How to easily model doubly curved shells with variable radii of curvature

Studies on shells have always been a special topic in mechanics due to the complexity of their geometry. Researchers introduced the differential geometry to investigate thin shells as a general framework of a wider problem. In fact, doubly-curved shells with variable radii of curvature are not easy to model with standard tools. This work aims to present a general framework, based on the mathematical description of doubly curved thick bodies, that can mechanically solve doubly-curved shells using a fast, accurate and reliable numerical tool termed Generalized Differential Quadrature (GDQ) method. The required equations will be presented. No geometrical approximation is present (only limited to the grid points used for the GDQ meth-od). The structural theory employed in all the numerical applications is a higher order unified formulation, which can easily model any kind of first and higher order shear deformation theory for laminated composite shell structures.