On the mechanics of laminated doubly-curved shells subjected to point and line loads

It is well-known that the implementation of concentrated forces, such as point and line loads, represents a challenging task, especially from the computational point of view, since a strong discontinuity has to be inserted in the structural model. The present paper aims to solve the static problem of laminated composite doubly-curved shell structures subjected to concentrated loads employing the Generalized Differential Quadrature (GDQ) as numerical tool, according to what has been shown by the authors in their previous work. Its accuracy and reliability features are proven for several grid distributions when the concentrated loads are modeled through the Dirac-delta function. The theoretical framework on which this approach is based is the Unified Formulation developed by Carrera, which allows to investigate several Higher-order Shear Deformation Theories (HSDTs). The differential geometry is used to describe accurately the reference surface of various doubly-curved shell structures. The validity of the current approach is shown comparing the GDQ results with the exact and semi-analytical results available in the literature. A posteriori recovery procedure based on the three-dimensional equilibrium equations for a shell structure is introduced to compute the through-the-thickness variation of strain, stress and displacement components by means of the GDQ method.