Innovative Recovery Procedure Applied to the Static Solution of Anisotropic Doubly-Curved Shells with Holes and Irregular Shape

In this work, higher-order theories with a unified formulation are adopted within a two-dimensional Equivalent Single Layer (ESL) framework, to determine the three-dimensional static response of laminated anisotropic doubly-curved shell structures, described by irregular domains and characterized by holes and discontinuities. Starting from the geometry description of the structure in curvilinear principal coordinates, the fundamental equations are derived from the minimum potential energy principle in weak form, employing higher-order Lagrange shape functions to interpolate the unknown displacement variables. An isogeometric mapping of the physical domain is introduced to make the equations suitable for arbitrarily-shaped structures. A numerical solution is obtained using the Generalized Differential Quadrature (GDQ) and Generalized Integral Quadrature (GIQ) methods for singly-connected domains. In addition, a finite element numerical solution of the theory is determined, employing various shape functions and discretizations to address discontinuities, holes, and cracks. In the post-processing stage, an efficient recovery procedure based on GDQ and GIQ is presented to reconstruct the response of the 3D solid. This procedure adopts a patch extracted from the physical domain to numerically evaluate derivatives and integrals. The accuracy of the proposed solution is validated through proper comparisons with numerical predictions from 3D models developed with commercial softwares. Parametric investigations are also performed, highlighting the importance of the recovery procedure and the selection of the kinematic model. Various structures with different curvatures are analyzed, featuring different lamination schemes, geometries, loading conditions and boundary conditions. The model proposed in this paper enables refined numerical solutions with a reduced computational effort compared to conventional numerical approaches. Moreover, it allows for accurate and efficient determination of strain and stress distributions in laminated, doubly-curved structures with holes and discontinuities, thus providing valuable insights for the design of complex structural components.