Aeroelastic sensitivity analysis of wings using automatic differentiation

Abstract

Flutter analysis of a general wing is carried out using ® nite element structural modeling (MSC/NASTRAN), a subsonic kernel function unsteady aerodynamics and a V± g type of solution (FAST). The shape of the wing cross section is generated by parameterization using the Joukowski transformation, so that shapes of varying thickness and camber can be obtained by varying the parameters. The CQUAD4 (quadrilateral) and CTRIA3 (triangular) membrane-bending shell elements, the CBAR beam element and the CSHEAR shear panel element from MSC/ NASTRAN have been used in this study. The validation of ® nite element modeling is done by performing dynamic analysis of an AGARD swept wing model. The sensitivity ofutter speed of the wing to shape parameters, namely, aspect ratio, area, taper ratio, and sweep angle is obtained using a central difference scheme in conjunction with automatic differentiation (ADIFOR). The sensitivity ofutter speed to modal parameters, namely, natural frequency, generalized mass, and generalized aerodynamic forces is computed using ADIFOR. In this paper, validation of ® nite element modeling using MSC/ NASTRAN is done for dynamic analysis of a swept wing, and the results are compared with previously published results. To encour- age the use of the new methods presented, they are implemented using industry standard tools such as MSC/NASTRAN. The airfoil shape is generated by transforming a circle into an airfoil so that shapes of varying thickness and camber can be obtained by vary- ing the parameters. Finite element discretization of the wing skins, spars, and ribs is done, and a free vibration analysis of the wing is performed. The natural frequencies and mode shapes obtained are used to generate the generalized aerodynamic forces required forutter analysis using FAST, 7 which employs subsonic kernel function unsteady aerodynamics. The sensitivity ofutter speed to shape and modal parameters is computed using a combination of central difference scheme and automatic differentiation software ADIFOR. Optimization techniques that use these sensitivity deriva- tives are useful in the design stage, and these can be integrated into the design process for an optimum design.