1. Introduction

Two finite solid shell elements with transverse shear (the 9-node quadrangle MEC3QU9H and the 7-node triangle MEC3TR7H) are introduced into Code_Aster in the calculation of shell structures of any shape. To represent this type of structures, until now, with Code_Aster, we used plate elements with plane facets that induced parasitic flexions and shells of revolution that were too limiting on the type of structure [R3.07.02]. The development was carried out for isotropic materials with linear kinematics for small displacements and small deformations. This formulation can be extended to anisotropic materials [Annexe 1] and to nonlinear kinematics (large displacements and large rotations) [R3.07.05].

To solve chained thermomechanical problems, one must first use the finite elements of thermal shells with 7 and 9 knots described in [R3.11.01].

The mechanical continuous problem is developed below by describing the kinematics of Hencky-Mindlin-Naghdi shells (hypothesis of straight or plane sections) supplemented by a transverse distortion and the law of thermo-elasto-plastic behavior. Thanks to a penalization parameter, it is possible to go from a theory with shear to a theory without shear. The selected finite elements are then presented, which are isoparametric quadratic elements that allow for a fine representation of curved geometry and good stress estimates. The interpolation and the integration method are also described.

Finally, the development is validated on a few test cases.

The nonlinear kinematics of these shells are covered in the reference documentation [R3.07.05].