Continuum Shape Sensitivity for Nonlinear Transient Aeroelastic Gust Response

Abstract

A Continuum Sensitivity Equation (CSE) method was developed for the transient fluidstructure interaction problems to support computationally efficient optimization of aeroelastic design problems. The continuum sensitivity equations and sensitivity boundary conditions are derived for a built-up joined beam structure under transient aerodynamic loads. The CSE method avoids the need to calculate problematic mesh sensitivity required by the discrete method, and thus is more computationally efficient for shape sensitivity calculation. For nonlinear problems, when the Newton-Raphson method is used, the tangent stiffness matrix of the last iteration yields the desired matrix for solving the linear sensitivity equations in the current Galerkin finite element formulation. For built-up structures with stress discontinuity at the joints, the total form CSE is easier to implement than the local form. In this paper, benchmark examples with analytical sensitivity results will be solved for verification purpose, comparison between local form and total form CSE is made, and the coupled fluid-structure physics and continuum sensitivity equations for gust response of a nonlinear joined beam with an airfoil model are posed and solved. The results are compared to the results obtained by finite difference (FD) method.