Laminated shell model with second-order expansion of the reciprocals of Lamé coefficients Hα, Hβ and interlayer continuities fulfilment

Abstract

A multilayered, technical shell model accounting for the layerwise kinematics is developed, aimed to conjugate overall and local scale factors. It is based on a third-order zig-zag approximation of in-plane displacements, to satisfy a priori the interlayer stress continuity conditions, a constant transverse displacement and a second-order expansion of Lamé's coefficients across the thickness. The traction-free boundary conditions on transverse shear stresses at the upper and lower bounding surfaces are also enforced. As in any zig-zag model, the unknowns (the three displacements and the two shear rotations on the reference shell surface, as in conventional equivalent single-layer shell models) do not depend on the number of constituent layers, so that the present shell model is cost-effective. Furthermore, linear and third-order single-layer shell models and a linear zig-zag shell model can be obtained as particular cases. Numerical applications concern laminated cylindrical shell and shell panel samples wherein solutions from different two-dimensional models and the three-dimensional elasticity solution are available for comparisons.