1. Introduction

In order to be able to analyze the behavior of slender structures such as plates, or curved surfaces approximated by facets, whose middle sheet is eccentric with respect to the plane of application of the forces, the concept of eccentricity of the middle sheet with respect to the mesh surface is introduced. The displacement fields varying linearly in the thickness of the plate originate from the mesh surface, that is to say, at the level of the mesh surface, the only degrees of translational freedom are necessary to describe the displacement.

The introduction of kinematics into the expression of deformation work makes it possible to obtain the membrane, flexural and transverse shear rigidities of the eccentric element from those of the equivalent non-eccentric element and from the eccentric distance. All the calculations (excluding specific post-processing) are therefore done in a design coordinate system attached to the mesh plane. By default, the results are therefore obtained in the mesh coordinate system. For some post-treatments, it is possible to automatically have these results in other frames insofar as the user indicates the position of the post-processing plane in relation to the mesh plane.

The eccentric distance between the mesh plane and the middle sheet of the plate is given in AFFE_CARA_ELEM at the same level as the thickness. A positive \(d\) eccentricity means that the mean surface of the plate is actually at a distance \(dn\) from the meshed plate element, the direction \(n\) being given by the normal to the element (see [§4.1] of the reference documentation [R3.07.03] of the plate elements for the construction of this normal).

The notations adopted are those of the note [R3.07.03] on the plate elements DKT, DST, DKQ, DSQ and Q4G.