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

A finite element formulation for refuted linear analysis of multilayered sh ell structures of moderate thickness is presented. An underlying shell mode l is a direct extension of the first-order shear-deformation theory of Reis sner-Mindlin type. A refined theory with seven unknown kinematic fields is developed: (i) by introducing an assumption of a zig-zag (i.e. layer-wise l inear) variation of displacement held through the thickness, and (ii) by as suming an independent transverse shear stress fields in each layer in the f ramework of Reissner's mixed variational principle. The introduced transver se shear stress unknowns are eliminated on the cross-section level. At this process, the interlaminar equilibrium conditions (i.e. the interlaminar sh ear stress continuity conditions) are imposed. As a result, the weak form o f constitutive equations (the so-called weak form of Hooke's law) is obtain ed for the transverse strains-transverse stress: resultants relation. A fin ite element approximation is based on the four-noded isoparametric element. To eliminate the shear locking effect, the assumed strain variational conc ept is used. Performance of the derived finite element is illustrated with some numerical examples. The results are compared with the exact three-dime nsional solutions, as well as with the analytical and numerical solutions o btained by the classical, the first-order and some representative refined m odels. Copyright (C) 2000 John Wiley & Sons, Ltd.