Accurate inter-laminar recovery for plates and doubly-curved shells with variable radii of curvature using layer-wise theories

The present work illustrates a general formulation for higher-order layer-wise (LW) theories. It aims to analyze doubly-curved laminated shells and panels when soft-core properties are selected. The present approach has its own roots in the Carrera Unified Formulation (CUF) for which the stretching effect of each layer is not neglected. CUF allows to take the kinematic expansion order as a free parameter for the representation of any higher order formulation. This paper shows the explicit fundamental operators for the LW approach when static analysis is investigated. The mathematical problem is solved using a strong formulation approach, termed Generalized Differential Quadrature (GDQ) method. Moreover, the so-called Generalized Integral Quadrature (GIQ) method is used for evaluating the through-the-thickness quantities of the theory such as the stiffness constants, computed layer by layer. Numerical applications are related to the recovery of the inter-laminar stresses and strains that have been compared to reference solutions obtained by a commercial three-dimensional (3D) FEM code.