A coupled global–local shell model with continuous interlaminar shear stresses

In this paper layered composite 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 in-plane equilibrium in terms of stresses and a constraint which enforces the correct shape of warping through the thickness. Within a four-node element the warping displacements are interpolated with layerwise cubic functions in thickness direction and constant shape throughout the element reference surface. Elimination of stress, warping and Lagrange parameters on element level leads to a mixed hybrid shell element with 5 or 6 nodal degrees of freedom. The implementation in a finite element program is simple. The computed interlaminar shear stresses are automatically continuous at the layer boundaries. Also the stress boundary conditions at the outer surfaces are fulfilled and the integrals of the shear stresses coincide exactly with the independently interpolated shear forces without introduction of further constraints. The essential feature of the element formulation is the fact that it leads to usual shell degrees of freedom, which allows application of standard boundary or symmetry conditions and computation of shell structures with intersections.