Self-adaptive predictor-corrector algorithms for static nonlinear structural analysis
(Previously announced in STAR as N81-33495)
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(Previously announced in STAR as N81-33495)
A method is presented to calculate analytically the sensitivity derivatives of wing static aeroelastic characteristics with respect to wing shape parameters. The wing aerodynamic response under fixed total load is predicted with Weissinger's L-method; its structural response is obtained with Giles' equivalent plate method. The characteristics of interest include the spanwise distribution of lift, trim angle of attack, rolling and pitching moments, wind induced drag, as well as the divergence dynamic pressure. The shape parameters considered are the wing area, aspect ratio, taper ratio, sweep angle, and tip twist angle. Results of sensitivity studies indicate that: (1) approximations based on analytical sensitivity derivatives can be used over wide ranges of variations of the shape parameters considered, and (2) the analytical calculation of sensitivity derivatives is significantly less expensive than the conventional finite-difference alternative.
A method is presented to calculate analytically the sensitivity derivatives of wing static aeroelastic characteristics with respect to wing shape parameters. The wing aerodynamic response under fixed total load is predicted using Weissinger's L-method; its structural response is obtained with Giles' equivalent plate method. The characteristics of interest in this study include the spanwise distribution of lift, trim angle of attack, rolling and pitching moments, wing induced drag as well as the divergence dynamic pressure. The shape parameters considered are the wing area, aspect ratio, taper ratio, sweep angle and tip twist angle. Results of sensitivity studies indicate that (1) approximations based on analytical sensitivity derivatives can be used for wide ranges of variations of the shape parameters considered and (2) the analytical calculation of sensitivity derivatives is significantly less expensive than the conventional finite difference alternative.
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A rigorous theory and the corresponding computational algorithms were developed for through-the-thickness analysis of composite plates. This type of analysis is needed in order to find the elastic stiffness constants of a plate. Additionally, the analysis is used to post-process the resulting plate solution in order to find approximate three-dimensional displacement, strain, and stress distributions throughout the plate. It was decided that the variational-asymptotical method (VAM) would serve as a suitable framework in which to solve these types of problems. Work during this reporting period has progressed along two lines: (1) further evaluation of neo-classical plate theory (NCPT) as applied to shear-coupled laminates; and (2) continued modeling of plates with nonuniform thickness.
The main purpose of this research was to develop a rigorous theory and corresponding computational algorithms for through-the-thickness analysis of composite plates. This type of analysis is needed in order to find the elastic stiffness constants for a plate and to post-process the resulting plate solution in order to find approximate three-dimensional displacement, strain, and stress distributions throughout the plate. This also requires the development of finite deformation plate equations which are compatible with the through-the-thickness analyses. After about one year's work, we settled on the variational-asymptotical method (VAM) as a suitable framework in which to solve these types of problems. VAM was applied to laminated plates with constant thickness in the work of Atilgan and Hodges. The corresponding geometrically nonlinear global deformation analysis of plates was developed by Hodges, Atilgan, and Danielson. A different application of VAM, along with numerical results, was obtained by Hodges, Lee, and Atilgan. An expanded version of this last paper was submitted for publication in the AIAA Journal.
Dynamic measurements of fluctuating static pressure levels were made using flush mounted high frequency response pressure transducers at eleven locations in the circuit of the National Transonic Facility (NTF) over the complete operating range of this wind tunnel. Measurements were made at test section Mach numbers from 0.2 to 1.2, at pressure from 1 to 8.6 atmospheres and at temperatures from ambient to -250 F, resulting in dynamic flow disturbance measurements at the highest Reynolds numbers available in a transonic ground test facility. Tests were also made independently at variable Mach number, variable Reynolds number, and variable drivepower, each time keeping the other two variables constant thus allowing for the first time, a distinct separation of these three important variables. A description of the NTF emphasizing its flow quality features, details on the calibration of the instrumentation, results of measurements with the test section slots covered, downstream choke, effects of liquid nitrogen injection and gaseous nitrogen venting, comparisons between air and nitrogen, isolation of the effects of Mach number, Reynolds number, and fan drive power, and identification of the sources of significant flow disturbances is included. The results indicate that primary sources of flow disturbance in the NTF may be edge-tones generated by test section sidewall re-entry flaps and the venting of nitrogen gas from the return leg of the tunnel circuit between turns 3 and 4 in the cryogenic mode of operation. The tests to isolate the effects of Mach number, Reynolds number, and drive power indicate that Mach number effects predominate. A comparison with other transonic wind tunnels shows that the NTF has low levels of test section fluctuating static pressure especially in the high subsonic Mach number range from 0.7 to 0.9.
Dynamic measurements of fluctuating static pressure levels were taken with flush-mounted, high-frequency response pressure transducers at 11 locations in the circuit of the National Transonic Facility (NTF) across the complete operating range of this wind tunnel. Measurements were taken at test-section Mach numbers from 0.1 to 1.2, at pressures from 1 to 8.6 atm, and at temperatures from ambient to -250 F, which resulted in dynamic flow disturbance measurements at the highest Reynolds numbers available in a transonic ground test facility. Tests were also made by independent variation of the Mach number, the Reynolds number, or the fan drive power while the other two parameters were held constant, which for the first time resulted in a distinct separation of the effects of these three important parameters.
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Explore the source record for details and available documents.
Explore the source record for details and available documents.
Finite element models can be used to model and predict the hysteresis and energy dissipation exhibited by nonlinear joints in structures. As a result of the nonlinearity, the frequency and damping of a mode is dependent on excitation amplitude, and when the modes remain uncoupled, quasi-static modal analysis has been shown to efficiently predict this behavior. However, in some cases the modes have been observed to couple such that the frequency and damping of one mode is dependent on the amplitude of other modes. To model the interactions between modes, one must integrate the dynamic equations in time, which is several orders of magnitude more expensive than quasi-static analysis. This work explores an alternative where quasi-static forces are applied in the shapes of two or more modes of vibration simultaneously, and the resulting load–displacement curves are used to deduce the effect of other modes on the effective frequency and damping of the mode in question. This methodology is demonstrated on a simple 2D cantilever beam structure with a single bolted joint which exhibits micro-slip nonlinearity over a range of vibration amplitudes. The predicted frequency and damping are compared with those extracted from a few expensive dynamic simulations of the structure, showing that the quasi-static approach produces reasonable albeit highly conservative bounds on the observed dynamics. This framework is also demonstrated on a 3D structure where dynamic simulations are infeasible.
Utilizing a continuous beam model, this report compares the potential stresses imposed on the beam from a random environment with those resulting from a typical static load analysis or test simulation. The Miles' equation used to develop peak response accelerations is shown to become a force equation in the hands of strength assessment personnel. This may prove to be unrealistic since hardware dynamic stresses are related to deflection rather than load. Correlation of the stress state for any static analysis or test with the actual dynamic response stress is strictly dependent upon how well the static deflections simulate the predominant dynamic mode shape. The report proposes that the general shape of this predominant mode, along with the peak response accelerations of major masses be used in strength assessments. From these data, a tailored enforced displacement loading may prove to be more effective in reproducing random induced stresses on flight hardware.
Component reliability analysis for 250 volt-ampere static inverter
The Test Stand 1C at the Air Force Astronautic Laboratory (AFAL), Edwards AFB, Calif., was originally designed for F-1 liquid propellant engines. The stand was modified to handle a five and one half segment Solid Rocket Motor (SRM) Titan 34D vertical static firing test. The main design drivers and analysis effort utilized in the modification of the test stand are discussed.
A probabilistic static stress analysis methodology has been developed to estimate the reliability of a composite structure. Closed form stress analysis methods are the primary analytical tools used in this methodology. These structural mechanics methods are used to identify independent variables whose variations significantly affect the performance of the structure. Once these variables are identified, scatter in their values is evaluated and statistically characterized. The scatter in applied loads and the structural parameters are then fitted to appropriate probabilistic distribution functions. Numerical integration techniques are applied to compute the structural reliability. The predicted reliability accounts for scatter due to variability in material strength, applied load, fabrication and assembly processes. The influence of structural geometry and mode of failure are also considerations in the evaluation. Example problems are given to illustrate various levels of analytical complexity.
Relaxed static stability and stability augmentation with active controls were investigated for subsonic transport aircraft. Analytical and simulator evaluations were done using a contemporary wide body transport as a baseline. Criteria for augmentation system performance and unaugmented flying qualities were evaluated. Augmentation control laws were defined based on selected frequency response and time history criteria. Flying qualities evaluations were conducted by pilots using a moving base simulator with a transport cab. Static margin and air turbulence intensity were varied in test with and without augmentation. Suitability of a simple pitch control law was verified at neutral static margin in cruise and landing flight tasks. Neutral stability was found to be marginally acceptable in heavy turbulence in both cruise and landing conditions.
The use of NASTRAN at Bell Helicopter Company for structural static and dynamic analysis of a helicopter airframe is described. Analysis of airframe internal loads, main rotor isolation systems, and airframe vibration is discussed. The use of each rigid format for these types of analysis is summarized. Suggested improvements to NASTRAN to increase its effectiveness in performing helicopter airframe analysis are given.