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Geometry parametrization for high-fidelity multidisciplinary optimization is an important and complex problem. We present a CAD-free geometry parametrization method using a free-from deformation volume approach. This approach yields several important advantages over other parametrization techniques, the most of important of which is the efficient computation of analytic derivatives for gradient-based optimization. A parallel, hybrid, algebraic-linear-elasticity mesh perturbation scheme which produces high quality perturbed meshes with low computational effort is also presented. We couple an Euler CFD solver with a finite-element model that uses fourth-order degenerate shell elements. As a demonstration problem, we perform the aerostructural redesign of a subsonic wing for transonic flight conditions. We show that this optimization problem captures some of the complex multidisciplinary trade-offs inherent in wing design.

The ability to discriminate minute deviations from circularity is dependent upon global summation mechanisms integrating information along entire contours. The aim of this study was to determine how the strength of global summation depends on various stimulus features. To determine if the strength of global summation differs between shapes, contour discrimination for various contour shapes, generated by applying a sinusoidal modulation to the radius of a circle (radial frequency - RF - patterns), was measured. Shapes differed in frequency (number of lobes RF3, RF5 and RF20) and amplitude ('sharpness' of the lobes ranged between 0 and 20× thresholds for detecting deviation from a circle). Low amplitudes test discrimination against a circle while high amplitudes measure sensitivity for highly non-circular shapes (e.g. five-pointed star-shapes). The ability to integrate information along contours was assessed by comparing the effect of applying radial deformations to the entire contour or to only fractions (various number of cycles). Results show that discrimination thresholds remain in the hyperacuity range for low amplitudes, but increase for higher amplitudes. Concerning signal integration, discrimination, expressed as a function of the amount of contour deformed, exhibits a shallow and a steep regime. Discrimination improves only slowly as more contour cycles are deformed until the point when the entire pattern is modulated, when sensitivity increases substantially. The initial shallow regime is well captured by probability summation. The increase in sensitivity when the entire pattern is modulated compared to a single cycle provides evidence for global pooling. The pattern of integration and the existence of global pooling is dependent on shape frequency. The two-part behavior is independent of shape amplitude but is only seen for low RFs (3 and 5). Data for RF20 follow the prediction of probability summation. We next investigated various stimulus characteristics and their effect on integration strength. Global pooling exceeding probability summation is evident for different pattern sizes, presentation times and for high as well as low absolute contrasts. Only if the contrasts of different fractions of a contour shape are individually scaled to match their respective visibilities is integration strength below the level of probability summation. This explains the lack of apparent global pooling in previous studies employing mixed contrasts. The marked increase in performance for discriminating completely modulated RF patterns argues in favor of highly specialized, global shape mechanisms that are seen over a wide range of stimulus configurations. The results indicate global, non-linear mechanisms, which respond most strongly when stimulated by the entire pattern and comparatively weakly when only stimulated by parts of it.

The NASA Common Research Model (CRM) has become a standard test case for verification and validation of Reynolds averaged Navier-Stokes computational fluid dynamics codes. In this paper we evaluate the suitability of the CRM for aerostructural and aeroelastic optimization studies. Since the CRM was originally intended for aerodynamic studies only, the undeformed geometry is not available. To address this issue, we designed a jig shape and the corresponding wingbox structure for the CRM using an inverse design procedure. The results are verified by computing the drag coefficient of the aerostructural solution with the jig shape at the nominal CRM operating conditions. The drag differs by less than one drag count relative to the CRM original shape. Using the CRM jig geometry, a sample high-fidelity aerostructural optimization is performed to determine the potential decrease in fuel burn for a long-range design mission when varying wing planform and airfoil shapes. The optimization increases the aspect ratio of the wing from 9.0 to 12.6 and reduces the fuel burn by 8.8%. We also perform a series of gust load analysis on both the initial and optimized designs and determine that the optimized structure is critical under gust loads. The aerostructural optimization produces a high aspect ratio wing with effective passive aeroelastic tailoring, but additional load cases with cruise-like lift distributions are required to produce a more realistic wing design.

This paper presents a comparison of methods for aerostructural analysis and optimization. The aerostructural analysis problem is solved in parallel using a panel method coupled to a finite-element solver. The coupled nonlinear aerostructural system is solved using a nonlinear block Gauss-Seidel, nonlinear block Jacobi, Newton-Krylov or approximate Newton-Krylov approach. The approximate Newton-Krylov method is shown to be an efficient and robust solution technique. An adjoint-based sensitivity method is developed that achieves a high-level of accuracy when compared to complex-step calculations. Three levels of parallelism are exploited within the present aerostructural optimization framework: optimization-level, system-level and discipline-level parallelism. The efficient and robust solution method and accurate gradient evaluation technique provide a powerful tool for aerostructural design optimization. Aerostructural induced drag minimization results are presented for a typical subsonic turboprop aircraft wing.