This conference paper was submitted for presentation at the NAFEMS World Congress 2025, held in Salzburg, Austria from May 19–22, 2025.

Abstract

Multidisciplinary optimization (MDO) has emerged as a critical approach in the design of aircraft wings, enabling the simultaneous consideration of aerodynamic performance and structural integrity. This integrative method is essential in addressing the complex interactions between disciplines, optimizing the overall wing performance rather than focusing on isolated aspects. A keystone of this process is the accurate determination of interdisciplinary gradients, specifically between the structural and aerodynamic domains. These gradients, which represent sensitivities to changes in the wing geometry, are crucial for guiding gradient based optimization algorithms toward optimal solutions. Traditional methods for retrieving these sensitivities often employ free-form deformation (FFD) techniques. Although Free Form Deformation allows modifications to the outer wing shape, accounting for changes to the internal structural elements, such as rib and spar positioning or rotation, remains challenging. This constraint narrows the scope of optimizations, potentially overlooking crucial design improvements achievable through concurrent modifications of both outer and inner wing configurations. To bridge this gap, recent efforts have turned toward CAD-based approaches that integrate finite difference methods to compute the required sensitivities. However, finite difference methods are known to suffer from numerical inaccuracies due to truncation and discretization errors. These inaccuracies propagate through the optimization process, leading to imprecise sensitivities and, consequently, slower convergence rates. In this study, we propose a novel methodology utilizing algorithmic differentiation (AD) to retrieve more precise interdisciplinary gradients. AD, unlike finite differences, computes exact derivatives by systematically applying chain rules of differentiation, thereby eliminating numerical errors. The approach utilizes a differentiated CAD kernel to obtain exact sensitivities of node coordinates with respect to geometric design parameters. The optimizer subsequently uses these geometric sensitivities to adjust the wing's geometrical design parameters. The updated node coordinates are then mapped to the newly generated wing shape in each iteration, ensuring a seamless integration between the geometric model and the optimization process. For demonstration purposes and to minimize computational efforts, simple formulas are employed to estimate the lift-to-drag ratio of the wing shape. This approximation ensures that the focus remains on evaluating the effectiveness of the AD-based CAD sensitivities without excessive computational overhead. The improved accuracy and efficiency of the proposed method have significant implications for the design and optimization of aircraft wings. Precise sensitivities enable a more efficient exploration of the design space, facilitating innovative solutions that improve aerodynamic performance while maintaining structural robustness. This method also addresses the limitations of existing techniques, offering a comprehensive framework that seamlessly integrates the geometric, aerodynamic, and structural aspects of wing design. By doing so, it facilitates faster and more efficient MDO processes, contributing to advancements in aerospace engineering.