Structural modeling of geometrically nonlinear rotary beams for applications on helicopter rotors using the finite element method

Abstract

This research project purposes the computational implementation of a geometrically non-linear rotary beam formulation which stems from the variational asymptotic method (VAM). The method VAM proposes the representation of a three-dimensional formulation of a geometrically non-linear beam in terms of two complementary formulations: 1) a one-dimensional formulation (1D), compact and geometrically exact along the beam reference line, and 2) a two-dimensional analysis (2D), generally linear, set at each beam cross-section. The combination of the 1D and 2D formulations leads to an accurate beam formulation, with high computational performance in comparison with similar three-dimensional formulations. The finite element method, associated with the Newton-Raphson method, is applied to numerically solve the equations representing the one-dimensional beam formulation for obtaining both the static and dynamic beam responses in terms of geometric parameters, materials properties, rotary speed and external loading. Although this project is limited to the structural study of beams with simple geometry, and homogenous and isotropic materials, the beam model can be generalized to be applied to simulating helicopter blades modeled as initially curved composite beams. This beam formulation can also be numerically integrated to the Generalized Dynamic Wake Model, resulting in a compact, accurate and computationally efficient aeroelastic model suitable for applications to the study of the aeroelastic behavior of flexible blades and rotor stability under prescribed operational conditions. (AU)