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Results for “Nonlinear Analysis”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
NASA NTRS1981

A family of solution algorithms for nonlinear structural analysis based on relaxation equations

A family of hierarchical algorithms for nonlinear structural equations are presented. The algorithms are based on the Davidenko-Branin type homotopy and shown to yield consistent hierarchical perturbation equations. The algorithms appear to be particularly suitable to problems involving bifurcation and limit point calculations. An important by-product of the algorithms is that it provides a systematic and economical means for computing the stepsize at each iteration stage when a Newton-like method is employed to solve the systems of equations. Some sample problems are provided to illustrate the characteristics of the algorithms.

Park, K. C.↗
DOE OSTI2022

Nonlinear spectral analysis of ion acoustic solitons arising from a streaming charged object using the numerical inverse scattering transform

Observations of nonlinear coherent plasma phenomena in spacecraft and terrestrial experiments often rely on visual identification of solitary modes because nonlinear coherent modes are broadband in a Fourier transform based analysis. We implement an alternative spectral decomposition known as the inverse scattering transform and demonstrate its ability to successfully isolate nonlinear modes on the homogeneous and forced Korteweg–De Vries equation which models these nonlinear modes. We also demonstrate for the first time that this decomposition is useful when forcing is applied. This is because the stable modes generated by localized forcing are similar to the homogeneous solutions where the inverse scattering transform is a rigorous decomposition. This spectral technique is then applied to simulations of ion acoustic waves generated by a 10 mm spherical debris object interacting with the ionospheric plasma orbiting at 2000 km altitude. The algorithm is found to successfully detect the resultant solitons. This demonstrates the feasibility of using this spectral technique as a real time analysis tool for screening spacecraft data for nonlinear solitary modes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1976

A method for the analysis of nonlinearities in aircraft dynamic response to atmospheric turbulence

An analytical method is developed which combines the equivalent linearization technique for the analysis of the response of nonlinear dynamic systems with the amplitude modulated random process (Press model) for atmospheric turbulence. The method is initially applied to a bilinear spring system. The analysis of the response shows good agreement with exact results obtained by the Fokker-Planck equation. The method is then applied to an example of control-surface displacement limiting in an aircraft with a pitch-hold autopilot.

Sidwell, K.↗
NASA NTRS1975

Estimation and Analysis of Nonlinear Stochastic Systems

The algebraic and geometric structures of certain classes of nonlinear stochastic systems were exploited in order to obtain useful stability and estimation results. The class of bilinear stochastic systems (or linear systems with multiplicative noise) was discussed. The stochastic stability of bilinear systems driven by colored noise was considered. Approximate methods for obtaining sufficient conditions for the stochastic stability of bilinear systems evolving on general Lie groups were discussed. Two classes of estimation problems involving bilinear systems were considered. It was proved that, for systems described by certain types of Volterra series expansions or by certain bilinear equations evolving on nilpotent or solvable Lie groups, the optimal conditional mean estimator consists of a finite dimensional nonlinear set of equations. The theory of harmonic analysis was used to derive suboptimal estimators for bilinear systems driven by white noise which evolve on compact Lie groups or homogeneous spaces.

Marcus, S. I.↗
NASA NTRS1980

Research in nonlinear structural and solid mechanics

Nonlinear analysis of building structures and numerical solution of nonlinear algebraic equations and Newton's method are discussed. Other topics include: nonlinear interaction problems; solution procedures for nonlinear problems; crash dynamics and advanced nonlinear applications; material characterization, contact problems, and inelastic response; and formulation aspects and special software for nonlinear analysis.

Mccomb, H. G., Jr.↗
DOE OSTI2015

Design and simulation of a gyroklystron amplifier

In the present paper, a design methodology of the gyroklystron amplifier has been described and subsequently used for the design of a typically selected 200 kW, Ka-band, four-cavity gyroklystron amplifier. This conceptual device design has been validated through the 3D particle-in-cell (PIC) simulation and nonlinear analysis. Commercially available PIC simulation code “MAGIC” has been used for the electromagnetic study at the different location of the device RF interaction structure for the beam-absent case, i.e., eigenmode study as well as for the electron beam and RF wave interaction behaviour study in the beam present case of the gyroklystron. In addition, a practical problem of misalignment of the RF cavities with drift tubes within the tube has been also investigated and its effect on device performance studied. The analytical and simulation results confirmed the validity of the gyroklystron device design. The PIC simulation results of the present gyroklystron produced a stable RF output power of ∼218 kW for 0% velocity spread at 35 GHz, with ∼45 dB gain, 37% efficiency, and a bandwidth of 0.3% for a 70 kV, 8.2 A gyrating electron beam. The simulated values of RF output power have been found in agreement with the nonlinear analysis results within ∼5%. Further, the PIC simulation has been extended to study a practical problem of misalignment of the cavities axis and drift tube axis of the gyroklystron amplifier and found that the RF output power is more sensitive to misalignments in comparison to the device bandwidth. The present paper, gyroklystron device design, nonlinear analysis, and 3D PIC simulation using commercially available code had been systematically described would be of use to the high-power gyro-amplifier tube designers and research scientists.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1977

Development of a moderately sized finite element program for nonlinear structural analysis

AGGIE 1 is a computer program for predicting the linear and nonlinear, static and dynamic structural response of two- and three-dimensional continuum solids. The program is based on isoparametric finite elements and allows for 2-D plane stress, plane strain, and axisymmetric analyses and general 3-D analyses. Large strain kinematics is based on the total Lagrangian formulation. Materially nonlinear models include several elastic-plastic work-hardening models as well as an incompressible Mooney-Rivlin model. Included in this report is a brief description of the theoretical bases of the program, the material models used, the element library and the overall program organization. Instructions for data input preparation are given in detail. Several sample problems are given along with the required program input and program generated solutions.

Haisler, W. E.↗
NASA NTRS1987

Concurrent algorithms for transient nonlinear FE analysis

A two-parameter class of time-stepping algorithms for nonlinear structural dynamics is investigated. What sets the present method apart from other concurrent algorithms is the fact that it can be used to some advantage in sequential machines as well. Thus, substantial speed-ups are obtained on a single processor as the number of subdomains is increased. An additional O(p) speed-up is obtained when p processors are utilized. The test case discussed is being repeated for a mesh comprising four times as many elements, in an effort to understand how the large scale asymptotic speed-ups are attained. A three dimensional example involving finite deformations and free body motions is also being pursued. A code optimized for concurrency in the Alliant FX8 computer is being finalized. This will provide the means for testing the performance of the algorithm in a multiprocessor environment.

Ortiz, M.↗
NASA NTRS1990

Low velocity impact analysis with NASTRAN

A nonlinear elastic force-displacement relationship is used to calculate the transient impact force and local deformation at the point of contact between impactor and target. The nonlinear analysis and transfer function capabilities of NASTRAN are used to define a finite element model that behaves globally linearly elastic, and locally nonlinear elastic to model the local contact behavior. Results are presented for two different structures: a uniform cylindrical rod impacted longitudinally; and an orthotropic plate impacted transversely. Calculated impact force and transient structural response of the targets are shown to compare well with results measured in experimental tests.

Trowbridge, Daniel A.↗
NASA NTRS1990

Low velocity impact analysis with NASTRAN

A nonlinear elastic force-displacement relationship is used to calculate the transient impact force and local deformation at the point of contact between impactor and target. The nonlinear analysis and transfer function capabilities of NASTRAN are used to define a finite element model that behaves globally linearly elastic, and locally nonlinear elastic to model the local contact behavior. Results are presented for two different structures: a uniform cylindrical rod impacted longitudinally; and an orthotropic plate impacted transversely. Calculated impact force and transient structural response of the targets are shown to compare well with results measured in experimental tests.

Trowbridge, Daniel A.↗
NASA NTRS1991

Low velocity impact analysis with NASTRAN

A nonlinear elastic force-displacement relationship is used to calculate the transient impact force and local deformation at the point of contact between impactor and target. The nonlinear analysis and transfer function capabilities of NASTRAN are used to define a finite element model that behaves globally linearly elastic, and locally nonlinear elastic to model the local contact behavior. Results are presented for two different structures: a uniform cylindrical rod impacted longitudinally; and an orthotropic plate impacted transversely. Calculated impact force and transient structural response of the targets are shown to compare well with results measured in experimental tests.

Trowbridge, D. A.↗
NASA NTRS1991

Linear and nonlinear dynamic analysis by boundary element method

An advanced implementation of the direct boundary element method (BEM) applicable to free-vibration, periodic (steady-state) vibration and linear and nonlinear transient dynamic problems involving two and three-dimensional isotropic solids of arbitrary shape is presented. Interior, exterior, and half-space problems can all be solved by the present formulation. For the free-vibration analysis, a new real variable BEM formulation is presented which solves the free-vibration problem in the form of algebraic equations (formed from the static kernels) and needs only surface discretization. In the area of time-domain transient analysis, the BEM is well suited because it gives an implicit formulation. Although the integral formulations are elegant, because of the complexity of the formulation it has never been implemented in exact form. In the present work, linear and nonlinear time domain transient analysis for three-dimensional solids has been implemented in a general and complete manner. The formulation and implementation of the nonlinear, transient, dynamic analysis presented here is the first ever in the field of boundary element analysis. Almost all the existing formulation of BEM in dynamics use the constant variation of the variables in space and time which is very unrealistic for engineering problems and, in some cases, it leads to unacceptably inaccurate results. In the present work, linear and quadratic isoparametric boundary elements are used for discretization of geometry and functional variations in space. In addition, higher order variations in time are used. These methods of analysis are applicable to piecewise-homogeneous materials, such that not only problems of the layered media and the soil-structure interaction can be analyzed but also a large problem can be solved by the usual sub-structuring technique. The analyses have been incorporated in a versatile, general-purpose computer program. Some numerical problems are solved and, through comparisons with available analytical and numerical results, the stability and high accuracy of these dynamic analysis techniques are established.

Ahmad, Shahid↗
NASA NTRS1987

Exploiting symmetries in the modeling and analysis of tires

A simple and efficient computational strategy for reducing both the size of a tire model and the cost of the analysis of tires in the presence of symmetry-breaking conditions (unsymmetry in the tire material, geometry, or loading) is presented. The strategy is based on approximating the unsymmetric response of the tire with a linear combination of symmetric and antisymmetric global approximation vectors (or modes). Details are presented for the three main elements of the computational strategy, which include: use of special three-field mixed finite-element models, use of operator splitting, and substantial reduction in the number of degrees of freedom. The proposed computational stategy is applied to three quasi-symmetric problems of tires: linear analysis of anisotropic tires, through use of semianalytic finite elements, nonlinear analysis of anisotropic tires through use of two-dimensional shell finite elements, and nonlinear analysis of orthotropic tires subjected to unsymmetric loading. Three basic types of symmetry (and their combinations) exhibited by the tire response are identified.

Noor, Ahmed K.↗
NASA NTRS1983

A quasi-Newton versus a homotopy method for nonlinear structural analysis

The globally convergent quasi-Newton minimization algorithm and the homotopy algorithms are discussed in detail and their effectiveness in solving certain classes of highly nonlinear problems of structural analysis is demonstrated. The application of the double dogleg strategy controls the directions and step-lengths of the quasi-Newtonian algorithm and overcomes the problem of nonpositive definite Hessians being produced during the iteration process. The algorithms are applied to a centrally loaded clamped beam, the snap-through of a shallow arch, and a shallow reticulated dome.

Kamat, M. P.↗
DOE OSTI2014

Parameter sensitivity analysis of nonlinear piezoelectric probe in tapping mode atomic force microscopy for measurement improvement

The equations of motion for a piezoelectric microcantilever are derived for a nonlinear contact force. The analytical expressions for natural frequencies and mode shapes are obtained. Then, the method of multiple scales is used to analyze the analytical frequency response of the piezoelectric probe. The effects of nonlinear excitation force on the microcantilever beam's frequency and amplitude are analytically studied. The results show a frequency shift in the response resulting from the force nonlinearities. This frequency shift during contact mode is an important consideration in the modeling of AFM mechanics for generation of more accurate imaging. Also, a sensitivity analysis of the system parameters on the nonlinearity effect is performed. The results of a sensitivity analysis show that it is possible to choose parameters such that the frequency shift minimizes. Certain parameters such as tip radius, microcantilever beam dimensions, and modulus of elasticity have more influence on the nonlinearity of the system than other parameters. By changing only three parameters—tip radius, thickness, and modulus of elasticity of the microbeam—a more than 70% reduction in nonlinearity effect was achieved.

36 MATERIALS SCIENCE↗
NASA NTRSDate not supplied

Nonlinear Buckling Analysis of Tow-Steered Composite Cylinders with Cutouts

The buckling and postbuckling behavior of two composite tow-steered shells with cutouts of different sizes is assessed using nonlinear finite element (FE) analysis and compared to experimental measurements. The cylindrical shells are manufactured using an automated fiber placement system, where the shells’ fiber orientation angles vary continuously around the shell circumference from ±10 degrees on the crown and keel to ±45 degrees on the sides. One shell features thickness variations due to tow overlaps that result from application of all 24 tows during each pass of the fiber placement system. The second shell uses the system’s tow drop/add capability to achieve a more uniform wall thickness without overlaps. Unreinforced cutouts of two different sizes—the first smaller cutout representing a passenger door on a commercial aircraft and the second larger cutout a cargo door—were machined into each of the two cylinders resulting in a total of four test cases. These cylinders were tested in axial compression and buckled elastically in previous work and are now analyzed using nonlinear FE models to compare bifurcation buckling loads as well as the load-displacement response in the prebuckling and postbuckling regimes. For all four shells analyzed, the prebuckling stiffness, buckling load, and deformation mode sequence throughout the loading-unloading cycle is accurately reproduced by the models. In particular, the shells first buckle locally around the cutouts in a stable (super-critical) manner with only a slight decrease in axial stiffness, which occurs due to the favorable load redistribution facilitated by tow steering. The shells then buckle globally in an unstable (sub-critical) manner with diamond-shaped buckles forming to the left and right of the cutouts. The buckling load of all shells with cutouts is at least 82% of the buckling load of the pristine shells without cutouts. Overall, the ability to sustain local buckling phenomena, and the relatively small reductions in global buckling load compared to pristine shells without cutouts, demonstrates the great potential of using tow steering to mitigate the adverse effects of cutouts in axially-compressed shell structures.

composites↗
NASA NTRSDate not supplied

Nonlinear Buckling Analysis of Tow-Steered Composite Cylinders with Cutouts

The buckling and postbuckling behavior of two composite tow-steered shells with cutouts of different sizes is assessed using nonlinear finite element (FE) analysis and compared to experimental measurements. The cylindrical shells are manufactured using an automated fiber placement system, where the shells’ fiber orientation angles vary continuously around the shell circumference from 10 degrees on the crown and keel to 45 degrees on the sides. One shell features thickness variations due to tow overlaps that result from application of all 24 tows during each pass of the fiber placement system. The second shell uses the system’s tow drop/add capability to achieve a more uniform wall thickness without overlaps. Unreinforced cutouts of two different sizes—the first smaller cutout representing a passenger door on a commercial aircraft and the second larger cutout a cargo door—were machined into each of the two cylinders resulting in a total of four test cases. These cylinders were tested in axial compression and buckled elastically in previous work and are now analyzed using nonlinear FE models to compare bifurcation buckling loads as well as the load-displacement response in the prebuckling and postbuckling regimes. For all four shells analyzed, the prebuckling stiffness, buckling load, and deformation mode sequence throughout the loading-unloading cycle is accurately reproduced by the models. In particular, the shells first buckle locally around the cutouts in a stable (super-critical) manner with only a slight decrease in axial stiffness, which occurs due to the favorable load redistribution facilitated by tow steering. The shells then buckle globally in an unstable (sub-critical) manner with diamond-shaped buckles forming to the left and right of the cutouts. The buckling load of all shells with cutouts is at least 82% of the buckling load of the pristine shells without cutouts. Overall, the ability to sustain local buckling phenomena, and the relatively small reductions in global buckling load compared to pristine shells without cutouts, demonstrates the great potential of using tow steering to mitigate the adverse effects of cutouts in axially-compressed shell structures.

Buckling↗