh.