Rotor Blade Analysis Using the Mixed Finite-Element Method

摘要

Accurate and efficient analysis of rotorcraft blades has long been a challenge. Using classic finite-element methods, it is possible to model blades of geometry, but a high price is paid for this capability in the form of large models with correspondingly large computational costs. It is possible in many applications to reduce computational costs by employing a technique called modal reduction, which seeks to collapse the analytical model to a handful of coordinates. Unfortunately, the modal reduction process is often ineffective for a rotor blade composed of finite elements that parameterize all unknown quantities as displacements. The reason is that the blade s axial force, which is the most critical factor in determining the blade s bending stiffness, is composed of contributions that nearly cancel, one from the axial displacement, and one from the bending displacements. Thus, the error in the axial force can be expected to be significantly larger than the error in either of the contributions; this is an example of the classic 'small difference of large quantities' conundrum that often confronts numerical analysts.