Recent developments from a continuing effort to provide an equivalent plate representation for aircraft structural analysis are described. Previous work provided an equivalent plate analysis formulation that is capable of modeling aircraft wing structures with a general planform such as cranked wing boxes. However, the modeling is restricted to representing wing boxes having symmetric cross sections. Further developments, which are described, allow modeling of wing cross sections having asymmetries that can arise from airfoil camber or from thicknesses being different in the upper and lower cover skins. An implementation of thermal loadings, which are described as temperature distributions over the planform of the cover skins, has been included. Spring supports have been added to provide for a more general set of boundary conditions. Numerical results are presented to assess the effect of wing camber on the static and dynamic response of an example wing structure under pressure and thermal loading. These results are compared with results from a finite element analysis program to indicate how well a cambered wing box can be represented with an equivalent plate formulation.

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Further Generalization of an Equivalent Plate Representation for Aircraft Structural Analysis

A recently developed methodology for aircraft structural design, based on nonlinear airloads, is extended to include a modal-based optimization option and is employed with a new computational aerodynamics code for loads analysis. Nonlinear maneuver loads are evaluated by a computational scheme that efficiently combines fluid dynamics iterations with iterations for elastic shape deformations and trim corrections. An efficient design process is obtained by performing several structural optimization runs during one maneuver load analysis, where each optimization is based on the interim nonconverged airloads. To allow for the efficient application of the method with large finite element structural models and many constraints, the discrete-coordinate optimization scheme is replaced by a modal-based optimization where a set of low-frequency vibration modes of the baseline structure is used to represent the structure throughout the optimization, both for response analysis and for sensitivity analysis. Comparative modal-based and discrete-coordinate design cases are shown to converge to the same optimal design variable values, even though they do not follow the same path. Two flow solvers are used, one of which is a newly developed Euler/Navier-Stokes computational aerodynamics code that is capable of handling complex geometries by using the Chimera overset grid method. The method avoids the problem of mesh discontinuities due to elastic shape deformations and control surface deflections because the displacements of each component affect only the component's mesh. The method is demonstrated with a wing-fuselage-elevator transport aircraft model performing symmetric and antisymmetric maneuvers at Mach 0.85.

Structural Optimization Using Computational Aerodynamics

Computational-fluid-dynamics-based aeroelastic analysis and structural design optimization—a researcher’s perspective

Amethodologyofperformingstructuraloptimizationwithstaticaeroelasticconsiderationsispresentedforwhich the aerodynamic loads are provided by nonlinear computational aerodynamics schemes. Two main subjects that are studied are the evaluation of airloads on a maneuvering e exible aircraft and their integration with a structural optimization code. A computational aerodynamics code originally developed for solving Euler or Navier ‐Stokes equations for a e xed-shape cone guration is modie ed to incorporate aeroelastic effects. Computational efe ciency is obtained when several aeroelastic trim corrections and optimization runs are performed during the process of e owe eld convergence,such thattheaerodynamicloadsandthestructuraldesign convergesimultaneously.Amodal structuralmodelisusedforelastic-shapeupdates,andatrimcorrectionsalgorithmisusedforvaryingtheincidences and control surface dee ections for obtaining user-dee ned maneuvers. The nonlinear maneuver loads can be combined with linear design cases in a multidisciplinary structural optimization scheme. The method is demonstrated with a wing‐fuselage‐elevator transport aircraft model performing symmetric and antisymmetric maneuvers at Mach 0.85. Thenumber of iterations required for convergenceof thecombined maneuver ‐optimization analysis is typically almost the same as that of regular computational aerodynamics analysis for a e xed-shape cone guration.

Structural Optimization of Flight Vehicles with Computational-Fluid-Dynamics-Based Maneuver Loads

The coupling of a nonlinear aerodynamics program with a structural analysis program to include the effects of static aeroelasticity in early preliminary design studies is described. A nonlinear, full potential aerodynamics method with capability to model geometric details of a complete aircraft in supersonic flow is used. The deflections of the lifting surfaces are calculated using an equivalent plate structural representation which can readily accommodate the changes in stiffness and geometric properties required during the preliminary design process. An iterative solution procedure is used to obtain consistent aerodynamic loads and structural deflections at the specified flight conditions. The volume of data transmitted between programs is minimized. The procedure is applied to a complete aircraft and the numerical results illustrate the aeroelastic effects on pressure distribution as well as total forces and moments. During this design study, the thickness distribution of the wing cover skins was initially sized based on rigid loads and subsequently resized under aeroelastic loads. Comparisons are made between these nonlinear aeroelastic results and results obtained from linear aerodynamic methods applied to a rigid shape during conceptual design studies.

Integrating nonlinear aerodynamic and structural analysis for a complete fighter configuration

An iterative procedure for the static aeroelastic design of a flexible wing at supersonic speeds has been developed. The procedure combines a nonlinear, full-potential solver (NCOREL) with an equivalent plate structural analysis method. The NCOREL method yields significantly improved aerodynamic estimates compared to linear theory. The equivalent plate structural analysis method demonstrates an order of magnitude reduction in computer memory and execution time compared to finite-element methods. A highly swept wing is analyzed at high lift using this aeroelastic procedure. The results indicate that the wing deforms favorably due to aerodynamic loading and, consequently, that the inviscid drag levels do not vary at the required lift coefficient although the angle of attack varies significantly. A sensitivity analysis of the type required for optimization studies was also performed with the aeroelastic design procedure.

G. L. Giles

Papers

Combined, nonlinear aerodynamic and structural method for the aeroelastic design of a three-dimensional wing in supersonic flow