1. Introduction

Our analysis starts from the weak formulation of the balance under a loading of pressure type following activated by the keyword TYPE_CHARGE: “SUIV” in the STAT_NON_LINE [U4.32.01] command. The difference compared to classical geometric linear analysis is that pressure acts on the deformed geometry and no longer on the initial geometry. This new geometry is obtained from the transform of the initial mean surface subjected to large displacements and rotations [R3.07.05]. The notations are inspired by [R3.07.05].

This transform can be parameterized exactly like the initial surface using the reduced coordinates of the associated isoparametric element: the co-variant or contra-variant references are built at each point of the deformed surface. The writing of the virtual pressure work with this parametrization is done in the deformed configuration using the associated iso-parametric elements. The result is an independence of the area of integration with the movements that is used to express the variation in the virtual work of the external pressure forces in relation to said movements. This has an important advantage compared to the method applied for pressure that follows the facets of 3D elements [R3.03.04]. In fact, this last method, based on an updated Lagrangian formulation, leads to non-linear terms that are difficult to linearize, coming from the Jacobian transformation with respect to the reference configuration.

The finite element objects obtained by linearization with respect to the incremental displacements of the virtual work of the external pressure forces are to be updated at each iteration of the Newton algorithm of STAT_NON_LINE. We emphasize the fact that the contribution of subsequent pressure to the tangent stiffness matrix is not symmetric, and we recall that the geometric part of the tangent matrix is already non-symmetric [bib2].