On an improved 3D stress analysis for elastic composite shells

•The developed 2D models deliver the complete 3D stress state in inhomogeneous elastic shells.•The computing time to setup the stiffness matrix of the recommended model is independent of the number of layers.•The recommended model requires only a fractional amount of computing time in comparison with the other models.•Use of standard nodal degrees of freedom allows computation of shell intersection problems. In this paper inhomogeneous shells subjected to static loading are considered. The theory is based on a multi–field functional, where the associated Euler-Lagrange equations include besides the global shell equations formulated in stress resultants, the local equilibrium in terms of stresses. Within representative volume elements the displacement field is enriched with warping displacements and relative thickness displacements. Elimination of a set of parameters by static condensation leads to a material matrix for the stress resultants. It is used in displacement based elements or in mixed elements with the usual 5 or 6 nodal degrees of freedom. A second model, where decoupling of the local and global boundary value problems is assumed, proves to be computationally very effective.