Geometrically Nonlinear Analysis of Axial Rotors

This master thesis work is focused on the analysis of complex rotating systems, subjected to plausible operating conditions in the practical reality of aeronautical applications. The rotordynamic effects introduced by the centrifugal force are here evaluated; in particular, the analysis will be carried out considering discs with constant and variable thickness, which are assumed to be keyed to the hub or supported by a flexible, deformable shaft. The contributions of the pre-stress are obtained through the integration of a three-dimensional state of tension, which is generated by the centrifugal and thermal loads, multiplied by the non-linear terms of the deformation field. The weak form of the governing equations is solved using the finite element method. A series of high fidelity 1D elements have been developed in accordance with the CUF theory, which allows to go beyond the kinematic assumptions of classical beam theories. Following the component-wise (CW) approach, Lagrange-like polynomial expansions have been adopted to develop more refined displacement theories. Lagrange-expansions LE elements allow the user to model each structural element of the rotor with an arbitrary degree of accuracy using different displacement theories or meshes with local refinement. This allows to obtain very reliable results, with a much lower computational cost than traditional FEM codes. Furthermore, the MUL2 code based on the Carrera Unified Formulation CUF has the potential to perform linearized and non-linear analysis, which will be applied here to numerous models of structures of common aeronautical application.