Coupling Global and Local Aspects of Cross-Sectional Optimization for Rotor Blades

Abstract

Additional investigation of the optimization of cross-sectional properties for rotor blades was performed with methodology based on the Genetic Algorithm (GA). In previous work by the authors, a multilevel optimization was conducted using gradient-based methods that are appropriate for continuous variables. In contrast to that work, here optimization is conducted with the main focus of assessing the impact of discrete variables that are inherent to the problem at both local and global levels. The GA was modified based on existing routines in MATLAB to make the code suitable for the methodology presented and to utilize interfaces with the multi-body dynamics program DYMORE, used for global analysis, and the cross-sectional analysis program VABS, used at the local level. At the first exploratory phase of the optimization, values of discrete variables are determined using the GA along with several promising regions for global minima that serve as starting points for the second phase optimization, which deals only with continuous variables. Furthermore, if more than one optimal design exists, further analysis is performed to pick the best design from among candidate configurations. ptimization of the cross-sectional layout of composite rotor blades is a challenging problem because of the large number of design parameters and the wide-ranging impact of those parameters on overall vehicle characteristics. The availability of high-fidelity structural beam analysis tools naturally allows a hierarchical decomposition of the problem that separates the local (cross-sectional) sub-problem from the global optimization. By encapsulating the intricate details of the cross-sectional design into a relatively small number of equivalent beam properties, one can significantly reduce the overall complexity of the optimization. An additional advantage of such a decoupled approach is that it follows a venerable tradition of analyzing rotorcraft systems by splitting three-dimensional (3D) problems into separate sub-problems over the crosssection (2D) and span (1D). Modern computer tools for analyzing composite rotor blades with arbitrary cross-sectional configurations such as VABS 1, 2 provide a fast and accurate means of assessing both static and dynamic structural properties of rotor blades in terms of an equivalent beam models. Calculation of the cross-sectional stiffness matrix is conducted using a finite element discretization. Results of this calculation also include a set of cross-sectional stress/strain recovery relations. Once the equivalent cross-sectional stiffnesses are obtained, a beam analysis can be conducted very rapidly, for various loading and boundary conditions as appropriate. Results from the 1D analysis can then be fed back into 2D recovering relations to obtain detailed stress and strain components over the cross-section. The overall analysis possesses accuracy comparable to that of 3D finite element methods with a reduction in computational cost by two to three orders of magnitude. 3 Optimization based on a parametric cross-sectional model was considered in Ref. 4. The layout was sufficiently realistic to allow optimization of a baseline cross-section in which the ply angles, thicknesses, and spar location were varied in order to place the shear center in a specified location while holding the crosssectional stiffnesses within a specified tolerance. This work was focused on the lower level of optimization and was continued with a still higher level of realism in Ref. 5.