High-order methods for the mechanical characterization of laminated shell structures

Two-dimensional theories are crucial in commercial software for industrial applications, serving as the standard for conducting mechanical analyses of thin-walled components. Despite the ongoing advancement of computational resources, which aids in making full three-dimensional analyses less time consuming, the necessity of shell elements persists. This is especially true when it becomes necessary to explore a vast number of drafts with low accuracy, such as in early stages of design, or when analyzing complex large structures typical of transport industry. Notably, the integration of high-order theories augments the precision of 2D analyses, producing results comparable to those derived from fully 3D analyses. In this context, the establishment of a unified framework that facilitates the straightforward adjustment of kinematic order becomes paramount, especially when progressing through different project stages, each demanding varying levels of accuracy. In this thesis, various shell kinematics are employed in conjunction with methods facilitating the construction of shell elements with high in-plane order. Specifically, the discontinuous Galerkin (DG) and Isogeometric Analysis (IGA) methods are adopted. The formulated approaches enable the modeling of generally-curved shells with arbitrary lamination sequences. Higher-order theories are combined with DG for both linear and non-linear mechanical analyses of shells for the first time. Cut-outs are represented using the implicit mesh technique, employing a level-set function to implicitly define the integration domain on active elements. The discontinuous nature of DG basis functions is also exploited for studying a damaged plate with a through-the-thickness crack. For structures composed of multiple shells, IGA is applied, enforcing coupling between patches and boundary conditions through a variationally consistent weak formulation along conforming and trimmed boundaries. In this approach, the boundary of the embedded domain is defined explicitly using trimming curves. Local refinement in critical areas is achieved by either adopting auxiliary IGA boundary layers or implementing local refinement with additional DG elements. The thesis also provides the main implementation details of the proposed methods. Numerical examples are presented to showcase the accuracy and efficiency of the proposed approaches. The results of all tests are systematically compared with reference solutions obtained either analytically or through commercially available FEM software.