A small perturbation based optimization approach for the frequency placement of high aspect ratio wings

Design denotes the transformation of an identified need to its physical embodiment in a traditionally iterative approach of trial and error. Conceptual design plays a prominent role but an almost infinite number of possible solutions at the outset of design necessitates fast evaluations. The corresponding practice of empirical equations and low fidelity analyses becomes obsolete in the light of novel concepts. Ever increasing system complexity and resource scarcity mandate new approaches to adequately capture system characteristics.;Contemporary concerns in atmospheric science and homeland security created an operational need for unconventional configurations. Unmanned long endurance flight at high altitudes offers a unique showcase for the exploration of new design spaces and the incidental deficit of conceptual modeling and simulation capabilities. Structural and aerodynamic performance requirements necessitate light weight materials and high aspect ratio wings resulting in distinct structural and aeroelastic response characteristics that stand in close correlation with natural vibration modes.;The present research effort evolves around the development of an efficient and accurate optimization algorithm for high aspect ratio wings subject to natural frequency constraints. Foundational corner stones are beam dimensional reduction and modal perturbation redesign. Local and global analyses inherent to the former suggest corresponding levels of local and global optimization. The present approach departs from this suggestion. It introduces local level surrogate models to capacitate a methodology that consists of multi level analyses feeding into a single level optimization. The innovative heart of the new algorithm originates in small perturbation theory. A sequence of small perturbation solutions allows the optimizer to make incremental movements within the design space. It enables a directed search that is free of costly gradients. System matrices are decomposed based on a Timoshenko stiffness effect separation. The formulation of respective linear changes falls back on surrogate models that approximate cross sectional properties. Corresponding functional responses are readily available. Their direct use by the small perturbation based optimizer ensures constitutive laws and eliminates a previously necessary optimization at the local level. The scope of the present work is derived from an existing configuration such as a conceptual baseline or a prototype that experiences aeroelastic instabilities. Due to the lack of respective design studies in the traditional design process it is not uncommon for an initial wing design to have such stability problems. The developed optimization scheme allows the effective redesign of high aspect ratio wings subject to natural frequency objectives. Its successful application is demonstrated by three separate optimization studies.;The implementation results of all three studies confirm that the gradient liberation of the new methodology brings about great computational savings. A generic wing study is used to indicate the connection between the proposed methodology and the aeroelastic stability problems outlined in the motivation. It is also used to illustrate an important practical aspect of structural redesign, i.e., a minimum departure from the existing baseline configuration. The proposed optimization scheme is naturally conducive to this practical aspect by using a minimum change optimization criterion. However, only an elemental formulation truly enables a minimum change solution. It accounts for the spanwise significance of a structural modification to the mode of interest. This idea of localized reinforcement greatly benefits the practical realization of structural redesign efforts.;The implementation results also highlight the fundamental limitation of the proposed methodology. The exclusive consideration of mass and stiffness effects on modal response characteristics disregards other disciplinary problems such as allowable stresses or buckling loads. Both are of central importance to the structural integrity of an aircraft but are currently not accounted for in the proposed optimization scheme. The concluding discussion thus outlines the need for respective constraints and/or additional analyses to capture all requirements necessary for a comprehensive structural redesign study.