Multilayered Shell Theories Accounting for Layerwise Mixed Description, Part 2: Numerical Evaluations

Abstract

The mixed layerwise shell theories that are presented in the companion article (E. Carrera, Multilayered Shell Theories Accounting for Layerwise Mixed Description, Part 1: Governing Equations' AIAA Journal, Vol. 37, No. 9, 1999, pp. 1107-1116) are evaluated here by solving several problems related to orthotropic cross-ply laminated, circular, cylindrical, and spherical shells subjected to static loadings for which closed-form solutions are given. Particular cases related to layerwise and equivalent single-layer models, based on classical displacement formulations, are evaluated for comparison purpose. A further comparison with three-dimensional elasticity exact solutions and to other higher-order shear deformations studies have been made. Results are given in the form of tables and diagrams. Approximations introduced by Donnell's shallow shell theories are evaluated for most of the problems. It has been concluded that the proposed mixed layerwise theories leads to a better description than the related analyses, which are based on displacement formulations. An excellent agreement, with respect to the exact solution, has been found for displacement and transverse stress components. These stresses have been herein calculated a priori. The importance of an adequate description of curvature terms related to the shell thickness to radii ratio h/R is also underlined. These effects have been contrasted by extensive use of fictitious interfaces in the conduced layerwise investigations.