Sensitivity Analysis of a Strongly Coupled Aero-Structural System Using Direct and Adjoint Methods

In this paper, we perform the sensitivity analysis of an aeroelastic system in steady-state conditions with respect to design parameters of the jig-shape of the system. The gradient of coupled system characteristic functions are computed analytically using either the discrete direct differentiation method or the discrete adjoint vector method, which make the designer potentially able to use analytical gradients taking fluid-structure coupling into account during the local shape optimization process of a coupled system. The influence coefficients matrix approach and beam theory are applied to calculate the structural displacements due to the aerodynamic loads and the nonlinear Euler equations or Reynoldsaveraged Navier-Stokes equations can be used to evaluate the aerodynamic loads, which are then transfered to the structural model through a consistent and conservative process. The discrete direct and adjoint systems of equations of both disciplines are derived and a lagged fixed-point-like iterative scheme is employed to solve for the coupled set of equations. Finally, the coupled direct and adjoint methods are applied to three different three-dimensional configurations, and the successful implementation of these methods is verified.

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