Multidimensional Finite Element Models for Geometrically Nonlinear Dynamic Analyses of Rotating Blades

Abstract This study introduces multidimensional finite element models for conducting geometrically nonlinear analyses on rotating structures. The mathematical framework employed is based on the Carrera Unified Formulation, which provides a systematic approach for generating one-dimensional, two-dimensional, and three-dimensional finite element models with varying levels of accuracy. The multidimensional models developed using CUF consist of solid and beam elements. These models utilize a specialized 1D kinematic formulation that solely encompasses displacements as degrees of freedom. This formulation is achieved by combining Lagrange polynomials defined within sub-regions (or elements) bounded by an arbitrary number of points (or nodes). These characteristics align with conventional solid finite elements, facilitating a straightforward summation of inertial and elastic contributions at the shared interface nodes. The governing equations of the models incorporate the effects of rotation, including the Coriolis term and the spin softening matrix. The Green-Lagrange strain tensor’s linear and nonlinear terms are also considered in formulating the 3D and 1D finite elements. Numerical simulations have been conducted on various blade configurations. The obtained nonlinear solutions are compared with linearized ones and validated against results from existing literature.