Higher-Order Formulation for the Mechanical Analysis of Laminated and Latticed Shells with Complex Geometries and Materials

In a context where complex shape generation principles for generally-curved structures have increasingly extended their possibilities, the study of doubly-curved shells with variable radii of curvature is still an open topic, as proven by the huge number of papers published in the last decades. Many scientists and engineers, in literature, have increasingly developed refined approaches able to investigate their mechanical behavior in an accurate manner. The need of advanced methods of analysis is even more pronounced if innovative constituents and materials are employed. Laminates, Functionally Graded Materials (FGMs), Carbon Nanotubes (CNTs) reinforced media, Variable Angle Tow (VAT) composites, are only few examples of advanced materials that could require proper structural models for an accurate analysis. A theoretical framework based on Higher-order Shear Deformation Theories (HSDTs) is here developed to study the mechanical response of different laminated shell structures with complex geometries, as well as of composite latticed panels and shells (also labeled as gridshells). These last ones are typically encountered in aerospace and building structures, due to their combined properties of transparency and lightness [1,2]. It should be noted that the governing equations of similar complex problems cannot be easily solved in an analytical sense. Thus, a numerical tool based on the Differential Quadrature (DQ) and Integral Quadrature (IQ) methods is developed to obtain and solve the strong and weak formulations of the fundamental systems in hand [3,4]. This methodology allows us to obtain accurate and reliable results, as here verified against the available literature, for different combinations of the geometric and stiffness parameters.