The lateral hulls of multi-shelled ships such as Catamarans or Trimarans can be considered as rigid solids, or compared to thin walled beams in multi-layered materials for the global statical or dynamical behaviour of the ship. Unfortunately this approximation no longer holds after a detailed study of the hulls.
Working in these problems we proceed to a fine analysis of the stress field at the neighbourhood of the linkage shell-arm or of the holes for access input to the hull itself. Analysis with a beam model is inadequate and the shell theory must be more appropriate. Numerous papers have been devoted to shell elements, see References 1 to 8 to mention just a few. Some of them require a reduced or selective integration We choose to start from the Ahmad element,'3*14 which is suitable for moderate thick shells.". l 6 The final aim of this paper is to explain how to build up a multi-layered equivalent homogeneous shell element which is both economical and accurate. Some examples will be given and compared with those obtained with the Ahmad finite element.
GEOMETRY
As for the plate element, we consider only quadrilateral (QS) or triangular (T6) curvilinear elements in the global Cartesian system (0, x, y, z) (see Figure 1).
Let P(x, y, z ) be a point of the mean surface with local curvilinear co-ordinates (r, q, v = 0), v being in the thickness direction. The geometry is defined by At each point P(s, q, 0) a local orthogonal right-handed basis with unit vectors (el, e,, e3) can be built up using a 3