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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Combined compressive and shear buckling analysis of hypersonic aircraft structural sandwich panels

The combined-load (compression and shear) buckling equations were established for orthotropic sandwich panels by using the Rayleigh-Ritz method to minimize the panel total potential energy. The resulting combined-load buckling equations were used to generate buckling interaction curves for super-plastically-formed/diffusion-bonded titanium truss-core sandwich panels and titanium honeycomb-core sandwich panels having the same specific weight. The relative combined-load buckling strengths of these two types of sandwich panels are compared with consideration of their sandwich orientations. For square and nearly square panels of both types, the combined load always induces symmetric buckling. As the panel aspect ratios increase, antisymmetric buckling will show up when the loading is shear-dominated combined loading. The square panel (either type) has the highest combined buckling strength, but the combined load buckling strength drops sharply as the panel aspect ratio increases. For square panels, the truss-core sandwich panel has higher compression-dominated combined load buckling strength. However, for shear dominated loading, the square honeycomb-core sandwich panel has higher shear-dominated combined load buckling strength.

Ko, William L.↗
NASA NTRS1992

Combined compressive and shear buckling analysis of hypersonic aircraft sandwich panels

The combined-load (compression and shear) buckling equations were established for orthotropic sandwich panels by using the Rayleigh-Ritz method to minimize the panel total potential energy. The resulting combined-load buckling equations were used to generate buckling interaction curves for super-plastically-formed/diffusion-bonded titanium truss-core sandwich panels and titanium honeycomb-core sandwich panels having the same specific weight. The relative combined-load buckling strengths of these two types of sandwich panels are compared with consideration of their sandwich orientations. For square and nearly square panels of both types, the combined load always induces symmetric buckling. As the panel aspect ratios increase, antisymmetric buckling will show up when the loading is shear-dominated combined loading. The square panel (either type) has the highest combined buckling strength, but the combined load buckling strength drops sharply as the panel aspect ratio increases. For square panels, the truss-core sandwich panel has higher compression-dominated load buckling strength. However, for shear dominated loading, the square honeycomb-core sandwich panel has higher shear-dominated combined load buckling strength.

Ko, William L.↗
NASA NTRS2010

Fracture Mechanics Analyses of the Slip-Side Joggle Regions of Wing-Leading Edge Panels

The Space Shuttle Orbiter wing comprises of 22 leading edge panels on each side of the wing. These panels are part of the thermal protection system that protects the Orbiter wings from extreme heating that take place on the reentry in to the earth atmosphere. On some panels that experience extreme heating, liberation of silicon carbon (SiC) coating was observed on the slip side regions of the panels. Global structural and local fracture mechanics analyses were performed on these panels as a part of the root cause investigation of this coating liberation anomaly. The wing-leading-edge reinforced carbon-carbon (RCC) panels, Panel 9, T-seal 10, and Panel 10, are shown in Figure 1 and the progression of the stress analysis models is presented in Figure 2. The global structural analyses showed minimal interaction between adjacent panels and the T-seal that bridges the gap between the panels. A bounding uniform temperature is applied to a representative panel and the resulting stress distribution is examined. For this loading condition, the interlaminar normal stresses showed negligible variation in the chord direction and increased values in the vicinity of the slip-side joggle shoulder. As such, a representative span wise slice on the panel can be taken and the cross section can be analyzed using plane strain analysis.

Raju, Ivatury S.↗
NASA NTRS2010

Design of Fiber Reinforced Foam Sandwich Panels for Large Ares V Structural Applications

The preliminary design of three major structural components within NASA's Ares V heavy lift vehicle using a novel fiber reinforced foam composite sandwich panel concept is presented. The Ares V payload shroud, interstage, and core intertank are designed for minimum mass using this panel concept, which consists of integral composite webs separated by structural foam between two composite facesheets. The HyperSizer structural sizing software, in conjunction with NASTRAN finite element analyses, is used. However, since HyperSizer does not currently include a panel concept for fiber reinforced foam, the sizing was performed using two separate approaches. In the first, the panel core is treated as an effective (homogenized) material, whose properties are provided by the vendor. In the second approach, the panel is treated as a blade stiffened sandwich panel, with the mass of the foam added after completion of the panel sizing. Details of the sizing for each of the three Ares V components are given, and it is demonstrated that the two panel sizing approaches are in reasonable agreement for thinner panel designs, but as the panel thickness increases, the blade stiffened sandwich panel approach yields heavier panel designs. This is due to the effects of local buckling, which are not considered in the effective core property approach.

Bednarcyk, Brett A.↗
NASA NTRS1959

Experimental Investigation of Flutter of Buckled Curved Panels Having Longitudinal Stringers at Transonic and Supersonic Speeds

Panel-flutter tests have been made at transonic and supersonic speeds With particular reference to buckled curved panels with longitudinal stringers. Other panel configurations were also tested in an attempt to determine effects of skin thickness, curvature, stringers, buckling, pressure differential, and Mach number on the dynamic pressure necessary to start flutter. For buckled curved panels with longitudinal stringers, the dynamic pressure required to start flutter was increased by increasing the skin thickness and increasing the pressure differential across the panel. There was no apparent effect of Mach number variation from 1.3 to 2.0. None of the curved panels failed because of flutter although the dynamic pressure at the start of flutter was exceeded by a factor of 3 in many cases. curved panels and four flat panels failed because of flutter. The flat panels fluttered at lower dynamic pressures than the curved panels and four flat panels failed because of flutter.

Tuovila, W. J.↗
NASA NTRS1993

Hypersonic panel flutter in a rarefied atmosphere

Panel flutter is a form of dynamic aeroelastic instability resulting from the interaction between motion of an aircraft structural panel and the aerodynamic loads exerted on that panel by air flowing past one of the faces. It differs from lifting surface flutter in the sense that it is not usually catastrophic, the panel's motion being limited by nonlinear membrane stresses produced by the transverse displacement. Above some critical airflow condition, the linear instability grows to a limit cycle . The present investigation studies panel flutter in an aerodynamic regime known as 'free molecule flow', wherein intermolecular collisions can be neglected and loads are caused by interactions between individual molecules and the bounding surface. After collision with the panel, molecules may be reflected specularly or reemitted in diffuse fashion. Two parameters characterize this process: the 'momentum accommodation coefficient', which is the fraction of the specularly reflected molecules; and the ratio between the panel temperature and that of the free airstream. This model is relevant to the case of hypersonic flight vehicles traveling at very high altitudes and especially for panels oriented parallel to the airstream or in the vehicle's lee. Under these conditions the aerodynamic shear stress turns out to be considerably larger than the surface pressures, and shear effects must be included in the model. This is accomplished by means of distributed longitudinal and bending loads. The former can cause the panel to buckle. In the example of a simply-supported panel, it turns out that the second mode of free vibration tends to dominate the flutter solution, which is carried out by a Galerkin analysis. Several parametric studies are presented. They include the effects of (1) temperature ratio; (2) momentum accommodation coefficient; (3) spring parameters, which are associated with how the panel is connected to adjacent structures; (4) a parameter which relates compressive end load to its value which would cause classical column buckling; (5) a parameter proportional to the pressure differential between the front and back faces; and (6) initial curvature. The research is completed by an investigation into the possibility of accounting for molecular collisions, which proves to be infeasible given the speeds of current mainframe supercomputers.

Resende, Hugo B.↗
NASA NTRS1994

Panel to review EOSDIS plans

Formed in Jan. 1992, the Panel to Review EOSDIS Plans was charged with advising NASA on its plans for developing the Earth Observing System (EOS) Data and Information System (EOSDIS). Specifically, the panel was asked to do the following: assess the validity of the engineering and technical underpinnings of the EOSDIS; assess its potential value to scientific users; suggest how technical risk can be minimized; and assess whether current plans are sufficiently resilient to be adaptable to changing technology and requirements such as budget environments, data volumes, new users, and new databases. The panel completed an interim report (Addendum A) and transmitted it to NASA and other interested parties in the government on 9 Apr. 1992. Because of a delay in NASA's plans to select the contractor for EOSDIS, the panel was not able to complete its review of the program according to the original government request. With the issuance of a letter report (Addendum B) on 28 Sep. 1992, the panel became inactive until such time as NASA could release the details of the contractor's proposed architecture, schedule, and costs for developing EOSDIS. In early 1993, NASA awarded the contract for the EOSDIS Core System (ECS). On 20 Apr. 1993, NASA asked the panel to reconvene to do the following: ( 1) complete its review of NASA's approach to the EOSDIS architecture and implementation; (2) appraise NASA's responses to the panel's previous recommendations; and (3) review the planning for EOSDIS in the context of NASA's role in the Global Change Data and Information System (GCDIS) implementation plan. To respond to the NASA charge, the panel met three times in 1993 including sessions with NASA officials and the EOSDIS contractor. In addition, several of the panel members visited individual Distributed Active Archive Centers (DAAC's) to obtain additional views of EOSDIS. The panel has now obtained substantial information on the EOSDIS budget, contractor work program, and current baseline architecture that was not previously available, due to procurement restrictions. This report presents the panel's findings and recommendations based on this additional information.

Source record↗
NASA NTRS1995

Analytical comparison of three stiffened panel concepts

Three stiffened panel concepts are evaluated to find optimized designs for integral stiffeners in the barrels of Reusable Launch Vehicle fuel tanks. The three panel concepts considered are a T-stiffened panel, a panel with one blade stiffener centered between each pair of T-stiffeners, and a panel with two blade stiffeners equally spaced between each pair of T-stiffeners. The panels are optimized using PASCO for a range of compressive loads, and the computed areal weight for each panel is used to compare the concepts and predict tank weights. The areal weight of the T-stiffened panel with one blade is up to seven-percent lower than the other panel concepts. Two tank construction methods are compared for a representative tank design with three barrels. In the first method, 45-degree circumferential sections of a barrel are each designed to carry the same maximum load in the barrel. In the second method, each barrel section is designed for the maximum load in that section. Representative tanks designed with the first method are over 250 lb heavier than tanks designed using the second method. Optimized panel designs and areal weights are also computed for variation of the nominal panel length and skin thickness.

Maloney, Jill M.↗
NASA NTRS1996

Analysis and Tests of Reinforced Carbon-Epoxy/Foam-Core Sandwich Panels with Cutouts

The results of a study of a low-cost structurally efficient minimum-gage shear-panel design that can be used in light helicopters are presented. The shear-panel design is based on an integrally stiffened syntactic-foam stabilized-skin with an all-bias-ply tape construction for stabilized-skin concept with an all-bias-ply tape construction for the skins. This sandwich concept is an economical way to increase the panel bending stiffness weight penalty. The panels considered in the study were designed to be buckling resistant up to 100 lbs/in. of shear load and to have an ultimate strength of 300 lbs/in. The panel concept uses unidirectional carbon-epoxy tape on a syntactic adhesive as a stiffener that is co-cured with the skin and is an effective concept for improving panel buckling strength. The panel concept also uses pultruded carbon-epoxy rods embedded in a syntactic adhesive and over-wrapped with a bias-ply carbon-epoxy tape to form a reinforcing beam which is an effective method for redistributing load around rectangular cutout. The buckling strength of the reinforced panels is 83 to 90 percent of the predicted buckling strength based on a linear buckling analysis. The maximum experimental deflection exceeds the maximum deflection predicted by a nonlinear analysis by approximately one panel thickness. The failure strength of the reinforced panels was two and a half to seven times of the buckling strength. This efficient shear-panel design concept exceeds the required ultimate strength requirement of 300 lbs/in by more than 100 percent.

Baker, Donald J.↗
NASA NTRS1998

Response of Composite Fuselage Sandwich Side Panels Subjected to Internal Pressure and Axial Tension

The results from an experimental and analytical study of two composite sandwich fuselage side panels for a transport aircraft are presented. Each panel has two window cutouts and three frames and utilizes a distinctly different structural concept. These panels have been evaluated with internal pressure loads that generate biaxial tension loading conditions. Design limit load and design ultimate load tests have been performed on both panels. One of the sandwich panels was tested with the middle frame removed to demonstrate the suitability of this two-frame design for supporting the prescribed biaxial loading conditions with twice the initial frame spacing of 20 inches. A damage tolerance study was conducted on the two-frame panel by cutting a notch in the panel that originates at the edge of a cutout and extends in the panel hoop direction through the window-belt area. This panel with a notch was tested in a combined-load condition to demonstrate the structural damage tolerance at the design limit load condition. Both the sandwich panel designs successfully satisfied all desired load requirements in the experimental part of the study, and experimental results from the two-frame panel with and without damage are fully explained by the analytical results. The results of this study suggest that there is potential for using sandwich structural concepts with greater than the usual 20-in. wide frame spacing to further reduce aircraft fuselage structural weight.

Rouse, Marshall↗
NASA NTRS2000

Aerospace Safety Advisory Panel Annual Report for 1999

This report covers the activities of the Aerospace Safety Advisory Panel (ASAP) for the calendar year 1999.This was a year of notable achievements and significant frustrations. Both the Space Shuttle and International Space Station (ISS) programs were delayed.The Space Shuttle prudently postponed launches after the occurrence of a wiring short during ascent of the STS-93 mission. The ISS construction schedule slipped as a result of the Space Shuttle delays and problems the Russians experienced in readying the Service Module and its launch vehicle. Each of these setbacks was dealt with in a constructive way. The STS-93 short circuit led to detailed wiring inspections and repairs on all four orbiters as well as analysis of other key subsystems for similar types of hidden damage. The ISS launch delays afforded time for further testing, training, development, and contingency planning. The safety consciousness of the NASA and contractor workforces, from hands-on labor to top management, continues high. Nevertheless, workforce issues remain among the most serious safety concerns of the Panel. Cutbacks and reorganizations over the past several years have resulted in problems related to workforce size, critical skills, and the extent of on-the-job experience. These problems have the potential to impact safety as the Space Shuttle launch rate increases to meet the demands of the ISS and its other customers. As with last year's report, these work- force-related issues were considered of sufficient import to place them first in the material that follows. Some of the same issues of concern for the Space Shuttle and ISS arose in a review of the launch vehicle for the Terra mission that the Panel was asked by NASA to undertake. Other areas the Panel was requested to assess included the readiness of the Inertial Upper Stage for the deployment of the Chandra X-ray Observatory and the possible safety impact of electromagnetic effects on the Space Shuttle. The findings and recommendations in this report do not highlight any major, immediate issues that might compromise the safe pursuit of the various NASA programs. They do, however, cover concerns that the Panel believes should be addressed in the interest of maintaining NASA's excellent safety record.The Panel is pleased to note that remedial efforts for some of the findings raised are underway. Given appropriate funding and cooperative efforts among the Administration, the Congress and the various contractors, the Panel is convinced that safety problems can be avoided or solved resulting in lower risk for NASA's human space and aeronautics programs. Section II of this report contains specific findings and recommendations generated by Panel activities during the calendar year 1999. Section III presents more detailed information in support of these findings and recommendations. A current roster of Panel members, consultants, and staff is included as Appendix A. Appendix B contains NASA's response to the findings and recommendations from the 1998 annual report. It has been augmented this year to include brief explanations of why the Panel classified the NASA response as " open,""continuing," or "closed." Appendix C lists the fact-finding activities of the Panel in 1999.

Blomberg, Richard D.↗
NASA NTRS2004

The Influence of Mesh Density on the Impact Response of a Shuttle Leading-Edge Panel Finite Element Simulation

A study was performed to examine the influence of varying mesh density on an LS-DYNA simulation of a rectangular-shaped foam projectile impacting the space shuttle leading edge Panel 6. The shuttle leading-edge panels are fabricated of reinforced carbon-carbon (RCC) material. During the study, nine cases were executed with all possible combinations of coarse, baseline, and fine meshes of the foam and panel. For each simulation, the same material properties and impact conditions were specified and only the mesh density was varied. In the baseline model, the shell elements representing the RCC panel are approximately 0.2-in. on edge, whereas the foam elements are about 0.5-in. on edge. The element nominal edge-length for the baseline panel was halved to create a fine panel (0.1-in. edge length) mesh and doubled to create a coarse panel (0.4-in. edge length) mesh. In addition, the element nominal edge-length of the baseline foam projectile was halved (0.25-in. edge length) to create a fine foam mesh and doubled (1.0- in. edge length) to create a coarse foam mesh. The initial impact velocity of the foam was 775 ft/s. The simulations were executed in LS-DYNA version 960 for 6 ms of simulation time. Contour plots of resultant panel displacement and effective stress in the foam were compared at five discrete time intervals. Also, time-history responses of internal and kinetic energy of the panel, kinetic and hourglass energy of the foam, and resultant contact force were plotted to determine the influence of mesh density. As a final comparison, the model with a fine panel and fine foam mesh was executed with slightly different material properties for the RCC. For this model, the average degraded properties of the RCC were replaced with the maximum degraded properties. Similar comparisons of panel and foam responses were made for the average and maximum degraded models.

Jackson, Karen E.↗
NASA NTRS2005

Evaluation of a Compression-Loaded-Stitched-Multi-Bay Fuselage Panel With Barely Visible Impact Damage

The experimental results from a stitched VaRTM carbon-epoxy composite panel tested under uni-axial compression loading are presented along with nonlinear finite element analysis prediction of the response. The curved panel is divided by frames and stringers into six bays with a column of three bays along the compressive loading direction. The frames are supported at the frame ends to resist out-of-plane translation. Back-to-back strain gages are used to record the strain and displacement transducers were used to record the out-of-plane displacements. In addition a full-field-displacement measurement technique that utilizes a camera-based-stereo-vision system was used to record the displacements. The panel was loaded to 1.5 times the predicted initial buckling load (1st bay buckling load, P(sub er) from the nonlinear finite element analysis and then was removed from the test machine for impact testing. After impacting with 20 ft-lbs of energy using a spherical impactor to produce barely visible damage the panel was loaded in compression until failure. The buckling load of the first bay to buckle was 97% of the buckling load before impact. The stitching constrained the impact damage from growing during the loading to failure. Impact damage had very little overall effect on panel stiffness. Panel stiffness measured by the full-field-displacement technique indicated a 13% loss in stiffness after impact. The panel failed at 1.64 times the first panel buckling load. The barely visible impact damage did not grow noticeably as the panel failed by global instability due to stringer-web terminations at the frame locations. The predictions from the nonlinear analysis of the finite element modeling of the entire specimen were very effective in the capture of the initial buckling and global behavior of the panel. In addition, the prediction highlighted the weakness of the panel under compression due to stringer web terminations. Both the test results and the nonlinear predictions serve to reinforce the severe penalty in structural integrity caused by the low cost manufacturing technique to terminate the stringer webs, and demonstrates the importance of this type of sub-component testing and high fidelity failure analysis in the design of a composite fuselage.

Baker, Donald J.↗
NASA NTRS2006

Configuration and Sizing of a Test Fixture for Panels Under Combined Loads

Future air and space structures are expected to utilize composite panels that are subjected to combined mechanical loads, such as bi-axial compression/tension, shear and pressure. Therefore, the ability to accurately predict the buckling and strength failures of such panels is important. While computational analysis can provide tremendous insight into panel response, experimental results are necessary to verify predicted performances of these panels to judge the accuracy of computational methods. However, application of combined loads is an extremely difficult task due to the complex test fixtures and set-up required. Presented herein is a comparison of several test set-ups capable of testing panels under combined loads. Configurations compared include a D-box, a segmented cylinder and a single panel set-up. The study primarily focuses on the preliminary sizing of a single panel test configuration capable of testing flat panels under combined in-plane mechanical loads. This single panel set-up appears to be best suited to the testing of both strength critical and buckling critical panels. Required actuator loads and strokes are provided for various square, flat panels.

Lovejoy, Andrew E.↗
NASA NTRS2003

Large thermal protection system panel

A protective panel for a reusable launch vehicle provides enhanced moisture protection, simplified maintenance, and increased temperature resistance. The protective panel includes an outer ceramic matrix composite (CMC) panel, and an insulative bag assembly coupled to the outer CMC panel for isolating the launch vehicle from elevated temperatures and moisture. A standoff attachment system attaches the outer CMC panel and the bag assembly to the primary structure of the launch vehicle. The insulative bag assembly includes a foil bag having a first opening shrink fitted to the outer CMC panel such that the first opening and the outer CMC panel form a water tight seal at temperatures below a desired temperature threshold. Fibrous insulation is contained within the foil bag for protecting the launch vehicle from elevated temperatures. The insulative bag assembly further includes a back panel coupled to a second opening of the foil bag such that the fibrous insulation is encapsulated by the back panel, the foil bag, and the outer CMC panel. The use of a CMC material for the outer panel in conjunction with the insulative bag assembly eliminates the need for waterproofing processes, and ultimately allows for more efficient reentry profiles.

Myers, Franklin K.↗
NASA NTRS2009

Hypervelocity Impact Performance of Open Cell Foam Core Sandwich Panel Structures

Metallic foams are a relatively new class of materials with low density and novel physical, mechanical, thermal, electrical and acoustic properties. Although incompletely characterized, they offer comparable mechanical performance to traditional spacecraft structural materials (i.e. honeycomb sandwich panels) without detrimental through-thickness channeling cells. There are two competing types of metallic foams: open cell and closed cell. Open cell foams are considered the more promising technology due to their lower weight and higher degree of homogeneity. Leading micrometeoroid and orbital debris shields (MMOD) incorporate thin plates separated by a void space (i.e. Whipple shield). Inclusion of intermediate fabric layers, or multiple bumper plates have led to significant performance enhancements, yet these shields require additional non-ballistic mass for installation (fasteners, supports, etc.) that can consume up to 35% of the total shield weight [1]. Structural panels, such as open cell foam core sandwich panels, that are also capable of providing sufficient MMOD protection, represent a significant potential for increased efficiency in hypervelocity impact shielding from a systems perspective through a reduction in required non-ballistic mass. In this paper, the results of an extensive impact test program on aluminum foam core sandwich panels are reported. The effect of pore density, and core thickness on shielding performance have been evaluated over impact velocities ranging from 2.2 - 9.3 km/s at various angles. A number of additional tests on alternate sandwich panel configurations of comparable-weight have also been performed, including aluminum honeycomb sandwich panels (see Figure 1), Nomex honeycomb core sandwich panels, and 3D aluminum honeycomb sandwich panels. A total of 70 hypervelocity impact tests are reported, from which an empirical ballistic limit equation (BLE) has been derived. The BLE is in the standard form suitable for implementation in risk analysis software, and includes the effect of panel thickness, core density, and facesheet material properties. A comparison between the shielding performance of foam core sandwich panel structures and common MMOD shielding configurations is made for both conservative (additional 35% non-ballistic mass) and optimistic (additional mass equal to 30% of bumper mass) considerations. Suggestions to improve the shielding performance of foam core sandwich panels are made, including the use of outer mesh layers, intermediate fabric/composite layers, and varying pore density.

Ryan, Shannon↗
NASA NTRS1995

Multi-angle Imaging SpectroRadiometer (MISR): Optical Characterization of the Spectralon Calibration Panels

The reflectance properties of an engineering model of the Spectralon panel intended for use within an On-Board Calibrator (OBC) on the NASA Multi-angle Imaging SpectroRadiometer (MISR) instrument have been fully characterized with regard to panel uniformity and isotropy in response to three incident laser wavelengths of 442, 632.8 and 859.9 nm. A regional variation in bidirectional reflectance function (BRF) across the surface of the engineering model (EM) panel, contributing to spatial non-uniformity at the +/-2% level has been measured at all three laser wavelengths. Further, a BRF anisotropy has been identified. The mechanism causing these departures from the ideal Lambertian surface may originate in the sanding of the Spectralon surface in the final stage of preparation. This is corroborated by measurements made on a 'pressed' polytetrafluoroethylene (PTFE) panel in which a greatly reduced anisotropy in panel BRF is measured. The EM panel BRF reveals deviation from a Lambertian characteristic manifest as an off-specular peak in the forward scattering direction. A common cross-over point at an angle of reflection of around 37 at which the BRF is constant within 0.4% for an illumination angle range of ui = 30 60 is observed at all three wavelengths. Two Spectralon protoflight panels which were fabricated after the engineering model was studied were also the subject of a uniformity study over part of the area of the Spectralon panels at the 442 nm wavelength. The analysis indicated that the panel uniformity satisfies the 0.5% criterion indicating improved panel preparation. However, the off specular peak in the forward scattering direction is essentially unchanged with the cross-over point at approximately 37.

Multi-angle Imaging SpectroRadiometer↗
NASA NTRS1972

Aeroelastic optimization of a panel in high Mach number supersonic flow.

Solution for a least-weight skin thickness distribution for a panel with a flutter parameter constraint. This panel weighs less than any similar constant thickness panel, but has the same critical supersonic panel flutter parameter. The panel rests on simple supports and is of sandwich construction. The span to chord ratio is large enough that the inertial, elastic, and aerodynamic behavior is one-dimensional. The Mach number is great enough that the aerodynamic forces acting on the upper panel surface may be accurately described by quasi-steady, linearized, supersonic aerodynamic theory. The final optimum design is obtained from theoretical and numerical methods adapted from optimal control theory. The results of this investigation show that the optimal panel thickness distribution is symmetric about the panel chord midpoint. Compared to a reference panel with constant thickness, optimum panels are found to be nearly 12% lighter.

Weisshaar, T. A.↗