Multilayered shell finite element with interlaminar continuous shear stresses: a refinement of the Reissner-Mindlin formulation

A nite element formulation for re ned linear analysis of multilayered shell structures of moderate thickness is presented. An underlying shell model is a direct extension of the rst-order shear-deformation theory of Reissner{Mindlin type. A re ned theory with seven unknown kinematic elds is developed: (i) by introducing an assumption of a zig-zag (i.e. layer-wise linear) variation of displacement eld through the thickness, and (ii) by assuming an independent transverse shear stress elds in each layer in the framework of Reissnerʹs mixed variational principle. The introduced transverse shear stress unknowns are eliminated on the cross-section level. At this process, the interlaminar equilibrium conditions (i.e. the interlaminar shear stress continuity conditions) are imposed. As a result, the weak form of constitutive equations (the so-called weak form of Hookeʹs law) is obtained for the transverse strains{transverse stress resultants relation. A nite element approximation is based on the four-noded isoparametric element. To eliminate the shear locking e ect, the assumed strain variational concept is used. Performance of the derived nite element is illustrated with some numerical examples. The results are compared with the exact three-dimensional solutions, as well as with the analytical and numerical solutions obtained by the classical, the rst-order and some representative re ned models