Stress and Modal Analysis of a Rotating Blade and the Effects of Nonlocality

The geometry of the rotor blades is designed and formed based on aerodynamic or similar fluid dynamics calculations. Therefore, their shape is restricted and does not offer much flexibility for solid mechanics part of the system design. This makes engineers do research on improvement on the materials for the rotor blades. Traditional metallic materials are limited for further improvements in weight reduction and aerodynamic performance on rotor blades with significant centrifugal loads. Larger densities of materials cause large stresses in rotating parts. Therefore, higher specific strengths are required from the material.  Whereas modern engineering materials such as foams and composites have much more flexible and tailorable mechanical properties, relatively better specific strength and lightweight in comparison to the traditional materials. However, their mechanical modelling might require more advanced techniques than classical continuum theory, due to their nonhomogeneous micro/nanostructures. Those inhomogeneities limit the capabilities of the classical continuum theory to handle the media as bulk materials. This brings out the need to have a scale dependency for a continuum theory since the classical theory has no consideration of the scale. Nonlocal continuum theory is one of the most advanced continuum theories in the literature that are successful in modelling such media with good accuracy. This study focuses on the stress analysis of a rotor blade, which is assumed to be made of a material of nonlocal characteristic, under quasi-static assumptions employing the finite element method. A full-scale fan blade model is chosen as the test case to represent the rotor blade for a modern high bypass ratio turbofan engine. The steady-state aerodynamic loads consist of the pressure, due to the airflow and the centrifugal load, due to the rotation applied to the fan blade finite element model. The inner surface of the disc is kept fixed while the tip of the blade is free. The blade and the disc are considered as a single body system for the sake of simplicity to remove contact nonlinearities from the system. For computational cost and simpler nonlocal expressions, local stresses are calculated using linear elements. Taking note that the shear behaviour is to be captured by inserting four rows of linear elements throughout the blade thickness. The nonlocal stresses are obtained by postprocessing the local stresses using the discretised version of the integral equation of the nonlocal continuum theory. The nonlocal continuum theory assumes that the stresses of the individual points depend on the strains of all the points that lie within the whole domain. This dependency is defined over an attenuation function which peaks when the distance between the points are zero and approaches to infinity when the distance between the points increase. There are three important constants to define the attenuation function and the nonlocal modulus; material constant, intrinsic and extrinsic lengths.  The effect of the changing nonlocal modulus on the nonlocal stresses in the blade is investigated by using different nonlocal attenuation functions, material constants and intrinsic length. The extrinsic length is to be kept the same which is the average thickness of the blade. The results of both the local and the nonlocal stress analyses are compared. It is showed that nonlocal stresses are greater than the local stresses. Furthermore, at the locations where the stress is concentrated, the maximum stress predicted with the classical continuum theory is lower than the one determined with the nonlocal theory. This directly affects the allowable dynamic loads to satisfy the desired fatigue life of such blades. It is also important to make safer designs with materials of those characteristics.