Advanced isogeometric methods for the simulation of complex structures: A focus on geometrically exact beams and laminated composite plates.

This thesis presents a series of innovative and computationally improved frameworks for accurately analyzing complex laminated plates and geometrically exact beams (GEB) by effectively combining the Isogeometric Analysis (IGA) approach with advanced structural theories. The study addresses two key problems in computational mechanics: accurate prediction of three-dimensional stress states in composite laminates, important in evaluating delamination, and the efficient, flexible modeling of slender beams experiencing arbitrary large deflections and rotations. Within an IGA Galerkin framework, this work provides a stress recovery procedure for laminated composite structures that is based on equilibrium. The method effectively reconstructs the full three-dimensional stress field from two-dimensional plate solutions that are computationally cost-effective by taking advantage of the high-order continuity that is inherent to NURBS basis functions. By applying Kirchhoff theory for anisotropic plates as a starting point, the framework's capabilities are progressively shown. Next, we move on to a more robust formulation which includes Higher-Order Shear Deformation Theory (HSDT) to investigate thick and Variable Stiffness Composite (VSC) plates, all without actual shear correction factors. An innovative method for GEB is presented by initially combining the computationally efficient Isogeometric Collocation (IGA-C) method with the intrinsic formulation of beam theory. A locking-free formulation with lower-order nonlinearities is obtained by avoiding the complexity of finite rotation parameterizations through this novel combination. The method's remarkable accuracy and efficiency are first proven for straight beams subjected to different loading scenarios and are then extended to include the more complex analysis of spatially curved and twisted beams. The proposed formulations show higher accuracy and a notable reduction in computational cost compared to traditional approaches across a range of validation studies against analytical, numerical, and 3D Finite Element benchmarks. This provides a powerful set of tools for the advanced design and analysis of modern engineering structures.