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A large deflection analysis was developed for NASTRAN level 16 as an alternative to Rigid Format 4. A progress report is presented for a long term, general nonlinear analysis NASTRAN project, which contains (1) the theory of the structural analysis and numerical analysis methods presently used, and (2) some simple test problems comparing the new analysis with Rigid Format 4.
A variable-gain, optimal, discrete, output feedback design approach that is applied to a nonlinear flight regime is described. The flight regime covers a wide angle-of-attack range that includes stall and post stall. The paper includes brief descriptions of the variable-gain formulation, the discrete-control structure and flight equations used to apply the design approach, and the high performance airplane model used in the application. Both linear and nonlinear analysis are shown for a longitudinal four-model design case with angles of attack of 5, 15, 35, and 60 deg. Linear and nonlinear simulations are compared for a single-point longitudinal design at 60 deg angle of attack. Nonlinear simulations for the four-model, multi-mode, variable-gain design include a longitudinal pitch-up and pitch-down maneuver and high angle-of-attack regulation during a lateral maneuver.
A procedure is presented for performing three-dimensional stress analysis of spiral bevel gears in mesh using the finite element method. The procedure involves generating a finite element model by solving equations that identify tooth surface coordinates. Coordinate transformations are used to orientate the gear and pinion for gear meshing. Contact boundary conditions are simulated with gap elements. A solution technique for correct orientation of the gap elements is given. Example models and results are presented.
A procedure is presented for performing three-dimensional stress analysis of spiral bevel gears in mesh using the finite element method. The procedure involves generating a finite element model by solving equations that identify tooth surface coordinates. Coordinate transformations are used to orientate the gear and pinion for gear meshing. Contact boundary conditions are simulated with gap elements. A solution technique for correct orientation of the gap elements is given. Example models and results are presented.
The National Aeronautics and Space Administration (NASA) Langley Research Center (LaRC) has been designing strain-gage balances for utilization in wind tunnels since its inception. The utilization of balances span over a wide variety of aerodynamic tests. A force balance is an inherently critically stressed component due to the requirements of measurement sensitivity. Research and analyses are done in order to investigate the structural integrity of the balances as well as developing an understanding of their performance in order to enhance their capability. Maximum loading occurs when all 6 components of the loads are applied simultaneously with their maximum value allowed (limit load). This circumstance normally does not occur in the wind tunnel. However, if it occurs, is the balance capable of handling the loads with an acceptable factor of safety? LaRC Balance 1621 was modeled and meshed in PATRAN for analysis in NASTRAN. For a complete analysis, it is necessary to consider all the load cases as well as use dense mesh near all the edges. Because of computer limitations, it is not possible to have one model with the dense mesh near all edges. In the present study, a dense mesh is limited to the surface corners where the cage and axial sections meet. Four different load combinations are used for the current analysis. Linear analysis is performed for each load case. In the case where the stress value is above linear elastic region, it is necessary to perform nonlinear analysis. It is also important to investigate the variables limiting the structural integrity of the balances. In order to investigate the possibility of modifying the existing balances to enhance the structural integrity, some modifications are done on this balance. The structural integrity of the balance after modification is investigated.
Advanced aircraft configurations that have been developed to increase fuel efficiency require advanced, novel structural concepts capable of handling the unique load conditions that arise. One such concept is the Pultruded Rod Stitched Efficient Unitized Structure (PRSEUS) developed by the Boeing Company. The PRSEUS concept is being investigated by NASA s Environmentally Responsible Aviation (ERA) Program for use in a hybrid-wing body (HWB) aircraft. This paper summarizes the analysis and test of a PRSEUS panel subjected to internal pressure, the first such pressure test for this structural concept. The pressure panel used minimum gauge skin, with stringer and frame configurations consistent with previous PRSEUS tests. Analysis indicated that for the minimum gauge skin panel, the stringer locations exhibit fairly linear response, but the skin bays between the stringers exhibit nonlinear response. Excellent agreement was seen between nonlinear analysis and test results in the critical portion at the center of the panel. The pristine panel was capable of withstanding the required 18.4 psi pressure load condition without exhibiting any damage. The impacted panel was capable of withstanding a pressure load in excess of 28 psi before initial failure occurred at the center stringer, and the panel was capable of sustaining increased pressure load after the initial failure. This successful PRSEUS panel pressure panel test was a critical step in the building block approach for enabling the use of this advanced structural concept on future aircraft, such as the HWB.
The present paper provides an overview of the state-of-the-art in the application of neural networks in problems of structural analysis and design, including a survey of published applications in structural engineering. Such applications have included, among others, the use of neural networks in modeling nonlinear analysis of structures, as a rapid reanalysis capability in optimal design, and in developing problem parameter sensitivity of optimal solutions for use in multilevel decomposition based design. While most of the applications reported in the literature have been restricted to the use of the multilayer perceptron architecture and minor variations thereof, other network architectures have also been successfully explored, including the ART network, the counterpropagation network and the Hopfield-Tank model.
A combination of classical plate theory and a supersonic aerodynamic model is used to study the aeroelastic flutter behavior of a proposed thermal protection system (TPS) for the NASA HIAD. The analysis pertains to the rectangular configurations currently being tested in a NASA wind-tunnel facility, and may explain why oscillations of the articles could be observed. An analysis using a linear flat plate model indicated that flutter was possible well within the supersonic flow regime of the wind tunnel tests. A more complex nonlinear analysis of the TPS, taking into account any material curvature present due to the restraint system or substructure, indicated that significantly greater aerodynamic forcing is required for the onset of flutter. Chaotic and periodic limit cycle oscillations (LCOs) of the TPS are possible depending on how the curvature is imposed. When the pressure from the base substructure on the bottom of the TPS is used as the source of curvature, the flutter boundary increases rapidly and chaotic behavior is eliminated.
Book on nonlinear systems analysis and design covering parameter mapping, symmetrical, transient and forced oscillations and stability analysis
A survey of the use of a combination of symbolic and numerical calculations is presented. Symbolic calculations primarily refer to the computer processing of procedures from classical algebra, analysis, and calculus. Numerical calculations refer to both numerical mathematics research and scientific computation. This survey is intended to point out a large number of problem areas where a cooperation of symbolic and numerical methods is likely to bear many fruits. These areas include such classical operations as differentiation and integration, such diverse activities as function approximations and qualitative analysis, and such contemporary topics as finite element calculations and computation complexity. It is contended that other less obvious topics such as the fast Fourier transform, linear algebra, nonlinear analysis and error analysis would also benefit from a synergistic approach.
The seismic load case has a significant impact on the design and cost of nuclear power plants. Given the need to substantially reduce cost, advanced reactor designers are looking to leverage numerical tools that enable seismic analysis of an integrated vessel/support/structure/soil system. Modern nonlinear analysis tools provide a solution, capturing dynamic coupling between components (including soil-structure interaction (SSI)) concurrent with nonlinear behavior in one or more parts of the system. Although these methods have a rich history of technical development and implementation, software quality assurance (SQA) following nuclear industry standards remains a significant burden for those wishing to adopt such methods for advanced reactor design and licensing. To reduce the SQA burden, this project will develop the guidance for SQA verification and validation (V&V) of coupled nonlinear SSI analysis tools, to include a test matrix of software features and test problems to support commercial grade dedication (CGD). The guidance is intended to be technology-neutral: supporting designers of all advanced reactors. To maximize the value of the project to reactor designers, the project team performed focused surveys of and interviews with advanced reactor designers. Additionally, the project surveyed members of the broader industry involved in reactor design and licensing. The aggregated industry feedback consists of written survey responses, live polling responses, focused interviews, and informal feedback provided after outreach presentations, collectively referred to as “survey results”. Herein, the survey results are reported, reviewed, and assessed to inform follow-on project activities. The survey results confirmed the familiarity of the industry with the coupled nonlinear SSI analysis. They also affirm the project need based upon the expressed intent to (1) incorporate nonlinear features and (2) pursue the coupled nonlinear SSI analysis to reduce seismic demands and construction costs. All reactor designers indicated their intent to incorporate two or more nonlinear features, and all reactor designer respondents opined that the coupled nonlinear SSI analysis would allow for the optimization of the reactor design and construction. However, the programmatic challenges, whether real or perceived, present a significant barrier to reactor designers. The barrier most commonly identified by the reactor designer population was regulatory risk, with 70% citing this as a reason not to pursue the approach. The perceived regulatory risk identified by the reactor designers underscores the importance of regulator engagement and dialogue in this project. Additionally, half of the reactor designers identified cost and lack of guidance as a deterrent. The survey results also provide insights to tailor specific aspects of the guidance document and test matrix. The project plans to prepare both a formal referenceable guidance document and a collaborative, web-based test matrix and problem set. The project will focus on more complete test problem definitions for the prioritized nonlinear features over shallower problem descriptions for a larger set of features. The nonlinearities prioritized as high based upon survey feedback include fluid-structure interaction and seismic isolation and energy dissipation devices. The nonlinearities prioritized as intermediate include nonlinear geomaterials, nonlinear concrete, nonlinear steel, and interface/contact nonlinearity. Deep embedment and the associated nonlinear phenomena are assigned the lowest priority based upon survey feedback.
Two computer programs developed according to two general types of exponential models for conducting nonlinear exponential regression analysis are described. Least squares procedure is used in which the nonlinear problem is linearized by expanding in a Taylor series. Program is written in FORTRAN 5 for the Univac 1108 computer.
Here, we conduct systematic studies of the optical characteristics of plasmonic nanoparticles that exhibit C 2v symmetry. In particular, we analyze three distinct geometric configurations: an L-type shape, a crescent, and a split-ring resonator shaped like the Greek letter π. Optical properties are examined using the finite-difference time-domain method. It is demonstrated that all three shapes exhibit two prominent plasmon modes associated with the two axes of symmetry. This is in addition to a wide range of resonances observed at high frequencies corresponding to quadrupole modes and peaks due to sharp corners. Next, to facilitate nonlinear analysis, we employ a semiclassical hydrodynamic model, where the electron pressure term is explicitly accounted for. This model goes beyond the standard Drude description and enables capturing nonlocal and nonlinear effects. Employing this model enables us to rigorously examine the second-order angular resolved nonlinear optical response of these nanoparticles in each of the three configurations. Two pumping regimes are considered, namely, continuous wave (CW) and pulsed excitations. For CW pumping, we explore the properties of the second harmonic generation (SHG). Polarization and angle-resolved SHG spectra are obtained, revealing strong dependence on the nanoparticle geometry and incident wave polarization. The C 2v symmetry is shown to play a key role in determining the polarization states and selection rules of the SHG signal. For pulsed excitations, we discuss the phenomenon of broadband terahertz (THz) generation induced by the difference-frequency generation . It is shown that the THz emission spectra exhibit unique features attributed to the plasmonic resonances and symmetry of the nanoparticles. The polarization of the generated THz waves is also examined, revealing interesting patterns tied to the nanoparticle geometry. To gain deeper insight, we propose an analytical theory that agrees very well with the numerical experiments. The theory shows that the physical origin of the THz radiation is the mixing of various frequency components of the fundamental pulse by the second-order nonlinear susceptibility. An expression for the far-field THz intensity is derived in terms of the incident pulse parameters and the nonlinear response tensor of the nanoparticle. The results presented in this work offer new insights into the linear and nonlinear optical properties of nanoparticles with C 2v symmetry. The demonstrated strong SHG response and efficient broadband THz generation hold great promise for applications in nonlinear spectroscopy, nanophotonics, and optoelectronics. The proposed theoretical framework also provides a valuable tool for understanding and predicting the nonlinear behavior of other related nanostructures.
A user-oriented computer program SISCAP (SIS Computer Analysis Program) for analyzing SIS mixers is described. The program allows arbitrary impedance terminations to be specified at all LO harmonics and sideband frequencies. It is therefore able to treat a much more general class of SIS mixers than the widely used three-frequency analysis, for which the harmonics are assumed to be short-circuited. An additional program, GETCHI, provides the necessary input data to program SISCAP. The SISCAP program performs a nonlinear analysis to determine the SIS junction voltage waveform produced by the local oscillator. The quantum theory of mixing is used in its most general form, treating the large signal properties of the mixer in the time domain. A small signal linear analysis is then used to find the conversion loss and port impedances. The noise analysis includes thermal noise from the termination resistances and shot noise from the periodic LO current. Quantum noise is not considered. Many aspects of the program have been adequately verified and found accurate.
A weakly nonlinear spatial instability of a two-dimensional planar viscous sheet for sinuous disturbances in a co-flowing inviscid gas stream is investigated theoretically, with an emphasis on the effect of the surrounding gas velocity. The solutions of the second-order interface disturbances are derived and the wave deformation has been computed. The results indicate that the second-order surface disturbance of the fundamental sinuous mode is varicose, which causes the thinning and the subsequent breakup of the liquid sheet. The nonlinear behaviors of the planar sheet are quite sensitive to variations in gas-to-liquid velocity ratio. The deviation of the velocity ratio from the value of unity leads to a larger growth rate, a larger second-order initial amplitude, and a shorter breakup length, and therefore enhances the instability. The growth rates predicted by the present nonlinear analysis according to the shortest breakup length are generally smaller than the linear predictions and can better conform to the experimental measures of Barreras et al. [“Linear instability analysis of the viscous longitudinal perturbation on an air-blasted liquid sheets,” Atomization Sprays 11, 139 (2001)]. Furthermore, the wave deformations of the most unstable disturbances are presented. The nonlinear instability of the planar sheet for a fixed velocity difference is performed. An equal increase of the gas and liquid velocity reduces the spatial growth rate and increases the breakup length, but generally has no influences on the second-order initial amplitude and the wavelength of the disturbance.
A program of analysis, design, and fabrication was conducted to develop welded metal bellows having a minimum change in effective diameter for cryogenic turbomachinery face seal applications. Linear analysis of the principle types of bellows provided identification of concepts capable of meeting basic operation requirements. For the 6-inch (.152 m) mean diameter, 1.5-inch free length bellows studied, nonlinear analysis showed that opposed and nested toroidal bellows plates stiffened by means of alternating stiffener rings were capable of maintaining constant effective diameter within 0.3% and 0.1% respectively under the operating conditions of interest. Changes in effective diameter were due principally to bellows axial deflection with pressure differential having a lesser influence. Fabrication problems associated with joining the thin bellows plates to the relatively heavy stiffener rings were encountered and precluded assembly and testing of a bellows core. Fabrication problems are summarized and recommended fabrication methods for future effort are presented.
The manufacturing of composites typically produces residual stresses that can significantly affect the final shape of the structure. The process of automated fiber placement (AFP) has become a prominent manufacturing technique in developing layups with tailored, variable stiffness morphology. The steered patterns of fiber tows with and without overlaps produce residual deformations that are distinctive from traditional layups. Digital image correlation was used to measure the AFP lamina coefficients of thermal expansion, which were incorporated into finite element analyses (FEA) to model the cooling phase of the cure cycle. The effects of nonlinear analysis and temperature-dependent lamina properties calculated using self-consistent field micromechanics, on the resulting residual deformation of shells, were also modeled. The predicted residual deformation was analyzed by considering out-of-roundness in cylindrical shells and compared to the experimental results. The shell FEA results were well-correlated with the overall deformed shape of the AFP cylinder with overlaps, while the shell FEA model of the AFP cylinder without overlaps did not show as good of qualitative match of the deformation pattern. Analytical correlation with measured results were insensitive to material softening at elevated temperatures, geometric nonlinearities, and variations in measured lamina thermal properties. To improve the accuracy of the residual deformation analysis, these results suggest that the thermo-chemical shrinkages preceding the cooldown should be considered, as well as possible variations in ply level microstructure due to the presence of the embedded fiber tow gaps and overlaps.
Rotational stability of turbopump components in the space shuttle main engine was studied via analysis of component and structural dynamic models. Subsynchronous vibration caused unacceptable migration of the rotor/housing unit with unequal load sharing of the synchronous bearings that resulted in the failure of the High Pressure Oxygen Turbopump. Linear analysis shows that a shrouded inducer eliminates the second critical speed and the stability problem, a stiffened rotor improves the rotordynamic characteristics of the turbopump, and installing damper boost/impeller seals reduces bearing loads. Nonlinear analysis shows that by increasing the "dead band' clearances, a marked reduction in peak bearing loads occurs.