Iteration-based adjoint method for the sensitivity analysis of static aeroelastic loads
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RESEARCH PAPER
Iteration-based adjoint method for the sensitivity analysis of static aeroelastic loads Yunhe Cheng1
· Qin Sun1
Received: 3 November 2019 / Revised: 12 August 2020 / Accepted: 19 August 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The sensitivity analysis of static aeroelastic loads can be analytically performed by virtue of a modified stiffness matrix. However, introducing a modified stiffness matrix into the calculation will incur extra computational cost. Additionally, the intrinsic drawback of the direct method is disadvantageous for the sensitivity calculation with a large number of design variables. This paper therefore presents a novel iteration-based adjoint method for the sensitivity analysis of static aeroelastic loads acting on flexible wing, the basis of which is the static aeroelastic calculation via loosely coupled iteration between the potential-flow panel model and the structural linear finite element model. By using an iterative approach for evaluating the adjoint variable, modification to the original stiffness matrix can be obviated. Moreover, this method is more competent for the structural sensitivity analysis with a very large number of design variables, since the adjoint variable is unrelated to the designs. A rectangular wing and a swept wing are employed to demonstrate the verification of the algorithms. The design sensitivities of applied nodal forces on the structure, lift per unit span, total lift and root bending moment are calculated and analyzed. The computational cost is also discussed to further demonstrate the efficiency of the proposed method. Keywords Static aeroelastic calculation · Sensitivity analysis · Adjoint method · Iterative procedure
1 Introduction Due to the increasing demands for elaborateness and light-weight in the design for modern aircraft, the static aeroelastic effects have more significant influence upon the aircraft performances, and are required to be taken into account in structural optimization. Additionally, the improvement of structural optimization complexity leads to substantial increase in the number of design variables (Venkataraman and Haftka 2004). Despite gradient-free algorithms are usually much easier to use in structural design cycle, gradient-based algorithms are currently the only viable avenue to solve the optimization problems parameterized with hundreds or more design variables
Responsible Editor: Nam Ho Kim Yunhe Cheng
[email protected] 1
School of Aeronautics, Northwestern Polytechnical University, Youyi West Road # 127, Xi’an, Shaanxi, China
(Martins and Hwang 2013; Martins and Kennedy 2019). Thus, design sensitivity analysis, assessing the variation of performance measures in response to the changes of design variables, plays an important role in gradient-based algorithms (Arora and Haug 1979; Adelman and Haftka 1986; Martins and Hwang 2013). Moreover, the cost and time of an optimization procedure depend predominantly on the calculation of design sensitivities (Adelman and Haf
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