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NASA NTRS1985

Nonlinear response and failure characteristics of internally pressurized composite cylindrical panels

Results of an experimental and analytical study of the nonlinear response and failure characteristics of internally pressurized 4- to 16-ply-thick graphite-epoxy cylindrical panels are presented. Specimens with clamped boundaries simulating the skin between two frames and two stringers of a typical transport fuselage were tested to failure. Failure results of aluminum specimens are compared with the graphite-epoxy test results. The specimens failed at their edges where the local bending gradients and interlaminar stresses are maximum. STAGS nonlinear two-dimensional shell analysis computer code results are used to identify regions of the panels where the response is independent of the axial coordinate. A geometrically nonlinear one-dimensional cylindrical panel analysis was derived and used to determine panel response and interlaminar stresses. Inclusion of the geometric nonlinearity was essential for accurate prediction of panel response. The maximum stress failure criterion applied to the predicted tensile stress in the fiber direction agreed best with the experimentally determined first damage pressures.

Boitnott, R. L.↗

NASA NTRS2001

The Nonlinear Response of Cracked Aluminum Shells Subjected to Combined Loads

The results of a numerical study of the nonlinear response of thin unstiffened aluminum cylindrical shells with a longitudinal crack are presented. The shells are analyzed with a nonlinear shelf analysis code that accurately accounts for global and structural response phenomena. The effects of initial crack length on the prebuckling, buckling and postbuckling responses of a typical shell subjected to axial compression loads, and subjected to combined internal pressure and axial compression loads are described. Both elastic and elastic-plastic analyses are conducted. Numerical results for a fixed initial crack length indicate that the buckling load decreases as the crack length increases for a given pressure load, and that the buckling load increases as the internal pressure load increases for a given crack length. Furthermore, results indicate that predictions from an elastic analysis for the initial buckling load of a cracked shell subjected to combined axial compression and internal pressure loads can be unconservative. In addition, the effect of crack extension on the initial buckling load is presented.

Rose, Cheryl A.↗

NASA NTRS1996

Effects of Combined Loads on the Nonlinear Response and Residual Strength of Damaged Stiffened Shells

Starnes, James H., Jr.↗

NASA NTRS1996

Nonlinear Response and Residual Strength of Damaged Stiffened Shells Subjected to Combined Loads

The results of an analytical study of the nonlinear response of stiffened fuselage shells with long cracks are presented. The shells are modeled with a hierarchical modeling strategy and analyzed with a nonlinear shell analysis code that maintains the shell in a nonlinear equilibrium state while the crack is grown. The analysis accurately accounts for global and local structural response phenomena. Fuselage skins, frames stringers and failsafe straps are included in the models. Results are presented for various combinations of internal pressure and mechanical bending, vertical shear and torsion loads, and the effects of crack orientation and location on the shell response are described. These results indicate that the nonlinear interaction between the in-plane stress resultants and the out-of-plane displacements near a crack can significantly affect the structural response of the shell, and the stress-intensity factors associated with a crack that are used to predict residual strength. The effects of representative combined loading conditions on the stress-intensity factors associated with a crack are presented. The effects of varying structural parameters on the stress-intensity factors associated with a crack, and on self-similar and non-self-similar crack-growth are also presented.

Starnes, James H., Jr.↗

DOE OSTI2023

Quantum interferometry and pathway selectivity in the nonlinear response of photosynthetic excitons

We propose a time–frequency resolved spectroscopic technique which employs nonlinear interferometers to study exciton–exciton scattering in molecular aggregates. A higher degree of control over the contributing Liouville pathways is obtained as compared to classical light. We show how the nonlinear response can be isolated from the orders-of-magnitude stronger linear background by either phase matching or polarization filtering. Both arise due to averaging the signal over a large number of noninteracting, randomly oriented molecules. We apply our technique to the Frenkel exciton model which excludes charge separation for the photosystem II reaction center. We show how the sum of the entangled photon frequencies can be used to select two-exciton resonances, while their delay times reveal the single-exciton levels involved in the optical process.

Science & Technology - Other Topics↗

NASA NTRS1984

Nonlinear response and failure characteristics of clamped internally pressurized graphite-epoxy cylindrical panels

The nonlinear response and failure characteristics of internally pressurized 4- to 16-ply cylindrical panels of graphite/epoxy are experimentally and analytically studied. Tests simulated the skin of a typical transport aircraft fuselage under loading to eventual failure. Aluminum test specimens were similarly tested and compared. All graphite/epoxy panels are found to withstand the internal pressures applied, which are well above the proof pressure loading expected for transport fuselage structures.

Boitnott, R. L.↗

NASA NTRS1992

Thermally-induced, geometrically nonlinear response of symmetrically laminated composite plates

This paper discusses the thermally-induced geometrically nonlinear response of symmetrically laminated composite plates. The plate response is due to a temperature increase that is uniform in the plane of the plate but has a slight gradient through the thickness. The case of a completely uniform temperature increase but with an initial out-of-plane imperfection in the plate is also considered. Because they are closely allied problems, thermal buckling and postbuckling are discussed. Using variational methods in conjunction with a Rayleigh-Ritz formulation, these responses are investigated for two laminates, a (+/- 45/0/90)s and a (+/- 45/02)s, under two different simple support conditions.

Meyers, C. A.↗

NASA NTRS1995

Subpiosecond Third Order Nonlinear Response in Polythiophene and Thiopene Based Thin Films

Ultrafast relaxation kinetics of the third order nonlinear susceptibility of polythiophene and polycondensed thiophene-based polymer was determined by the forward degenerate four-wave mixing technique. Deep into the absorption band the nonlinear response shows only a fast component (less than 900 fs at 587 nm) while at the edge of the absorption band at 642 nm a much slower and complex decay was measured.

Harris, D.↗

NASA NTRS1984

An elastic potential for the nonlinear response of unidirectional graphite composites

An elastic potential is proposed that is capable of modeling the reversible portion of the observed nonlinear response of unidirectional graphite fiber composites. The model includes both the stiffening stress-strain behavior as well as the softening Poisson's response for loading in the fiber direction. The model is compared with experimental results for Celion 6000/PMR-15 graphite-polyimide.

Pindera, M.-J.↗

NASA NTRS1989

Vortex creep and the internal temperature of neutron stars - Linear and nonlinear response to a glitch

The dynamics of pinned superfluid in neutron stars is determined by the thermal 'creep' of vortices. Vortex creep can respond to changes in the rotation rate of the neutron star crust and provide the observed types of dynamical relaxation following pulsar glitches. It also gives rise to energy dissipation, which determines the thermal evolution of pulsars once the initial heat content has been radiated away. The different possible regimes of vortex creep are explored, and it is shown that the nature of the dynamical response of the pinned superfluid evolves with a pulsar's age. Younger pulsars display a linear regime, where the response is linear in the initial perturbation and is a simple exponential relaxation as a function of time. A nonliner response, with a characteristic nonlinear dependence on the initial perturbation, is responsible for energy dissipation and becomes the predominant mode of response as the pulsar ages. The transition from the linear to the nonlinear regime depends sensitively on the temperature of the neutron star interior. A preliminary review of existing postglitch observations is given within this general evolutionary framework.

Alpar, M. A.↗

NASA NTRS1990

The nonlinear response of AE to the IMF Bs driver - A spectral break at 5 hours

The existence of a sharp break in the power spectrum of AE at about 5 hours is demonstrated. Several possible explanations of the nonlinear response of AE to the IMF Bs driver are briefly discussed, including: variable ionospheric conductivity (increasing with Bs) for the high frequency regime, and several AE saturation mechanisms for the low frequency regime.

Tsurutani, Bruce T.↗

NASA NTRS1989

Nonlinear response of composite tubes under combined thermomechanical loading

An analytical investigation was conducted to study the effect of material nonlinearities on the response of graphite/epoxy composite tubes subjected to combined axial and torsional loading. The endochronic theory of Valanis (1971) was employed to model the nonlinear response of the individual graphite/epoxy layers. Thermal loading was included in the analysis in order to incorporate the effect of residual stresses on subsequent mechanical response. The predictions of the analytical model are compared with the response of P75/934 graphite/epoxy tubes with a stacking sequence of (15/0/+/- 10/0/-15)s. Good qualitative correlation between analysis and experiment is obtained when microstructural details of the tube's cross-section, residual stresses and nonlinear effects are taken into account.

Derstine, M. S.↗

NASA NTRS2007

POD/MAC-Based Modal Basis Selection for a Reduced Order Nonlinear Response Analysis

A feasibility study was conducted to explore the applicability of a POD/MAC basis selection technique to a nonlinear structural response analysis. For the case studied the application of the POD/MAC technique resulted in a substantial improvement of the reduced order simulation when compared to a classic approach utilizing only low frequency modes present in the excitation bandwidth. Further studies are aimed to expand application of the presented technique to more complex structures including non-planar and two-dimensional configurations. For non-planar structures the separation of different displacement components may not be necessary or desirable.

Rizzi, Stephen A.↗

DOE OSTI2023

Superposition principle and nonlinear response in spin glasses

The extended principle of superposition has been a touchstone of spin-glass dynamics for almost 30 years. Here the Uppsala group has demonstrated its validity for the metallic spin glass, CuMn, for magnetic fields H up to 10 Oe at the reduced temperature T r = T/T g = 0.95, where T g is the spin-glass condensation temperature. For H > 10 Oe, they observe a departure from linear response which they ascribe to the development of nonlinear dynamics. The thrust of this paper is to develop a microscopic origin for this behavior by focusing on the time development of the spin-glass correlation length, ξ(t, t w ; H). Here, t is the time after H changes, and t w is the time from the quench for T > T g to the working temperature T until H changes. We connect the growth of ξ(t, t w ; H) to the barrier heights Δ(t w ) that set the dynamics. The effect of H on the magnitude of Δ (t w ) is responsible for affecting differently the two dynamical protocols associated with turning H off (TRM, or thermoremanent magnetization) or on (ZFC, or zero-field-cooled magnetization). This difference is a consequence of nonlinearity based on the effect of H on Δ (t w ). Superposition is preserved if Δ(t w ) is linear in the Hamming distance Hd (proportional to the difference between the self-overlap q EA and the overlap q[Δ(t w )]). However, superposition is violated if Δ(t w ) increases faster than linear in Hd. We have previously shown, through experiment and simulation, that the barriers Δ(t w ) do increase more rapidly than linearly with Hd through the observation that the growth of ξ(t,t w ;H) slows down as ξ(t,t w ; H) increases. In this paper, we display the difference between the zero-field-cooled ξ ZFC (t, t w ; H) and the thermoremanent magnetization ξ TRM (t, t w ; H) correlation lengths as H increases, both experimentally and through numerical simulations, corresponding to the violation of the extended principle of superposition in line with the finding of the Uppsala Group.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2026

Multiresolution Quantum Chemistry: Nonlinear Response Properties at the Basis Set Limit

We benchmark the accuracy of Dunning correlation-consistent Gaussian basis sets for computing frequencydependent second-order hyperpolarizabilities relevant to second-harmonic generation (SHG), using multiresolution analysis (MRA) as a reference. Basis set errors are analyzed using a unit-sphere representation of the effective hyperpolarizability vector, enabling direct assessment of directional error structure. We introduce a relative RMS total error metric that integrates directional deviations over the unit sphere and complement it with signed projection errors that distinguish over- and underestimation. Unsupervised clustering based on these signed directional metrics reveals four distinct convergence behaviors across a set of 68 molecules. Unitsphere visualizations of representative systems show that basis set errors are often highly anisotropic and localized along specific bond directions, even when global error measures appear small. Doubly augmented basis sets consistently outperform singly augmented ones, and core-polarization functions are required for uniform convergence in second-row systems. Overall, this work demonstrates that directional analysis combined with clustering provides a robust framework for understanding basis set convergence in nonlinear optical response properties.

Basis sets↗

NASA NTRS1965

Nonlinear response of an oscillating discharge to very high frequency signals Technical report no. 3, Jun. 1963 - Aug. 1965

Governing equation nonlinearities for oscillating plasma discharge response to very high frequency signals

PLASMA OSCILLATION↗

NASA NTRS1993

Nonlinear response of graphite-epoxy wide columns subject to eccentric load

It is shown that including the effects of bend-twist coupling and material nonlinearity on the large displacement flexural response of graphite-epoxy wide columns is necessary to adequately model their response. Results from static tests on 0(30)T and (30/0/-30 sub 5)s laminated specimens under eccentric axial compression are compared to a nonlinear analysis. The analysis is based on a Kantrovich expansion of the displacements in the width coordinate and a finite element representation in the axial coordinate. An incremental, updated Lagrangian formulation and element corotational coordinates are employed. Nonlinear elastic material behavior was measured in a separate set of material characterization tests, and these data are used to compute tangent stillnesses in the updated configuration.

Griffin, O. H., Jr.↗

NASA NTRS2012

Elastic-Plastic Nonlinear Response of a Space Shuttle External Tank Stringer: Thermal and Mechanical Loadings - Part 2

Elastic-plastic, large-deflection nonlinear thermo-mechanical stress analyses are performed for the Space Shuttle external tank s intertank stringers. Detailed threedimensional finite element models are developed and used to investigate the stringer s elastic-plastic response for different thermal and mechanical loading events from assembly through flight. Assembly strains caused by initial installation on an intertank panel are accounted for in the analyses. Thermal loading due to tanking was determined to be the bounding loading event. The cryogenic shrinkage caused by tanking resulted in a rotation of the intertank chord flange towards the center of the intertank, which in turn loaded the intertank stringer feet. The analyses suggest that the strain levels near the first three fasteners remain sufficiently high that a failure may occur. The analyses also confirmed that the installation of radius blocks on the stringer feet ends results in an increase in the stringer capability.

Knight, Norman F., Jr.↗