Inclusion of Geometrically Nonlinear Aeroelastic Effects into Gradient-Based Aircraft Optimization

Abstract

While aircraft have largely featured flexible wings for decades, more recently, aircraft structures have rapidly become more flexible. The pursuit of longer ranges and higher efficiency through higher aspect ratio wings, as well as the introduction of modern, light-weight materials has yielded moderately and very flexible aircraft configurations. Past accidents, such as the loss of the Helios High Altitude Long Endurance (HALE) aircraft have highlighted the limitations of linear analysis methods and demonstrated the peril of neglecting nonlinear effects when designing such aircraft. In particular, accounting for geometrical nonlinearities in flutter analyses become necessary in aircraft optimization, including transport aircraft, or future aircraft may require costly modifications late in the design process to fulfill certification requirements. As a result, there is a need to account for geometrical nonlinearities earlier in the design process and integrate these analyses directly into the multi-disciplinary design optimization (MDO) problems.

This thesis investigates geometrically nonlinear flutter problems and how these should be integrated into aircraft MDO problems. First, flutter problems with and without geometrical nonlinearities are discussed and a unifying interpretation is presented. Furthermore, methods for interpreting nonlinear flutter problems are proposed and differences between linear and nonlinear flutter problem interpretation are discussed. Next, a flutter constraint formulation which accounts for geometrically nonlinear effects using beam-based analyses is presented. The resulting constraint uses a Kreisselmeiser-Steinhauser aggregation function to yield a scalar constraint from flight envelope flutter damping values. While the constraint enforces feasibility over the entire flight envelope, how the flight envelope is sampled largely determines the flutter constraint’s accuracy. To this end, a constrained Maximin approach, which is applicable for non-hypercube spaces, is used to sample the flight envelope and obtain a low-discrepancy sample set. The flutter constraint is then implemented using a beam-based geometrically nonlinear aeroelastic simulation code, UM/NAST.

As gradient-based optimization methods are used in MDO due to the large number of design variables in aircraft design problems, the flutter constraint requires the recovery of flutter damping sensitivities. These are obtained by applying algorithmic differentiation (AD) to the UM/NAST code base. This enables the recovery of gradients for any solution type (static, modal, dynamic, and flutter/stability) with respect to any local design variable available within UM/NAST. The performance of the gradient prediction is studied and a hybrid primal-AD scheme is developed to obtain the coupled nonlinear aeroelastic sensitivities. After verifying the accuracy and performance of the gradient evaluation, the flutter constraint was implemented in a sample optimization problem.

Finally, a roadmap for including the beam-based flutter constraint within an aircraft design problem is presented using analyses of varying fidelity. To this end, analyses of appropriate fidelity are used depending on the output of interest. While a shell-based FEM model can recover stress distributions, and is therefore well-suited for strength constraints, they are ill-suited for geometrically nonlinear flutter constraints due to their computational cost. Analyses are presented for a high aspect ratio transport aircraft configuration to illustrate the proposed approach and highlight the necessity for the inclusion of a geometrically nonlinear flutter constraint.