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At least 1,135 records · Page 63

Progress in Integrated Fluid/Structure/Controls Computations Using High Fidelity Equations

Aeroelasticity that involves strong coupling of fluids, structures and controls is an important element in designing an aircraft. Computational aeroelasticity using low fidelity methods such as the linear aerodynamic flow equations coupled with the modal structural equations are well advanced. Though these low fidelity approaches are computationally less intensive, they are not adequate for the analysis of aircraft which can experience complex flow/structure interactions. Supersonic transports can experience vortex induced aeroelastic oscillations whereas subsonic transports can experience transonic buffet associated structural oscillations. Both aircraft may experience a dip in the flutter speed at the transonic regime. For accurate aeroelastic computations at these complex fluid/structure interaction situations, high fidelity equations such as the Navier-Stokes for fluids and the finite-elements for structures are needed. Using these high fidelity methods, design quantities such as structural stresses can be directly computed. Computations using these high fidelity equations require state-of-the-art large computational resources. This paper will describe the transition from potential equations to Euler/Navier-Stokes equations for fluids and from modal equations to finite element equations for structures. Complexities associated with grids for moving control surfaces will be discussed. All contents of the paper will be limited to those already presented at domestic conferences within U.S. such as those sponsored by AIAA. It will not include any materials related to HPCCP computational work.

Guruswamy, Guru P.↗

Test Activities in the Langley Transonic Dynamics Tunnel and a Summary of Recent Facility Improvements

The Langley Transonic Dynamics Tunnel (TDT) has provided a unique capability for aeroelastic testing for over forty years. The facility has a rich history of significant contributions to the design of many United States commercial transports, military aircraft, launch vehicles, and spacecraft. The facility has many features that contribute to its uniqueness for aeroelasticity testing, perhaps the most important feature being the use of a heavy gas test medium to achieve higher test densities compared to testing in air. Higher test medium densities substantially improve model-building requirements and therefore simplify the fabrication process for building aeroelastically scaled wind tunnel models. This paper describes TDT capabilities that make it particularly suited for aeroelasticity testing. The paper also discusses the nature of recent test activities in the TDT, including summaries of several specific tests. Finally, the paper documents recent facility improvement projects and the continuous statistical quality assessment effort for the TDT.

Cole, Stanley R.↗

Investigation of the Flow Physics Driving Stall-Side Flutter in Advanced Forward Swept Fan Designs

Flutter-free operation of advanced transonic fan designs continues to be a challenging task for the designers of aircraft engines. In order to meet the demands of increased performance and lighter weight, these modern fan designs usually feature low-aspect ratio shroudless rotor blade designs that make the task of achieving adequate flutter margin even more challenging for the aeroelastician. This is especially true for advanced forward swept designs that encompass an entirely new design space compared to previous experience. Fortunately, advances in unsteady computational fluid dynamic (CFD) techniques over the past decade now provide an analysis capability that can be used to quantitatively assess the aeroelastic characteristics of these next generation fans during the design cycle. For aeroelastic applications, Mississippi State University and NASA Glenn Research Center have developed the CFD code TURBO-AE. This code is a time-accurate three-dimensional Euler/Navier-Stokes unsteady flow solver developed for axial-flow turbomachinery that can model multiple blade rows undergoing harmonic oscillations with arbitrary interblade phase angles, i.e., nodal diameter patterns. Details of the code can be found in Chen et al. (1993, 1994), Bakhle et al. (1997, 1998), and Srivastava et al. (1999). To assess aeroelastic stability, the work-per-cycle from TURBO-AE is converted to the critical damping ratio since this value is more physically meaningful, with both the unsteady normal pressure and viscous shear forces included in the work-per-cycle calculation. If the total damping (aerodynamic plus mechanical) is negative, then the blade is unstable since it extracts energy from the flow field over the vibration cycle. TURBO-AE is an integral part of an aeroelastic design system being developed at Honeywell Engines, Systems & Services for flutter and forced response predictions, with test cases from development rig and engine tests being used to validate its predictive capability. A recent experimental program (Sanders et al., 2002) was aimed at providing the necessary unsteady aerodynamic and vibratory response data needed to validate TURBO-AE for fan flutter predictions. A comparison of numerical TURBO-AE simulations with the benchmark flutter data is given in Sanders et al. (2003), with the data used to guide the validation of the code and define best practices for performing accurate unsteady simulations. The agreement between the analyses and the predictions was quite remarkable, demonstrating the ability of the analysis to accurately model the unsteady flow processes driving stall-side flutter.

Sanders, Albert J.↗

Flutter Stability of the Efficient Low Noise Fan Calculated

The TURBO-AE aeroelastic code has been used to verify the flutter stability of the Efficient Low Noise Fan (ELNF), which is also referred to as the trailing-edge blowing fan. The ELNF is a unique technology demonstrator being designed and fabricated at the NASA Glenn Research Center for testing in Glenn's 9-by-15-Foot Low-Speed Wind Tunnel. In the ELNF, air can be blown out of slots near the trailing edges of the fan blades to fill in the wakes downstream of the rotating blades. This filling of the wakes leads to a reduction of the rotor-stator interaction (tone) noise that results from the interaction of wakes with the downstream stators. The ELNF will demonstrate a 1.6-EPNdB1 reduction in tone noise through wake filling, without increasing the broadband noise. Furthermore, the reduced blade row interaction will decrease the possibility of forced response and enable closer spacing of blade rows, thus reducing engine length and weight. During the design of the ELNF, the rotor blades were checked for flutter stability using the detailed aeroelastic analysis capability of the three-dimensional Navier-Stokes TURBOAE code. The aeroelastic calculations were preceded by steady calculations in which the blades were not allowed to vibrate. For each rotational speed, as the back-pressure was increased, the mass flow rate decreased, and the operating point moved along the constant speed characteristic (speed-line) from choke to stall as shown on the fan map. The TURBO-AE aeroelastic analyses were performed separately for the first two vibration modes (bending and torsion) and covered the complete range of interblade phase angles or nodal diameters at which flutter can occur. The results indicated that the ELNF blades would not encounter flutter at takeoff conditions. The calculations were then repeated for a part-speed condition (70-percent rotational speed), and the results again showed no flutter in the operating region. On the fan map (shown), the predicted flutter point at part speed condition was located beyond the stall line, which means that the ELNF will not encounter flutter since it will never operate beyond the stall line. All the calculations done so far have been for the nonblowing case, and selected calculations will be repeated with air blowing from the trailing edge of the fan.

Bakhle, Milind A.↗

Validation of the Lockheed Martin Morphing Concept with Wind Tunnel Testing

The Morphing Aircraft Structures (MAS) program is a Defense Advanced Research Projects Agency (DARPA) led effort to develop morphing flight vehicles capable of radical shape change in flight. Two performance parameters of interest are loiter time and dash speed as these define the persistence and responsiveness of an aircraft. The geometrical characteristics that optimize loiter time and dash speed require different geometrical planforms. Therefore, radical shape change, usually involving wing area and sweep, allows vehicle optimization across many flight regimes. The second phase of the MAS program consisted of wind tunnel tests conducted at the NASA Langley Transonic Dynamics Tunnel to demonstrate two morphing concepts and their enabling technologies with large-scale semi-span models. This paper will focus upon one of those wind tunnel tests that utilized a model developed by Lockheed Martin Aeronautics Company (LM). Wind tunnel success criteria were developed by NASA to support the DARPA program objectives. The primary focus of this paper will be the demonstration of the DARPA objectives by systematic evaluation of the wind tunnel model performance relative to the defined success criteria. This paper will also provide a description of the LM model and instrumentation, and document pertinent lessons learned. Finally, as part of the success criteria, aeroelastic characteristics of the LM derived MAS vehicle are also addressed. Evaluation of aeroelastic characteristics is the most detailed criterion investigated in this paper. While no aeroelastic instabilities were encountered as a direct result of the morphing design or components, several interesting and unexpected aeroelastic phenomenon arose during testing.

Ivanco, Thomas G.↗

Multi-Objective Flight Control for Drag Minimization and Load Alleviation of High-Aspect Ratio Flexible Wing Aircraft

As aircraft wings become much more flexible due to the use of light-weight composites material, adverse aerodynamics at off-design performance can result from changes in wing shapes due to aeroelastic deflections. Increased drag, hence increased fuel burn, is a potential consequence. Without means for aeroelastic compensation, the benefit of weight reduction from the use of light-weight material could be offset by less optimal aerodynamic performance at off-design flight conditions. Performance Adaptive Aeroelastic Wing (PAAW) technology can potentially address these technical challenges for future flexible wing transports. PAAW technology leverages multi-disciplinary solutions to maximize the aerodynamic performance payoff of future adaptive wing design, while addressing simultaneously operational constraints that can prevent the optimal aerodynamic performance from being realized. These operational constraints include reduced flutter margins, increased airframe responses to gust and maneuver loads, pilot handling qualities, and ride qualities. All of these constraints while seeking the optimal aerodynamic performance present themselves as a multi-objective flight control problem. The paper presents a multi-objective flight control approach based on a drag-cognizant optimal control method. A concept of virtual control, which was previously introduced, is implemented to address the pair-wise flap motion constraints imposed by the elastomer material. This method is shown to be able to satisfy the constraints. Real-time drag minimization control is considered to be an important consideration for PAAW technology. Drag minimization control has many technical challenges such as sensing and control. An initial outline of a real-time drag minimization control has already been developed and will be further investigated in the future. A simulation study of a multi-objective flight control for a flight path angle command with aeroelastic mode suppression and drag minimization demonstrates the effectiveness of the proposed solution. In-flight structural loads are also an important consideration. As wing flexibility increases, maneuver load and gust load responses can be significant and therefore can pose safety and flight control concerns. In this paper, we will extend the multi-objective flight control framework to include load alleviation control. The study will focus initially on maneuver load minimization control, and then subsequently will address gust load alleviation control in future work.

Aerolasticity↗

Structural Design Exploration of an Electric Powered Multi-Propulsor Wing Configuration

Advancements in aircraft electric propulsion may enable an expanded operational envelope for electrically powered vehicles compared to their internal combustion engine counterparts. High aspect ratio wings provide additional lift and drag reduction for a proposed multi-propulsor design, however, the challenge is to reduce the weight of wing structures while maintaining adequate structural and aeroelastic margins. Design exploration using a conventional design-and-build philosophy coupled with a finite element method (FEM)-based design of experiments (DOE) strategy are presented to examine high aspect ratio wing structures that have spanwise distributed electric motors. Multiple leading-edge-mounted engine masses presented a challenge to design a wing within acceptable limits for dynamic and aeroelastic stability. Because the first four primary bending eigenmodes of the proposed wing structure are very sensitive to outboard motor placement, safety-of-flight requirements drove the need for multiple spars, rib attachments, and outboard structural reinforcements in the design. Global aeroelasticity became an increasingly important design constraint during the on-going design process, with outboard motor pod flutter ultimately becoming a primary design constraint. Designers successively generated models to examine stress, dynamics, and aeroelasticity concurrently. This research specifically addressed satisfying multi-disciplinary design criteria to generate fluid-structure interaction solution sets, and produced high aspect ratio primary structure designs for the NASA Scalable Convergent Electric Propulsion Technology and Operations Research (SCEPTOR) project in the Aeronautic Research Mission Directorate at NASA. In this paper, a dynamics-driven, quasi-inverse design methodology is presented to address aerodynamic performance goals and structural challenges encountered for the SCEPTOR demonstrator vehicle. These results are compared with a traditional computer aided design based approach.

Moore, James B.↗

Investigating the Transonic Flutter Boundary of the Benchmark Supercritical Wing

This paper builds on the computational aeroelastic results published previously and generated in support of the second Aeroelastic Prediction Workshop for the NASA Benchmark Supercritical Wing configuration. The computational results are obtained using FUN3D, an unstructured grid Reynolds-Averaged Navier-Stokes solver developed at the NASA Langley Research Center. The analysis results focus on understanding the dip in the transonic flutter boundary at a single Mach number (0.74), exploring an angle of attack range of 􀀀1 to 8 and dynamic pressures from wind off to beyond flutter onset. The rigid analysis results are examined for insights into the behavior of the aeroelastic system. Both static and dynamic aeroelastic simulation results are also examined.

Heeg, Jennifer↗

Reduced Order Modeling for Transonic Aeroservoelastic Control Law Development

As aircraft become more flexible, aeroelastic considerations become increasingly important and complex, particularly for transonic flight where nonlinearities in the flow render linear analysis tools less effective. In order to analyze these aeroelastic interactions between the fluid and the structure efficiently, reduced order models (ROMs) are sometimes generated from and used in place of computational fluid dynamics solutions. In this paper, several aerodynamic ROMs are generated and coupled with structural models to form aeroelastic ROMs. The aerodynamic ROMs generated here include the effects of control surface motion. Hence, the aeroelastic ROMs presented here are appropriate for use in aeroservoelastic applications and are intended to be used for aeroservoelastic control law development. These ROMs are used to simulate a number of test cases with and without control surface involvement. Results show that several of the ROMs generated in the paper are able to predict results similar to solutions of higher-order computational methods.

Waite, Josiah M.↗

Investigation of Atmospheric Boundary-Layer Effects on Launch-Vehicle Ground Wind Loads

A launch vehicle ground-wind-loads program is underway at the NASA Langley Transonic Dynamics Tunnel. The objectives are to quantify key aerodynamic and structural characteristics that impact the occurrence of large wind-induced oscillations of a launch vehicle when exposed to ground winds prior to launch. Of particular interest is the dynamic response of a launch vehicle when a von Kármán vortex street forms in the wake of the vehicle resulting in quasiperiodic lift and drag forces. Vehicle response to these quasiperiodic forces can become quite large when the frequency of vortex shedding nears that of a lowly-damped structural mode thereby exciting a resonant response. Wind approaching the vehicle can be characterized by a varying speed with height and turbulence content. The combination of both the varying speed and turbulence content is referred to herein as the atmospheric boundary-layer. The importance of the atmospheric boundary-layer upon launch vehicle wind-induced oscillation response has long been questioned, and its effects are not well understood. Although there are several facilities around the world dedicated to replicating atmospheric boundary layers, the development of such a boundary layer in a wind tunnel capable of producing flight-representative Reynolds numbers for aeroelastically-scaled launch vehicle models has only recently been accomplished. The NASA Langley Transonic Dynamics Tunnel is capable of simulating flight-representative Reynolds numbers of launch vehicles on the pad and is uniquely capable of replicating many fluid-structure scaling parameters typical of aeroelastic tests. Recent test efforts successfully developed representative atmospheric boundary-layers for three launch sites in the Transonic Dynamics Tunnel, thereby allowing all known aerodynamic and fluid-structure coupling parameters to be simultaneously simulated for those sites. Dynamic aeroelastically-scaled models representative of typical large launch vehicles were constructed for testing. Aeroelastic scaling includes matching geometry, mode shapes, reduced frequencies, damping, running mass ratios, and running stiffness ratios. The models were tested in smooth uniform flow and then immersed in the atmospheric boundary-layer for comparison of these effects. Dynamic data were acquired measuring unsteady pressure, acceleration, and base bending moment. It was discovered that peak dynamic loads resulting from resonant wind-induced oscillation response are similar when acquired in either smooth uniform flow or an atmospheric boundary-layer. This indicates that resonant lock-in events are minimally impacted by representative turbulence and/or wind profile. Alternately, nonresonant wind-induced oscillation response events are stronger when acquired in an atmospheric boundary-layer. This indicates that a lowly-damped structural response will increase when exposed to an increased magnitude of random excitation, which is consistent with historical comparisons. Loads created by the resonant response events were substantially stronger than those from the nonresonant response events. Therefore, if testing is done to simply identify worst-case conditions and load magnitude, then smooth uniform flow is likely an adequate test technique. However, if nonresonant response loads are of primary interest, then atmospheric boundary-layer simulation is required.

Thomas G Ivanco↗

TPSAS-NF1676L-13635-DND

Objectives of AePW: Assess state-of-the-art Computational Aeroelasticity (CAe) methods as practical tools for the prediction of static and dynamic aeroelastic phenomena and responses on relevant geometries. - Perform comparative computational studies on selected test cases - Identify errors & uncertainties in computational aeroelastic methods - Identify gaps in existing aeroelastic databases - Provide roadmap of path forward (additional existing data sets, new experimental data sets, and analytical methods developments).

Walt Silva↗

Numerical Simulation of An Aspect Ratio 13.5 Common Research Model with Trailing Edge Mini-Flaps

This paper presents an aeroelastic modeling study of an aspect ratio 13.5 wind tunnel scale Common Research Model (CRM) with trailing edge mini-flaps. FUN3D is used for the aeroelastic steady and unsteady simulations at Mach 0.85 and dynamic pressure 230 psf. The aeroelastic simulation results are compared with the in-house developed VSPAERO aeroelastic model results. The incremental aerodynamic coefficients predicted by FUN3D and VSPAERO are close except when the mini-flap deflection angle is 10˚. The control reversal behavior is observed for the wing tip mini-flap. A series of dynamic pressure sweep simulations are performed to determine the control reversal onset point. Unsteady simulation results show that there is no buffet phenomenon observed at angle of attacks 0˚ and 2˚ when the mini-flap is deflected 10˚. The mini-flap oscillation simulations show the nonlinear behavior appears when the deflection angle is about 4˚.

Mini-flap↗

Classical Flutter Analysis of X-57 Aircraft Mod II, III, and IV Configurations

To support airworthiness assessment of the X-57 electric propulsion demonstrator aircraft, the National Aeronautics and Space Administration (NASA) completed classical flutter analysis of the Mod II, Mod III, and Mod IV aircraft configurations. Aeroelastic analysis was primarily performed using the ZAERO analysis code developed by Zona Technology. Supplemental computational fluid dynamics (CFD) flutter analysis for the Mod III and Mod IV configurations was performed using NASA’s FUN3D software to verify the aeroelastic behavior at deployed flaps conditions. The NASTRAN finite element models (FEMs) used for aeroelastic analysis were developed by NASA. The final Mod II FEM utilized shell elements for the wing and fuselage, and beam elements for the tail and wing control surfaces. For Mod III and Mod IV aircraft models, shell element wing FEMs developed throughout the Mod III/IV wing design cycle were utilized. The fuselage and empennage FEM components were shared between the Mod II, III, and IV aircraft models. ZAERO analyses predicted flutter boundaries were >60% beyond the X-57 flight-test envelope never exceed airspeed (V NE ) for all configurations. Aeroelastic Reynolds-averaged Navier–Stokes (RANS) CFD simulations using FUN3D of the Mod III/IV configurations predicted flap mode instability did not occur until at least speeds of 60% higher than the Mod III/IV maximum flap deployment airspeed (V FE ).

Keerti K. Bhamidipati↗

Edgewise Structural Damping of a 2.8-MW Land-Based Wind Turbine Rotor Blade

Modern wind turbines push the predictive capabilities of state-of-the-art aero-servo-elastic tools. The existing limitations hide across the numerical tool chain and can result in serious issues, such as missing aeroelastic instabilities during the design phase. Structural damping is an input that is usually hard to estimate, but also has a major impact on the turbine behavior. In this paper, we discuss an experiment that aims to accurately quantify the structural damping characterizing the edgewise modes of modern wind turbine blades. The experiment is carried out on a 2.8-MW land-based wind turbine and features a fast yaw actuation that induces an edgewise motion on one of the three blades. The Covariant-subspace system identification (Cov-SSI) method is then used to post-process the blade root moment to estimate the short-term edgewise structural damping. Despite limitations of the Cov-SSI method, which consistently under-predicts the absolute values of damping, we observe that structural damping decreases across the first three blade edgewise modes, which is different from the stiffness-proportional damping model that assumes that structural damping increases with the modes. This paper argues that a stiffness-proportional damping model, which is implemented in most aeroelastic tools, is therefore not conservative and might hide aeroelastic instabilities that can instead appear in the field.

17 WIND ENERGY↗

Aerodynamic Load Analysis of a Variable Camber Continuous Trailing Edge Flap System on a Flexible Wing Aircraft

This paper presents an investigative aerodynamic analysis conducted on the novel control surface known as a Variable Camber Continuous Trailing Edge Flap (VCCTEF). The VCCTEF is modeled as a control effector on the NASA Generic Transport Model (GTM) where wing flexibility is considered. Aerodynamic modeling of the aircraft is conducted using vortex-lattice method (VLM), and an aeroelastic model of the aircraft that utilizes a coupled finite-element analysis (FEA) vortex-lattice solution is employed. VLM solutions are used to determine quasi-steady aerodynamic loading over the aeroelastic wing structures with VCCTEF. The load data is used to calculate aerodynamic sensitivities to control surface deployment and is also integrated to determine overall hinge moments. This analysis is conducted for different flight conditions, where control sensitivities compare the VCCTEF effectiveness against conventional control surfaces. Hinge moment results provide insight into aeroelastic wing loads, and worst case hinge moments for the VCCTEF can be estimated. Results show that the VCCTEF offers greater control authority than conventional ailerons at cruise, and nominal flap settings are determined for a low-speed take-off condition where the VCCTEF maintains comparable control effectiveness. Worst case hinge moment values are presented, where for a possible VCCTEF configuration, the stiff wing model demonstrates up to a 5.90 percent increase in flap hinge moment relative to a rigid model, and a reduced stiffness model demonstrates up to an 11.42 percent increase.

Aeroelasticity↗

Improvements to the Simplified Loads Methodology in IEC 61400-2: November 22, 2021 - November 21, 2022

The "Simplified Loads Model" (SLM) of IEC 61400-2 provides a simple methodology to assess the structural integrity of a small wind turbine (SWT). The SLM is unique to the small wind turbine standard. It was included to allow SWT manufacturers with limited resources to undertake integrity checks at a reasonable cost in time and resources and avoid the expense of detailed aeroelastic simulations. Unfortunately, the SLM has gained the reputation of being overly conservative and this has reduced its value to the SWT community and its use in SWT design and certification. Conservatism in design standards is needed but excessive conservatism is not. The aim of this report is to address the principal areas of excess conservatism and recommend changes to the SLM that preserve its simplicity but reduce the excess. The changes for the ultimate loads are consistent with their treatment in aeroelastic modelling for certification and with related codes for wind loading on structures. The recommendations for a new fatigue design load case are also based on aeroelastic simulations, in this case of five SWTs of varying configurations with rated power from 2.4 to 50 kW. It is also pointed out the design load case for yawed operation omits an important term. The recommended inclusion of this term would make the SLM slightly more conservative for this case.

17 WIND ENERGY↗

Analyzing the Effects of Atmospheric Turbulent Fluctuations on the Wake Structure of Wind Turbines and Their Blade Vibrational Dynamics

In recent trends, a rising demand for renewable energy has driven wind turbines to larger proportions, where lighter blade designs are often adopted to reduce the costs associated with logistics and production. This causes modern utility-scale wind turbine blades to be inherently more flexible, and their amplified aeroelastic sensitivity results in complex multi-physics reactions to variant atmospheric conditions, including dynamic patterns of aerodynamic loading at the rotor and vortex structure evolutions within the wake. In this paper, we analyze the influence of inflow variance for wind turbines with large, flexible rotors through simulations of the National Rotor Testbed (NRT) turbine, located at Sandia National Labs’ Scaled Wind Farm Technology (SWiFT) facility in Lubbock, Texas. The Common Ordinary Differential Equation Framework (CODEF) modeling suite is used to simulate wind turbine aeroelastic oscillatory behavior and wind farm vortex wake interactions for a range of flexible NRT blade variations, operating in differing conditions of variant atmospheric flow. CODEF solutions of turbine operation in Steady-In-The-Average (SITA) wind conditions are compared to SITA wind conditions featuring a controlled gust-like pulse overimposed, to isolate the effects of typical wind fluctuations. Finally, simulations of realistic time-varying wind conditions from SWiFT meteorological tower measurements are compared to the solutions of SITA wind conditions. These increasingly complex atmospheric inflow variations are tested to show the differing effects evoked by various patterns of spatiotemporal atmospheric flow fluctuations. An analysis is presented for solutions of wind turbine aeroelastic response and vortex wake evolution, to elucidate the consequences of variant inflow, which pertain to wind turbine dynamics at an individual and farm-collective scale. The comparisons of simulated farm flow for SITA and measured fluctuating wind conditions show that certain regions of the wake contain up to a 12% difference in normalized axial velocity, due to the introduction of wind fluctuations. The findings of this study prove valuable for practical applications in wind farm control and optimization strategies, with particular significance for modern utility-scale wind power plants operating in variant atmospheric conditions.

Farrell, Alayna (ORCID:000000023555720X)↗

Level 12 NASTRAN experiences at General Dynamics, Convair Aerospace Division, Fort Worth Operations

The level 12 NASTRAN was used to support the NASA/LaRC advanced transport technology study, a predesign, short response time effort. Aeroelastic analyses were performed. NASTRAN calculated the vibration modes for the supported airfoil components and the entire unsupported vehicle. Other procedures were then used for the aeroelastic analysis, with procedure interfacing accomplished through use of the NASTRAN-produced restart tape. Stiffness matrices were used in static aeroelastic analyses; natural vibration modes were used for flutter and flight control system definition. Various level 12 NASTRAN characteristics were discovered and are discussed; e.g., the ability to solve singular matrices in rigid format 1, run times using multipoint constraints, restart tape problems, and the inaccurate stresses from the quad membrane when used with anisotropic materials.

Allen, M.↗