Computational Models for Laminated Doubly-Curved Shells with Variable Radii of Curvatures Using Weak and Strong Formulations

The study of doubly-curved shells has been growing in different engineering branches, such as mechanical, civil, aerospace and naval due to their practical applications to structural components, roofs, wings and hulls. Moreover the use of laminated composite materials is increasing due to the advantages that these materials give to these structures, such as lightness, stiffness and strength. It should be remarked that the use of laminated composite materials bring theoretical difficulties to the classical shell theories, since the anisotropic behavior of these structures does not allow to use classic thin shell theories anymore. For this reason higher order formulations and layer-wise modes have been introduced for this purpose, in order to avoid the computationally inefficient 3D elasticity. Another problem is related to the geometric description of these structures when variable radii of curvature are considered, due to the fact that the geometric parameters change point by point on the three-dimensional shell solid. In order to solve all these problems the present work employs a higher order formulation coupled with the differential geometry and a numerical technique based on strong and weak formulations. The present procedure leads to stable, accurate and reliable results for the structures at hand and allows to study complex structures without neglecting the curvature effect and the rotary inertia. Both the free vibration and the static problems will be discussed with a particular emphasis on the stress and strain recovery procedure, which is a major problem for the evaluation of the through-the-thickness quantities of shell structures.