A semi-analytical approach to sensitivity analysis with flexible multibody dynamics of a morphing forward wing section

Abstract

In the present paper, semi-analytical design sensitivity analysis of a morphing forward wing section modeled as a flexible multibody system is developed. The flexible multibody dynamics model consists of a flexible external wing skin and an actuation mechanism with rigid bodies. The floating frame of reference formulation is used for the formulation of the equations of motion, while time integration is carried out with the generalized-alpha method and Newton–Raphson iterations for the nonlinear analysis. These steps are considered in both the primal analysis and the developed efficient design sensitivity analysis. The calculation of the design sensitivities is based on direct differentiation and carried out with a semi-analytical approach. The responses of interest include the deviations of the wing profile from the targeted morphed geometry and the resulting stresses in the wing skin. The design variables considered in this work are geometric parameters, material parameters and loading parameters. The calculations with the shown method provide reliable and accurate results combined with high computational efficiency. The visualization of the computed sensitivity values gives an easy interpretation of the sensitivities and facilitates the understanding of the design engineer on how to change the design variables to improve the design of the system. The introduced sensitivity analysis enables future investigations, including the application of the method to gradient-based design optimization and uncertainty analysis.