Pseudo-nonlinear dynamic analysis of buckled pipes
NASA Astrophysics Data System (ADS)
Gültekin Sınır, B.
2013-02-01
In this study, the post-divergence behavior of fluid-conveying pipes supported at both ends is investigated using the nonlinear equations of motion. The governing equation exhibits a cubic nonlinearity arising from mid-plane stretching. Exact solutions for post-buckling configurations of pipes with fixed-fixed, fixed-hinged, and hinged-hinged boundary conditions are investigated. The pipe is stable at its original static equilibrium position until the flow velocity becomes high enough to cause a supercritical pitchfork bifurcation, and the pipe loses stability by static divergence. In the supercritical fluid velocity regime, the equilibrium configuration becomes unstable and bifurcates into multiple equilibrium positions. To investigate the vibrations that occur in the vicinity of a buckled equilibrium position, the pseudo-nonlinear vibration problem around the first buckled configuration is solved precisely using a new solution procedure. By solving the resulting eigenvalue problem, the natural frequencies and the associated mode shapes of the pipe are calculated. The dynamic stability of the post-buckling configurations obtained in this manner is investigated. The first buckled shape is a stable equilibrium position for all boundary conditions. The buckled configurations beyond the first buckling mode are unstable equilibrium positions. The natural frequencies of the lowest vibration modes around each of the first two buckled configurations are presented. Effects of the system parameters on pipe behavior as well as the possibility of a subcritical pitchfork bifurcation are also investigated. The results show that many internal resonances might be activated among the vibration modes around the same or different buckled configurations.
Nonlinear analysis of hydraulic buckling instability of ANS involute fuel plates
Sartory, W.K.
1993-03-01
The hydraulic buckling instability of the involute fuel plates and hydraulic coolant channels in the Advanced Neutron Source (ANS) uranium fission reactor is analyzed nonlinearly using the commercial ABAQUS finite element computer program for the fuel plates in conjunction with a user-written element for the two-dimensional fluid flow in the coolant channels. This methodology has been used for several purposes, including determination of the effect of the aluminum-clad plate plastic behavior and the effect of three-dimensional plate temperature distributions on hydraulic buckling. The present report concentrates on a study of the effect of hydraulic channel imperfections on buckling. The specific form of imperfection considered is an error in fluid channel thickness that is uniform within any one channel but that varies from one channel to the next. The calculated bifurcation (linear buckling) coolant velocity is about 45 m/s, whereas the present design coolant velocity is 25 m/s. At the design velocity, the calculated fluid-induced plate deflection due to the imperfection is somewhat less in magnitude and opposite in direction from the imperfection itself.
NASA Technical Reports Server (NTRS)
Nemeth, Michael P.
2014-01-01
Nonlinear and bifurcation buckling equations for elastic, stiffened, geometrically perfect, right-circular cylindrical, anisotropic shells subjected to combined loads are presented that are based on Sanders' shell theory. Based on these equations, a three-parameter approximate Rayleigh-Ritz solution and a classical solution to the buckling problem are presented for cylinders with simply supported edges. Extensive comparisons of results obtained from these solutions with published results are also presented for a wide range of cylinder constructions. These comparisons include laminated-composite cylinders with a wide variety of shell-wall orthotropies and anisotropies. Numerous results are also given that show the discrepancies between the results obtained by using Donnell's equations and variants of Sanders' equations. For some cases, nondimensional parameters are identified and "master" curves are presented that facilitate the concise representation of results.
Cooperative buckling and the nonlinear mechanics of nematic semiflexible networks
NASA Astrophysics Data System (ADS)
Foucard, L. C.; Price, J. K.; Klug, W. S.; Levine, A. J.
2015-09-01
We review the nonlinear mechanics of cross-linked networks of stiff filaments with a quenched anisotropic (nematic) alignment. A combination of numerical simulations and analytic calculations shows that the broken rotational symmetry of the filament orientational distribution leads to a dramatic nonlinear softening of the network at very small strain (on the order of 0.1%). We argue that one can understand this softening in terms of Euler buckling, i.e. the loss of further load-carrying capacity in compression within the network. With increasing shear strain, this source of geometric nonlinearity appears as heterogeneous nucleation (originating in particularly fragile regions, which may be identified by a linear stability analysis) and subsequently grows into ‘buckling scars’ that eventually spread throughout the system. We develop a simple mean-field model for the nonlinear mechanics of such networks and suggest applications of these ideas to a variety of fiber networks and biopolymer systems.
NASA Astrophysics Data System (ADS)
Kala, Zdeněk; Kala, Jiří
2012-09-01
The paper deals with the influence of correlation length, of Gauss random field, and of yield strength of a hotrolled I-beam under bending on the ultimate load carrying capacity limit state. Load carrying capacity is an output random quantity depending on input random imperfections. Latin Hypercube Sampling Method is used for sampling simulation. Load carrying capacity is computed by the programme ANSYS using shell finite elements and nonlinear computation methods. The nonlinear FEM computation model takes into consideration the effect of lateral-torsional buckling on the ultimate limit state.
On Buckling, Kink Boundaries and Kinking Nonlinear Elastic Solids
NASA Astrophysics Data System (ADS)
Shamma, Mohamed
The mechanical behavior of materials has been under investigation for decades. However, there is always unknown information to be researched and characterized. Extensive research has been performed on materials deforming by slip and twin mechanisms due to their presence in a lot of materials used in practical applications. Conversely, much less attention was directed to investigating the dislocation mechanism responsible for the fully reversible energy dissipating mechanical response of Kinking Nonlinear Elastic (KNE) solids. Herein, the buckling dislocation mechanism responsible for the KNE mechanical behavior of MAX phases is investigated. The main features of the buckling dislocation mechanism are identified that are globally applicable for layered structured materials as well. This was done by analyzing the deformation of a single crystal layered structure. The single crystal layered structure is a setup consisting of a pile of paper supported by sponge and ply wood in which paper buckles during compression. The displacement of the paper layers is studied in relation to dislocation nucleation across the layers called dislocation walls (DW). Schmid factor maps where developed that recognize the shape and progress of traction applied on the layers during deformation. Hence, the evolution of buckling dislocation mechanism that occurs in layered structures has been discovered distinguishing between two possible buckling modes (extrusion and indentation) that depend on the layered structure surrounding support and constraints. In situ neutron diffraction and ultrasonic bias stress techniques were used to perform in situ experiments on selected MAX phases to obtain information about the dislocation mechanism during its activity. Linear elastic Ti 2SC was investigated as well for comparison with Ti3SiC 2 and Ti2AlC MAX phases which demonstrate KNE mechanical response in bulk. The in situ ND results of textured Ti2AlC showed typical results except for the (0004) grains
Buckling Design and Analysis of a Payload Fairing One-Sixth Cylindrical Arc-Segment Panel
NASA Technical Reports Server (NTRS)
Kosareo, Daniel N.; Oliver, Stanley T.; Bednarcyk, Brett A.
2013-01-01
Design and analysis results are reported for a panel that is a 16th arc-segment of a full 33-ft diameter cylindrical barrel section of a payload fairing structure. Six such panels could be used to construct the fairing barrel, and, as such, compression buckling testing of a 16th arc-segment panel would serve as a validation test of the buckling analyses used to design the fairing panels. In this report, linear and nonlinear buckling analyses have been performed using finite element software for 16th arc-segment panels composed of aluminum honeycomb core with graphiteepoxy composite facesheets and an alternative fiber reinforced foam (FRF) composite sandwich design. The cross sections of both concepts were sized to represent realistic Space Launch Systems (SLS) Payload Fairing panels. Based on shell-based linear buckling analyses, smaller, more manageable buckling test panel dimensions were determined such that the panel would still be expected to buckle with a circumferential (as opposed to column-like) mode with significant separation between the first and second buckling modes. More detailed nonlinear buckling analyses were then conducted for honeycomb panels of various sizes using both Abaqus and ANSYS finite element codes, and for the smaller size panel, a solid-based finite element analysis was conducted. Finally, for the smaller size FRF panel, nonlinear buckling analysis was performed wherein geometric imperfections measured from an actual manufactured FRF were included. It was found that the measured imperfection did not significantly affect the panel's predicted buckling response
Buckling analysis of Big Dee Vacuum Vessel
Lightner, S.; Gallix, R.
1983-12-01
A simplified three-dimensional shell buckling analysis of the GA Technologies Inc., Big Dee Vacuum Vessel (V/V) was performed using the finite element program TRICO. A coarse-mesh linear elastic model, which accommodated the support boundary conditions, was used to determine the buckling mode shape under a uniform external pressure. Using this buckling mode shape, refined models were used to calculate the linear buckling load (P/sub crit/) more accurately. Several different designs of the Big Dee V/V were considered in this analysis. The supports for the V/V were equally-spaced radial pins at the outer diameter of the mid-plane. For all the cases considered, the buckling mode was axisymmetric in the toroidal direction. Therefore, it was possible to use only a small angular sector of a toric shell for the refined analysis. P/sub crit/ for the Big Dee is about 60 atm for a uniform external pressure. Also investigated in this analysis were the effects of geometrical imperfections and non-uniform pressure distributions.
Nonlinear contact between inner walls of deep sea pipelines in buckling process
NASA Astrophysics Data System (ADS)
Ma, Weilin; Yu, Jianxing; Zhou, Qingji; Xie, Bin; Cao, Jing; Li, Zhibo
2015-02-01
In order to study buckling propagation mechanism in deep sea pipelines, the contact between pipeline's inner walls in buckling process was studied. A two-dimensional ring model was used to represent the pipeline and a nonlinear spring model was adopted to simulate the contact between inner walls. Based on the elastoplastic constitutive relationship and the principle of virtual work theory, the coupling effect of pipeline's nonlinear large deformation and wall contact was included in the theoretical analysis with the aid of MATLAB, and the application scope of the theoretical model was also discussed. The calculated results show that during the loading process, the change in external pressure is closely related to the distribution of section stress, and once the walls are contacting each other, the external pressure increases and then remains stable after it reaches a specific value. Without fracture, the pipeline section will stop showing deformation. The results of theoretical calculations agree well with those of numerical simulations. Finally, in order to ensure reliability and accuracy of the theoretical results, the collapse pressure and propagation pressure were both verified by numerical simulations and experiments. Therefore, the theoretical model can be used to analyze pipeline's buckling deformation and contact between pipeline's inner walls, which forms the basis for further research on three-dimensional buckling propagation.
NASA Technical Reports Server (NTRS)
Hoff, N J; Klein, Bertram
1944-01-01
In the present part I of a series of reports on the inward bulge type buckling of monocoque cylinders the buckling load in combined bending and compression is first derived. Next the reduction in the buckling load because of a nonlinear direct stress distribution is determined. In experiments nonlinearity may result from an inadequate stiffness of the end attachments in actual airplanes from the existence of concentrated loads or cut-outs. The effect of a shearing force upon the critical load is investigated through an analysis of the results of tests carried out at GALCIT with 55 reinforced monocoque cylinders. Finally, a simple criterion of general instability is presented in the form of a buckling inequality which should be helpful to the designer of a monocoque in determining the sizes of the rings required for excluding the possibility of inward bulge type buckling.
Nonlinear buckling analyses of a small-radius carbon nanotube
NASA Astrophysics Data System (ADS)
Liu, Ning; Wang, Yong-Gang; Li, Min; Jia, Jiao
2014-04-01
Carbon nanotube (CNT) was first discovered by Sumio Iijima. It has aroused extensive attentions of scholars from all over the world. Over the past two decades, we have acquired a lot of methods to synthesize carbon nanotubes and learn their many incredible mechanical properties such as experimental methods, theoretical analyses, and computer simulations. However, the studies of experiments need lots of financial, material, and labor resources. The calculations will become difficult and time-consuming, and the calculations may be even beyond the realm of possibility when the scale of simulations is large, as for computer simulations. Therefore, it is necessary for us to explore a reasonable continuum model, which can be applied into nano-scale. This paper attempts to develop a mathematical model of a small-radius carbon nanotube based on continuum theory. An Isotropic circular cross-section, Timoshenko beam model is used as a simplified mechanical model for the small-radius carbon nanotube. Theoretical part is mainly based on modified couple stress theory to obtain the numerical solutions of buckling deformation. Meanwhile, the buckling behavior of the small radius carbon nanotube is simulated by Molecular Dynamics method. By comparing with the numerical results based on modified couple stress theory, the dependence of the small-radius carbon nanotube mechanical behaviors on its elasticity constants, small-size effect, geometric nonlinearity, and shear effect is further studied, and an estimation of the small-scale parameter of a CNT (5, 5) is obtained.
Nonlinear buckling analyses of a small-radius carbon nanotube
Liu, Ning Li, Min; Jia, Jiao; Wang, Yong-Gang
2014-04-21
Carbon nanotube (CNT) was first discovered by Sumio Iijima. It has aroused extensive attentions of scholars from all over the world. Over the past two decades, we have acquired a lot of methods to synthesize carbon nanotubes and learn their many incredible mechanical properties such as experimental methods, theoretical analyses, and computer simulations. However, the studies of experiments need lots of financial, material, and labor resources. The calculations will become difficult and time-consuming, and the calculations may be even beyond the realm of possibility when the scale of simulations is large, as for computer simulations. Therefore, it is necessary for us to explore a reasonable continuum model, which can be applied into nano-scale. This paper attempts to develop a mathematical model of a small-radius carbon nanotube based on continuum theory. An Isotropic circular cross-section, Timoshenko beam model is used as a simplified mechanical model for the small-radius carbon nanotube. Theoretical part is mainly based on modified couple stress theory to obtain the numerical solutions of buckling deformation. Meanwhile, the buckling behavior of the small radius carbon nanotube is simulated by Molecular Dynamics method. By comparing with the numerical results based on modified couple stress theory, the dependence of the small-radius carbon nanotube mechanical behaviors on its elasticity constants, small-size effect, geometric nonlinearity, and shear effect is further studied, and an estimation of the small-scale parameter of a CNT (5, 5) is obtained.
Euler buckling and nonlinear kinking of double-stranded DNA.
Fields, Alexander P; Meyer, Elisabeth A; Cohen, Adam E
2013-11-01
The bending stiffness of double-stranded DNA (dsDNA) at high curvatures is fundamental to its biological activity, yet this regime has been difficult to probe experimentally, and literature results have not been consistent. We created a 'molecular vise' in which base-pairing interactions generated a compressive force on sub-persistence length segments of dsDNA. Short dsDNA strands (<41 base pairs) resisted this force and remained straight; longer strands became bent, a phenomenon called 'Euler buckling'. We monitored the buckling transition via Förster Resonance Energy Transfer (FRET) between appended fluorophores. For low-to-moderate concentrations of monovalent salt (up to ∼150 mM), our results are in quantitative agreement with the worm-like chain (WLC) model of DNA elasticity, without the need to invoke any 'kinked' states. Greater concentrations of monovalent salts or 1 mM Mg(2+) induced an apparent softening of the dsDNA, which was best accounted for by a kink in the region of highest curvature. We tested the effects of all single-nucleotide mismatches on the DNA bending. Remarkably, the propensity to kink correlated with the thermodynamic destabilization of the mismatched DNA relative the perfectly complementary strand, suggesting that the kinked state is locally melted. The molecular vise is exquisitely sensitive to the sequence-dependent linear and nonlinear elastic properties of dsDNA. PMID:23956222
Buckling analysis of spent fuel basket
Lee, A.S.; Bumpas, S.E.
1995-05-01
The basket for a spent fuel shipping cask is subjected to compressive stresses that may cause global instability of the basket assemblies or local buckling of the individual members. Adopting the common buckling design practice in which the stability capacity of the entire structure is based on the performance of the individual members of the assemblies, the typical spent fuel basket, which is composed of plates and tubular structural members, can be idealized as an assemblage of columns, beam-columns and plates. This report presents the flexural buckling formulas for five load cases that are common in the basket buckling analysis: column under axial loads, column under axial and bending loads, plate under uniaxial loads, plate under biaxial loadings, and plate under biaxial loads and lateral pressure. The acceptance criteria from the ASME Boiler and Pressure Vessel Code are used to determine the adequacy of the basket components. Special acceptance criteria are proposed to address the unique material characteristics of austenitic stainless steel, a material which is frequently used in the basket assemblies.
Buckling analysis of planar compression micro-springs
Zhang, Jing; Sui, Li; Shi, Gengchen
2015-04-15
Large compression deformation causes micro-springs buckling and loss of load capacity. We analyzed the impact of structural parameters and boundary conditions for planar micro-springs, and obtained the change rules for the two factors that affect buckling. A formula for critical buckling deformation of micro-springs under compressive load was derived based on elastic thin plate theory. Results from this formula were compared with finite element analysis results but these did not always correlate. Therefore, finite element analysis is necessary for micro-spring buckling analysis. We studied the variation of micro-spring critical buckling deformation caused by four structural parameters using ANSYS software under two constraint conditions. The simulation results show that when an x-direction constraint is added, the critical buckling deformation increases by 32.3-297.9%. The critical buckling deformation decreases with increase in micro-spring arc radius or section width and increases with increase in micro-spring thickness or straight beam width. We conducted experiments to confirm the simulation results, and the experimental and simulation trends were found to agree. Buckling analysis of the micro-spring establishes a theoretical foundation for optimizing micro-spring structural parameters and constraint conditions to maximize the critical buckling load.
Buckling Testing and Analysis of Space Shuttle Solid Rocket Motor Cylinders
NASA Technical Reports Server (NTRS)
Weidner, Thomas J.; Larsen, David V.; McCool, Alex (Technical Monitor)
2002-01-01
A series of full-scale buckling tests were performed on the space shuttle Reusable Solid Rocket Motor (RSRM) cylinders. The tests were performed to determine the buckling capability of the cylinders and to provide data for analytical comparison. A nonlinear ANSYS Finite Element Analysis (FEA) model was used to represent and evaluate the testing. Analytical results demonstrated excellent correlation to test results, predicting the failure load within 5%. The analytical value was on the conservative side, predicting a lower failure load than was applied to the test. The resulting study and analysis indicated the important parameters for FEA to accurately predict buckling failure. The resulting method was subsequently used to establish the pre-launch buckling capability of the space shuttle system.
Nonlinear Guided Waves in Continuously Welded Rails for Buckling Prediction
NASA Astrophysics Data System (ADS)
Phillips, Robert; Bartoli, Ivan; Coccia, Stefano; Lanza di Scalea, Francesco; Salamone, Salvatore; Nucera, Claudio; Fateh, Mahmood; Carr, Gary
2011-06-01
Most modern railways use Continuous Welded Rail (CWR). A major problem is the almost total absence of expansion joints that can create severe issues such as buckling in hot weather and breakage in cold weather. A related critical parameter is the rail Neutral Temperature (NT), or the temperature at which the net longitudinal force in the rail is zero. In June 2008 the University of California, San Diego (UCSD), under the sponsorship of a Federal Railroad Administration (FRA) Office of Research and Development (R&D) grant, began work to develop a technique for in-situ measurement of NT and detection of incipient buckling in CWR. The method under investigation is based on ultrasonic guided waves, and the ultimate goal is to build and test a prototype that can be used in motion. A large-scale full rail track (70 feet in length) has been constructed at UCSD's Powell Structural Laboratories, the largest laboratories in the country for structural testing, to validate the NT measurement and buckling detection technique under rail heating conditions well controlled in the laboratory. This paper reports on the status of this project, including proof-of-principle results of stress measurement and buckling detection on a steel I-beam, and initial test results from the large-scale rail testbed at the Powell Labs. These results pave the road for the future development of the rail NT/buckling detection prototype.
Non-Linear Vibration and Thermal Buckling of AN Orthotropic Annular Plate with a Centric Rigid Mass
NASA Astrophysics Data System (ADS)
LI, S.-R.; ZHOU, Y.-H.; SONG, X.
2002-03-01
A computational analysis of the non-linear vibration and thermal post-buckling of a heated orthotropic annular plate with a central rigid mass is examined for the cases of immovably hinged as well as clamped constraint conditions of the outer edge. First, based on von Karman's plate theory and Hamilton's principles, the governing equations, in terms of the displacements of the middle plane, of the problem are derived. Then, upon assuming that harmonic responses of the system exist, the non-linear partial differential equations are converted into the corresponding non-linear ordinary differential equations through elimination of the time variable by using the Kantorovich time-averaging method. Finally, by applying a shooting method, the fundamental responses of the non-linear vibration and thermal post-buckling of the plate are numerically obtained. For some prescribed values of the parameters, such as the material rigidity ratio, temperature rise and so on, the curves of the fundamental frequency versus specified amplitude and the thermal post-buckled equilibrium paths of the plate are numerically presented.
An Improved Analysis of the Thermal Buckling of Silicon Sheet
NASA Technical Reports Server (NTRS)
Dillon, O. W., Jr.; Deangelis, R.
1984-01-01
Buckling problems on the production of wide and thin silicon sheet are discussed. Buckling occurs in all of the processes which are investigated for their potential in mass producing wide silicon sheet for use in making solar cells. It is a fact that the processes which produce good ribbon 2 cm in width do not yield the same quality product at 10 cm in width. Buckling develops precisely because the sheets are wide and very very thin. The buckling of very thin cantilever plates due to temperature variations in the axial direction is considered. The temperature variation in the width direction was determined. Axial temperature variations which cause very thin plates to buckle in a torsional mode are demonstrated. It is assumed that the particular variation of the stress function in the width direction and thereafter the analysis is exact.
The eigenvalue problem associated with the nonlinear buckling of a shear bending column
NASA Astrophysics Data System (ADS)
Nishimura, Isao
2011-04-01
This paper discusses the eigenvalue problem of a nonlinear differential equation that governs the stability of a shear bending column under extremely large deformation. What is taken into consideration is the geometrical nonlinearity while the material is supposed to be linear. The reason of a superbly stable buckling behavior of a slender rubber bearing is physically explained by pointing out the analogy that is similar to the nonlinear wave propagation expressed in KdV equation. The nonlinear boundary condition and the nonlinear term of the differential equation cancel each other and make the associated eigenvalue rather constant. In other words, as far as the material is supposed to be linear, the column does not buckle no matter how large the deformation is. This theoretical prediction is experimentally verified and successfully applied to a base isolation system of a lightweight structure.
Artery buckling analysis using a four-fiber wall model
Liu, Qin; Wen, Qi; Mottahedi, Mohammad; Han, Hai-Chao
2014-01-01
Artery bent buckling has been suggested as a possible mechanism that leads to artery tortuosity, which is associated with aging, hypertension, atherosclerosis, and other pathological conditions. It is necessary to understand the relationship between microscopic wall structural changes and macroscopic artery buckling behavior. To this end, the objectives of this study were to develop arterial buckling equations using a microstructure-based 4-fiber reinforced wall model, and to simulate the effects of vessel wall microstructural changes on artery buckling. Our results showed that the critical pressure increased nonlinearly with the axial stretch ratio, and the 4-fiber model predicted higher critical buckling pressures than what the Fung model predicted. The buckling equation using the 4-fiber model captures the experimentally observed reduction of critical pressure induced by elastin degradation and collagen fiber orientation changes in the arterial wall. These results improve our understanding of arterial stability and its relationship to microscopic wall remodeling, and the model provides a useful tool for further studies. PMID:24972920
Buckling Analysis of Debonded Sandwich Panel Under Compression
NASA Technical Reports Server (NTRS)
Sleight, David W.; Wang, John T.
1995-01-01
A sandwich panel with initial through-the-width debonds is analyzed to study the buckling of its faceskin when subject to an in-plane compressive load. The debonded faceskin is modeled as a beam on a Winkler elastic foundation in which the springs of the elastic foundation represent the sandwich foam. The Rayleigh-Ritz and finite-difference methods are used to predict the critical buckling load for various debond lengths and stiffnesses of the sandwich foam. The accuracy of the methods is assessed with a plane-strain finite-element analysis. Results indicate that the elastic foundation approach underpredicts buckling loads for sandwich panels with isotropic foam cores.
Buckling analysis of cylindrical shells with cracks
Limam, A.; Jullien, J.F.; Ouayou, B.S.
1995-12-31
In many areas of aeronautical nuclear and civil engineering practice, large thin-walled structural panels are increasingly becoming characteristic architectural features. Indeed, nuclear reactor vessels and cryogenic tanks of a launcher, for instance, are made up of several thin-walled panels welded together. Instability and buckling phenomenon present over-riding constraints on the design process. In addition, the presence of joints which are very often the origin of surface fissures poses increasing dangers on the overall stability of these structures. This research deals with the analysis of the effects of cracks on the behavior of cylindrical shells subject to external pressure. The study was divided into two major parts. In the first part, experiments were carried out with shells without cracks, in order to obtain reference data. A numerical study of various models explains the experimental results and shows the combined effect of the geometric imperfections and boundary conditions on the critical load. The second part focused on several experimental tests and numerical simulations on shells with in- depth fissures as a function of their population, orientation, length and position with respect to the welds or joints. The agreement between numerical and experimental results confirms the new possibility to design with the aid of the finite element program under the condition that the calculations are carried out by means of an appropriate numerical method.
Statistical analysis of imperfection effect on cylindrical buckling response
NASA Astrophysics Data System (ADS)
Ismail, M. S.; Purbolaksono, J.; Muhammad, N.; Andriyana, A.; Liew, H. L.
2015-12-01
It is widely reported that no efficient guidelines for modelling imperfections in composite structures are available. In response, this work evaluates the imperfection factors of axially compressed Carbon Fibre Reinforced Polymer (CFRP) cylinder with different ply angles through finite element (FE) analysis. The sensitivity of imperfection factors were analysed using design of experiment: factorial design approach. From the analysis it identified three critical factors that sensitively reacted towards buckling load. Furthermore empirical equation is proposed according to each type of cylinder. Eventually, critical buckling loads estimated by empirical equation showed good agreements with FE analysis. The design of experiment methodology is useful in identifying parameters that lead to structures imperfection tolerance.
Buckling analysis of laminated thin shells in a hot environment
NASA Technical Reports Server (NTRS)
Gotsis, Pascal K.; Guptil, James D.
1993-01-01
Results are presented of parametric studies to assess the effects of various parameters on the buckling behavior of angle-ply, laminated thin shells in a hot environment. These results were obtained by using a three-dimensional finite element analysis. An angle-ply, laminated thin shell with fiber orientation of (theta/-theta)(sub 2) was subjected to compressive mechanical loads. The laminated thin shell had a cylindrical geometry. The laminate contained T300 graphite fibers embedded in an intermediate-modulus, high-strength (IMHS) matrix. The fiber volume fraction was 55 percent and the moisture content was 2 percent. The residual stresses induced into the laminate structure during the curing were taken into account. Parametric studies were performed to examine the effect on the critical buckling load of the following parameters: cylinder length and thickness, internal hydrostatic pressure, different ply thicknesses, different temperature profiles through the thickness of the structure, and different lay up configurations and fiber volume fractions. In conjunction with these parameters the ply orientation was varied from 0 deg to 90 deg. Seven ply angles were examined: 0 deg, 15 deg, 30 deg, 45 deg, 60 deg, 75 deg, and 90 deg. The results show that the ply angle theta and the laminate thickness had significant effects on the critical buckling load. The fiber volume fraction, the fiber orientations, and the internal hydrostatic pressure had important effects on the critical buckling load. The cylinder length had a moderate influence on the buckling load. The thin shell with (theta/-theta)(sub 2) or (theta/-theta)(sub s) angle-ply laminate had better buckling-load performance than the thin shell with (theta)(sub 4) angle-ply laminate. The temperature profiles through the laminate thickness and various laminates with the different ply thicknesses has insignificant effects on the buckling behavior of the thin shells.
Nonlinear and Buckling Behavior of Curved Panels Subjected to Combined Loads
NASA Technical Reports Server (NTRS)
Hilburger, Mark W.; Nemeth, Michael P.; Starnes, James H., Jr.
2001-01-01
The results of an analytical study of the nonlinear and buckling response characteristics of curved panels subjected to combined loads are presented. Aluminum and laminated composite panels are considered in the study and a flat and shallow curved panel configurations are considered as well. The panels are subjected to combined axial compression and transverse tension or compression loads or combined axial compression and inplane shear loads. Results illustrating the effects of various combined load states on the buckling response of the panels are presented. In addition, results illustrating the effects of laminate orthotropy and anisotropy and panel curvature on the panel response are presented. The results indicate that panel curvature can have a significant effect on the nonlinear and buckling behavior of the panels subjected to combined loads. Results are included that show that geometrically perfect panels do not exhibit bifurcation points for some combined loads. Results are also presented that show the effects of laminate orthotropy and anisotropy on the interaction of combined loads.
Buckling analysis of geodesically stiffened composite panels with discrete stiffeners
NASA Astrophysics Data System (ADS)
Gurdal, Zafer; Grall, Bruno
1994-09-01
A computationally efficient analysis is developed to predict the buckling loads of geodesically stiffened composite panels with discrete plate-like stiffeners under in-plane loads. The procedure accounts for the contribution of the in-plane extensional and out-of-plane bending stiffnesses of the stiffeners through the use of a Lagrange multipliers technique in an energy method solution. The analysis is capable of predicting the buckling loads of grid-stiffened panels for a variety of stiffener aspect ratios and stiffener laminate stacking sequences. It can also be used to design panels with variable density grid stiffeners across the panel width. Results of the proposed analysis showed that the buckling loads of geodesically stiffened panels are predicted more accurately, especially in the case of panels with shallow stiffeners, compared to an earlier analysis that assumes the stiffeners to be beam-like components. For plate-like stiffeners, laminate stacking sequence of the stiffeners is found to have a substantial effect on the critical load of a panel. It was demonstrated that the optimal stiffener is not always unidirectional, and tailoring the stiffener ply sequence can lead to improvement in panel stability. It was also shown that panels with a variable grid density can lead to designs with improved buckling performance compared to uniform density panels.
Gao, Li; Zhang, Yihui; Zhang, Hui; Doshay, Sage; Xie, Xu; Luo, Hongying; Shah, Deesha; Shi, Yan; Xu, Siyi; Fang, Hui; Fan, Jonathan A; Nordlander, Peter; Huang, Yonggang; Rogers, John A
2015-06-23
Large-scale, dense arrays of plasmonic nanodisks on low-modulus, high-elongation elastomeric substrates represent a class of tunable optical systems, with reversible ability to shift key optical resonances over a range of nearly 600 nm at near-infrared wavelengths. At the most extreme levels of mechanical deformation (strains >100%), nonlinear buckling processes transform initially planar arrays into three-dimensional configurations, in which the nanodisks rotate out of the plane to form linear arrays with "wavy" geometries. Analytical, finite-element, and finite-difference time-domain models capture not only the physics of these buckling processes, including all of the observed modes, but also the quantitative effects of these deformations on the plasmonic responses. The results have relevance to mechanically tunable optical systems, particularly to soft optical sensors that integrate on or in the human body. PMID:25906085
Numerical analysis of linear buckling of wind turbine blade with different trailing bonding models
NASA Astrophysics Data System (ADS)
Zhang, J. D.; Xu, Y.
2013-12-01
The work focus on the linear buckling analysis of wind turbine blade with different trailing bonding models. Based on finite element model, it has been demonstrated that there are some differences for buckling load factor between different models. Several different models are valid for buckling analysis.
NASA Astrophysics Data System (ADS)
Prakash, T.; Sundararajan, N.; Ganapathi, M.
2007-01-01
Here, the dynamic thermal buckling behavior of functionally graded spherical caps is studied considering geometric nonlinearity based on von Karman's assumptions. The formulation is based on first-order shear deformation theory and it includes the in-plane and rotary inertia effects. The material properties are graded in the thickness direction according to the power-law distribution in terms of volume fractions of the material constituents. The effective material properties are evaluated using homogenization method. The governing equations obtained using finite element approach are solved employing the Newmark's integration technique coupled with a modified Newton-Raphson iteration scheme. The pressure load corresponding to a sudden jump in the maximum average displacement in the time history of the shell structure is taken as the dynamic buckling load. The present model is validated against the available isotropic case. A detailed numerical study is carried out to highlight the influences of shell geometries, power law index of functional graded material and boundary conditions on the dynamic buckling load of shallow spherical shells.
High-Fidelity Buckling Analysis of Composite Cylinders Using the STAGS Finite Element Code
NASA Technical Reports Server (NTRS)
Hilburger, Mark W.
2014-01-01
Results from previous shell buckling studies are presented that illustrate some of the unique and powerful capabilities in the STAGS finite element analysis code that have made it an indispensable tool in structures research at NASA over the past few decades. In particular, prototypical results from the development and validation of high-fidelity buckling simulations are presented for several unstiffened thin-walled compression-loaded graphite-epoxy cylindrical shells along with a discussion on the specific methods and user-defined subroutines in STAGS that are used to carry out the high-fidelity simulations. These simulations accurately account for the effects of geometric shell-wall imperfections, shell-wall thickness variations, local shell-wall ply-gaps associated with the fabrication process, shell-end geometric imperfections, nonuniform applied end loads, and elastic boundary conditions. The analysis procedure uses a combination of nonlinear quasi-static and transient dynamic solution algorithms to predict the prebuckling and unstable collapse response characteristics of the cylinders. Finally, the use of high-fidelity models in the development of analysis-based shell-buckling knockdown (design) factors is demonstrated.
NASA Astrophysics Data System (ADS)
El-Sayed, Sami Ibrahim
Delamination is an important mode of failure in laminated and sandwich composites. This study describes a cohesive layer model which has been successfully employed to predict the initiation and track the growth of delamination. A significant feature of the present model is that it can be used for geometrically nonlinear problems as it is formulated in terms of appropriate stresses and strains. A finite element approach which could account for the contact between delaminated surfaces as well as the progressive failure of the cohesive layer was employed to study several test cases. As a preliminary, examples of a double cantilever and a compressed beam specimens were studied in detail to identify the role of the key parameters of the model, viz. the thickness of the cohesive layer and the strength and stiffness of the cohesive layer material. It is found that the model is fairly robust and is not sensitive to changes in parameters other than the critical strain energy release rates in the opening and shearing modes respectively. This was followed by an investigation of delamination growth in columns and rings made of laminated composite material as well as sandwich columns. A dynamic analysis incorporating appropriate damping with a sufficiently slow rate of application of load was implemented to closely simulate quasi-static loading. Experimental results are found to corroborate the accuracy of the model. In laminated composites, matrix cracking was found to have a significant effect in the advanced stages of loading history and this has been accounted for by the implementation of a micro-mechanical model installed in the material in conjunction with the cohesive layer model placed along the potential delamination. Better correlation with experimental results was thus achieved. It was observed in experiments that the interfacial crack in sandwich structures may not remain at the interface and tends to kink into the core. A kinking model which is based on identifying
Jiang, H.; Sun, Y.; Rogers, J. A.; Huang, Y.; Arizona State Univ.; Univ. of Illinois; Northwestern Univ.
2008-04-01
The precisely controlled buckling of stiff thin films (e.g., Si or GaAs nano ribbons) on the patterned surface of elastomeric substrate (e.g., poly(dimethylsiloxane) (PDMS)) with periodic inactivated and activated regions was designed by Sun et al. [Sun, Y., Choi, W.M., Jiang, H., Huang, Y.Y., Rogers, J.A., 2006. Controlled buckling of semiconductor nanoribbons for stretchable electronics. Nature Nanotechnology 1, 201-207] for important applications of stretchable electronics. We have developed a post-buckling model based on the energy method for the precisely controlled buckling to study the system stretchability. The results agree with Sun et al.'s (2006) experiments without any parameter fitting, and the system can reach 120% stretchability.
NASA Astrophysics Data System (ADS)
Byun, Wanil; Kim, Min Ki; Park, Kook Jin; Kim, Seung Jo; Chung, Minho; Cho, Jin Yeon; Park, Sung-Han
2011-12-01
The supercavitating vehicle is an underwater vehicle that is surrounded almost completely by a supercavity to reduce hydrodynamic drag substantially. Since the cruise speed of the vehicle is much higher than that of conventional submarines, the drag force is huge and a buckling may occur. The buckling phenomenon is analyzed in this study through static and dynamic approaches. Critical buckling load and pressure as well as buckling mode shapes are calculated using static buckling analysis and a stability map is obtained from dynamic buckling analysis. When the finite element method (FEM) is used for the buckling analysis, the solver requires a linear static solver and an eigenvalue solver. In this study, these two solvers are integrated and a consolidated buckling analysis module is constructed. Furthermore, Particle Swarm Optimization (PSO) algorithm is combined in the buckling analysis module to perform a design optimization computation of a simplified supercavitating vehicle. The simplified configuration includes cylindrical shell structure with three stiffeners. The target for the design optimization process is to minimize total weight while maintaining the given structure buckling-free.
Buckling of spherical capsules.
Knoche, Sebastian; Kierfeld, Jan
2011-10-01
We investigate buckling of soft elastic capsules under negative pressure or for reduced capsule volume. Based on nonlinear shell theory and the assumption of a hyperelastic capsule membrane, shape equations for axisymmetric and initially spherical capsules are derived and solved numerically. A rich bifurcation behavior is found, which is presented in terms of bifurcation diagrams. The energetically preferred stable configuration is deduced from a least-energy principle both for prescribed volume and prescribed pressure. We find that buckled shapes are energetically favorable already at smaller negative pressures and larger critical volumes than predicted by the classical buckling instability. By preventing self-intersection for strongly reduced volume, we obtain a complete picture of the buckling process and can follow the shape from the initial undeformed state through the buckling instability into the fully collapsed state. Interestingly, the sequences of bifurcations and stable capsule shapes differ for prescribed volume and prescribed pressure. In the buckled state, we find a relation between curvatures at the indentation rim and the bending modulus, which can be used to determine elastic moduli from experimental shape analysis. PMID:22181297
Post Buckling Progressive Failure Analysis of Composite Laminated Stiffened Panels
NASA Astrophysics Data System (ADS)
Anyfantis, Konstantinos N.; Tsouvalis, Nicholas G.
2012-06-01
The present work deals with the numerical prediction of the post buckling progressive and final failure response of stiffened composite panels based on structural nonlinear finite element methods. For this purpose, a progressive failure model (PFM) is developed and applied to predict the behaviour of an experimentally tested blade-stiffened panel found in the literature. Failure initiation and propagation is calculated, owing to the accumulation of the intralaminar failure modes induced in fibre reinforced composite materials. Hashin failure criteria have been employed in order to address the fiber and matrix failure modes in compression and tension. On the other hand, the Tsai-Wu failure criterion has been utilized for addressing shear failure. Failure detection is followed with the introduction of corresponding material degradation rules depending on the individual failure mechanisms. Failure initiation and failure propagation as well as the post buckling ultimate attained load have been numerically evaluated. Final failure behaviour of the simulated stiffened panel is due to sudden global failure, as concluded from comparisons between numerical and experimental results being in good agreement.
COMPPAP - COMPOSITE PLATE BUCKLING ANALYSIS PROGRAM (IBM PC VERSION)
NASA Technical Reports Server (NTRS)
Smith, J. P.
1994-01-01
The Composite Plate Buckling Analysis Program (COMPPAP) was written to help engineers determine buckling loads of orthotropic (or isotropic) irregularly shaped plates without requiring hand calculations from design curves or extensive finite element modeling. COMPPAP is a one element finite element program that utilizes high-order displacement functions. The high order of the displacement functions enables the user to produce results more accurate than traditional h-finite elements. This program uses these high-order displacement functions to perform a plane stress analysis of a general plate followed by a buckling calculation based on the stresses found in the plane stress solution. The current version assumes a flat plate (constant thickness) subject to a constant edge load (normal or shear) on one or more edges. COMPPAP uses the power method to find the eigenvalues of the buckling problem. The power method provides an efficient solution when only one eigenvalue is desired. Once the eigenvalue is found, the eigenvector, which corresponds to the plate buckling mode shape, results as a by-product. A positive feature of the power method is that the dominant eigenvalue is the first found, which is this case is the plate buckling load. The reported eigenvalue expresses a load factor to induce plate buckling. COMPPAP is written in ANSI FORTRAN 77. Two machine versions are available from COSMIC: a PC version (MSC-22428), which is for IBM PC 386 series and higher computers and compatibles running MS-DOS; and a UNIX version (MSC-22286). The distribution medium for both machine versions includes source code for both single and double precision versions of COMPPAP. The PC version includes source code which has been optimized for implementation within DOS memory constraints as well as sample executables for both the single and double precision versions of COMPPAP. The double precision versions of COMPPAP have been successfully implemented on an IBM PC 386 compatible running
Buckling Analysis of a Honeycomb-Core Composite Cylinder with Initial Geometric Imperfections
NASA Technical Reports Server (NTRS)
Cha, Gene; Schultz, Marc R.
2013-01-01
Thin-walled cylindrical shell structures often have buckling as the critical failure mode, and the buckling of such structures can be very sensitive to small geometric imperfections. The buckling analyses of an 8-ft-diameter, 10-ft-long honeycomb-core composite cylinder loaded in pure axial compression is discussed in this document. Two loading configurations are considered configuration 1 uses simple end conditions, and configuration 2 includes additional structure that may more closely approximate experimental loading conditions. Linear eigenvalue buckling analyses and nonlinear analyses with and without initial geometric imperfections were performed on both configurations. The initial imperfections were introduced in the shell by applying a radial load at the midlength of the cylinder to form a single inward dimple. The critical bifurcation buckling loads are predicted to be 924,190 lb and 924,020 lb for configurations 1 and 2, respectively. Nonlinear critical buckling loads of 918,750 lb and 954,900 lb were predicted for geometrically perfect configurations 1 and 2, respectively. Lower-bound critical buckling loads for configurations 1 and 2 with radial perturbations were found to be 33% and 36% lower, respectively, than the unperturbed critical loads. The inclusion of the load introduction cylinders in configuration 2 increased the maximum bending-boundary-layer rotation up to 11%.
A NASTRAN DMAP alter for linear buckling analysis under dynamic loading
NASA Technical Reports Server (NTRS)
Aiello, Robert A.; Grady, Joseph E.
1989-01-01
A modification to the NASTRAN solution sequence for transient analysis with direct time integration (COSMIC NASTRAN rigid format 9) was developed and incorporated into a DMAP alter. This DMAP alter calculates the buckling stability of a dynamically loaded structure, and is used to predict the onset of structural buckling under stress-wave loading conditions. The modified solution sequence incorporates the linear buckling analysis capability (rigid format 5) of NASTRAN into the existing Transient solution rigid format in such a way as to provide a time dependent eigensolution which is used to assess the buckling stability of the structure as it responds to the impulsive load. As a demonstration of the validity of this modified solution procedure, the dynamic buckling of a prismatic bar subjected to an impulsive longitudinal compression is analyzed and compared to the known theoretical solution. In addition, a dynamic buckling analysis is performed for the analytically less tractable problem of the localized dynamic buckling of an initially flawed composite laminate under transverse impact loading. The addition of this DMAP alter to the transient solution sequence in NASTRAN facilitates the computational prediction of both the time at which the onset of dynamic buckling occurs in an impulsively loaded structure, and the dynamic buckling mode shapes of that structure.
Thermo-mechanical buckling analysis of FGM plate using generalized plate theory
NASA Astrophysics Data System (ADS)
Sharma, Kanishk; Kumar, Dinesh; Gite, Anil
2016-05-01
This paper investigates the thermo-mechanical buckling behavior of simply-supported FGM plate under the framework of generalized plate theory (GPT), which includes classical plate theory (CPT), first order shear deformation theory (FSDT) and higher order shear deformation theory (HSDT) as special cases. The governing equations for FGM plate under thermal and mechanical loading conditions are derived from the principle of virtual displacements and Navier-type solution is assumed for simply supported boundary condition. The efficiency and applicability of presented methodology is illustrated by considering various examples of thermal and mechanical buckling of FGM plates. The closed form solutions in the form of critical thermal and mechanical buckling loads, predicted by CPT, FSDT and HSDT are compared for different side-to-thickness of FGM plate. Subsequently, the effect of material gradation profile on critical buckling parameters is examined by evaluating the buckling response for a range of power law indexes. The effect of geometrical parameters on mechanical buckling of FGM plate under uni-axial and bi-axial loading conditions are also illustrated by calculating the critical load for various values of slenderness ratios. Furthermore a comparative analysis of critical thermal buckling loads of FGM plate for different temperature profiles is also presented. It is identified that all plate theories predicted approximately same critical buckling loads and critical buckling temperatures for thin FGM plate, however for thick FGM plates, CPT overestimates the critical buckling parameters. Moreover the critical buckling loads and critical buckling temperatures of FGM plate are found to be significantly lower than the corresponding homogenous isotropic ceramic plate (n=0).
A NASTRAN DMAP alter for linear buckling analysis under dynamic loading
NASA Technical Reports Server (NTRS)
Aiello, Robert A.; Grady, Joseph E.
1988-01-01
A unique modification to the NASTRAN solution sequence for transient analysis with direct time integration (COSMIC NASTRAN rigid format 9) was developed and incorporated into a DMAP alter. This DMAP alter calculates the buckling stability of a dynamically loaded structure, and is used to predict the onset of structural buckling under stress wave loading conditions. The modified solution sequence incorporates the linear buckling analysis capability (rigid format 5) of NASTRAN into the existing Transient solution rigid format in such a way as to provide a time dependent eigensolution which is used to assess the buckling stability of the structure as it responds to the impulsive load. As a demonstration of the validity of this modified solution procedure, the dynamic buckling of a prismatic bar subjected to an impulsive longitudinal compression is analyzed and compared to the known theoretical solution. In addition, a dynamic buckling analysis is performed for the analytically less tractable problem of the localized dynamic buckling of an initially flawed composite laminate under transverse impact loading. The addition of this DMAP alter to the transient solution sequence in NASTRAN facilitates the prediction of both time and mode of buckling.
A Nonlinear Theory of Bending and Buckling of Thin Elastic Shallow Spherical Shells
NASA Technical Reports Server (NTRS)
Kaplan, A; Fung, Y C
1954-01-01
The problem of the finite displacement and buckling, of a shallow spherical dome is investigated both theoretically and experimentally. Experimental results seem to indicate that the classical criterion of buckling is applicable to very shallow spherical domes for which the theoretical calculation was made. A transition to energy criterion for higher domes is also indicated.
NASA Astrophysics Data System (ADS)
Gunda, Jagadish Babu; Venkateswara Rao, Gundabathula
2016-04-01
Post-buckling and large amplitude free vibration analysis of composite beams with axially immovable ends is investigated in the present study using a simple intuitive formulation. Geometric nonlinearity of Von-Karman type is considered in the analysis which accounts for mid-plane stretching action of the beam. Intuitive formulation uses only two parameters: the critical bifurcation point and the axial stretching force developed due to membrane stretching action of the beam. Hinged-hinged, clamped-clamped and clamped-hinged boundary conditions are considered. Numerical accuracy of the proposed analytical closed-form solutions obtained from the intuitive formulation are compared to available finite element solutions for symmetric and asymmetric layup schemes of laminated composite beam which indicates the confidence gained on the present formulation.
New Nonlinear Multigrid Analysis
NASA Technical Reports Server (NTRS)
Xie, Dexuan
1996-01-01
The nonlinear multigrid is an efficient algorithm for solving the system of nonlinear equations arising from the numerical discretization of nonlinear elliptic boundary problems. In this paper, we present a new nonlinear multigrid analysis as an extension of the linear multigrid theory presented by Bramble. In particular, we prove the convergence of the nonlinear V-cycle method for a class of mildly nonlinear second order elliptic boundary value problems which do not have full elliptic regularity.
NASA Astrophysics Data System (ADS)
Zhang, Hui; Gao, Li; Zhang, Yihui; Xie, Xu; Doshay, Sage; Fang, Hui; Fan, Jonathan A.; Nordlander, Peter; Huang, Yonggang; Rogers, John A.; Deesha, Shad; Xu, Siyi
2015-09-01
Large scale, dense arrays of plasmonic nanodisks (Au) on low modulus, high elongation elastomeric substrates (PDMS) represent a class of tunable optical system, with reversible ability to shift plasmon resonances, originating from array deformation, over a range of nearly 600nm in the visible region. At the most extreme levels of mechanical deformation (strains <100%), non-linear buckling processes transform initially planar arrays into three dimensional configurations, in which the nanodisks rotate out of the plane, giving rise to an increase of transition rate, to form linear arrays with `wavy' geometries. Analytical and finite element models capture not only the physics of these buckling processes, including all of distinct modes that occur, but also the quantitative effects of these deformations on the plasmonic responses. The results have relevance to mechanically tunable optical systems, with potential relevance to soft optical sensors that integrate on or in the human body.
NASA Technical Reports Server (NTRS)
Starnes, James H., Jr.; Hilburger, Mark W.
2003-01-01
The results of an experimental and analytical study of the effects of initial imperfections on the buckling response of unstiffened thin-walled compression-loaded graphite-epoxy cylindrical shells are presented. The analytical results include the effects of traditional and nontraditional initial imperfections and uncertainties in the values of selected shell parameters on the buckling loads of the shells. The nonlinear structural analysis results correlate very well with the experimental results. The high-fidelity nonlinear analysis procedure used to generate the analytical results can also be used to form the basis of a new shell design procedure that could reduce the traditional dependence on empirical results in the shell design process. KEYWORDS: high-fidelity nonlinear structural analysis, composite shells, shell stability, initial imperfections
Buckling analysis for structural sections and stiffened plates reinforced with laminated composites.
NASA Technical Reports Server (NTRS)
Viswanathan, A. V.; Soong, T.-C.; Miller, R. E., Jr.
1972-01-01
A classical buckling analysis is developed for stiffened, flat plates composed of a series of linked flat plate and beam elements. Plates are idealized as multilayered orthotropic elements; structural beads and lips are idealized as beams. The loaded edges of the stiffened plate are simply supported and the conditions at the unloaded edges can be prescribed arbitrarily. The plate and beam elements are matched along their common junctions for displacement continuity and force equilibrium in an exact manner. Offsets between elements are considered in the analysis. Buckling under uniaxial compressive load for plates, sections and stiffened plates is investigated. Buckling loads are found as the lowest of all possible general and local failure modes and the mode shape is used to determine whether buckling is a local or general instability. Numerical correlations with existing analysis and test data for plates, sections and stiffened plates including boron-reinforced structures are discussed. In general, correlations are reasonably good.
Optimal Design of Grid-Stiffened Composite Panels Using Global and Local Buckling Analysis
Ambur, D.R.; Jaunky, N.; Knight, N.F. Jr.
1996-04-01
A design strategy for optimal design of composite grid-stiffened panels subjected to global and local buckling constraints is developed using a discrete optimizer. An improved smeared stiffener theory is used for the global buckling analysis. Local buckling of skin segments is assessed using a Rayleigh-Ritz method that accounts for material anisotropy and transverse shear flexibility. The local buckling of stiffener segments is also assessed. Design variables are the axial and transverse stiffener spacing, stiffener height and thickness, skin laminate, and stiffening configuration. The design optimization process is adapted to identify the lightest-weight stiffening configuration and pattern for grid stiffened composite panels given the overall panel dimensions, design in-plane loads, material properties, and boundary conditions of the grid-stiffened panel.
Optimal Design of Grid-Stiffened Composite Panels Using Global and Local Buckling Analysis
NASA Technical Reports Server (NTRS)
Ambur, Damodar R.; Jaunky, Navin; Knight, Norman F., Jr.
1996-01-01
A design strategy for optimal design of composite grid-stiffened panels subjected to global and local buckling constraints is developed using a discrete optimizer. An improved smeared stiffener theory is used for the global buckling analysis. Local buckling of skin segments is assessed using a Rayleigh-Ritz method that accounts for material anisotropy and transverse shear flexibility. The local buckling of stiffener segments is also assessed. Design variables are the axial and transverse stiffener spacing, stiffener height and thickness, skin laminate, and stiffening configuration. The design optimization process is adapted to identify the lightest-weight stiffening configuration and pattern for grid stiffened composite panels given the overall panel dimensions, design in-plane loads, material properties, and boundary conditions of the grid-stiffened panel.
NASA Technical Reports Server (NTRS)
Ko, William L.; Jackson, Raymond H.
1993-01-01
Combined inplane compressive and shear buckling analysis was conducted on flat rectangular sandwich panels using the Raleigh-Ritz minimum energy method with a consideration of transverse shear effect of the sandwich core. The sandwich panels were fabricated with titanium honeycomb core and laminated metal matrix composite face sheets. The results show that slightly slender (along unidirectional compressive loading axis) rectangular sandwich panels have the most desirable stiffness-to-weight ratios for aerospace structural applications; the degradation of buckling strength of sandwich panels with rising temperature is faster in shear than in compression; and the fiber orientation of the face sheets for optimum combined-load buckling strength of sandwich panels is a strong function of both loading condition and panel aspect ratio. Under the same specific weight and panel aspect ratio, a sandwich panel with metal matrix composite face sheets has much higher buckling strength than one having monolithic face sheets.
Torres, Fernando G; Troncoso, Omar P; Diaz, John; Arce, Diego
2014-11-01
Porcupine quills are natural structures formed by a thin walled conical shell and an inner foam core. Axial compression tests, differential scanning calorimetry (DSC), thermogravimetric analysis (TGA) and Fourier transform infrared spectroscopy (FT-IR) were all used to compare the characteristics and mechanical properties of porcupine quills with and without core. The failure mechanisms that occur during buckling were analyzed by scanning electron microscopy (SEM), and it was found that delamination buckling is mostly responsible for the decrease in the measured buckling stress of the quills with regard to predicted theoretical values. Our analysis also confirmed that the foam core works as an energy dissipater improving the mechanical response of an empty cylindrical shell, retarding the onset of buckling as well as producing a step wise decrease in force after buckling, instead of an instantaneous decrease in force typical for specimens without core. Cell collapse and cell densification in the inner foam core were identified as the key mechanisms that allow for energy absorption during buckling. PMID:25123434
Buckling and dynamic analysis of drill strings for core sampling
Ziada, H.H., Westinghouse Hanford
1996-05-15
This supporting document presents buckling and dynamic stability analyses of the drill strings used for core sampling. The results of the drill string analyses provide limiting operating axial loads and rotational speeds to prevent drill string failure, instability and drill bit overheating during core sampling. The recommended loads and speeds provide controls necessary for Tank Waste Remediation System (TWRS) programmatic field operations.
BUCKO- A BUCKLING ANALYSIS FOR RECTANGULAR PLATES WITH CENTRALLY LOCATED CUTOUTS
NASA Technical Reports Server (NTRS)
Nemeth, M. P.
1994-01-01
BUCKO is a computer program developed to predict the buckling load of a rectangular compression-loaded orthotropic plate with a centrally located cutout. The plate is assumed to be a balanced, symmetric laminate of uniform thickness. The cutout shape can be elliptical, circular, rectangular, or square. The BUCKO package includes sample data that demonstrates the essence of the program and its ease of usage. BUCKO uses an approximate one-dimensional formulation of the classical two-dimensional buckling problem following the Kantorovich method. The boundary conditions are considered to be simply supported unloaded edges and either clamped or simply supported loaded edges. The plate is loaded in uniaxial compression by either uniformly displacing or uniformly stressing two opposite edges of the plate. The BUCKO analysis consists of two parts: calculation of the inplane stress distribution prior to buckling, and calculation of the plate axial load and displacement at buckling. User input includes plate planform and cutout geometry, plate membrane and bending stiffnesses, finite difference parameters, boundary condition data, and loading data. Results generated by BUCKO are the prebuckling strain energy, inplane stress resultants, buckling mode shape, critical end shortening, and average axial and transverse strains at buckling. BUCKO is written in FORTRAN V for batch execution and has been implemented on a CDC CYBER 170 series computer operating under NOS with a central memory requirement of approximately 343K of 60 bit words. This program was developed in 1984 and was last updated in 1990.
Post-buckling behavior of a beam-column on a nonlinear elastic foundation with a gap
NASA Technical Reports Server (NTRS)
Kuznetsov, E. N.; Johns, T. G.
1980-01-01
The structural behavior of an elastic beam-column placed with a gap between two nonlinearity elastic layers each resting on a rigid foundation was examined. The beam-column was laterally supported at both ends and subjected to a uniform transverse load and axial compression. Its slenderness was such that the axial compressive force exceeds the amount that would be necessary to buckle it as a simple supported column. The elastic layers were represented by an elastic foundation with a strongly nonlinear specific reaction taken as a rapidly increasing function of the layer compression. The analytical model developed simulated the entire pattern of the deflection and stress state including layer and end support reactions, under gradually increasing axial force.
TRBUCKL - A NASTRAN DMAP ALTER FOR LINEAR BUCKLING ANALYSIS UNDER DYNAMIC LOADING
NASA Technical Reports Server (NTRS)
Aiello, R. A.
1994-01-01
Delaminations near the outer surface of a laminate are susceptible to local buckling and buckling-induced delamination propagation when the laminate is subjected to transverse impact loading. This results in a loss of stiffness and strength. TRBUCKL is an unique dynamic delamination buckling and delamination propagation analysis capability that can be incorporated into the structural analysis program, NASTRAN. This capability will aid engineers in the design of structures incorporating composite laminates. The capability consists of: (1) a modification of the direct time integration solution sequence which provides a new analysis algorithm that can be used to predict delamination buckling in a laminate subjected to dynamic loading; and (2) a new method of modeling the composite laminate using plate bending elements and multipoint constraints. The capability now exists to predict the time at which the onset of dynamic delamination buckling occurs, the dynamic buckling mode shape, and the dynamic delamination strain energy release rate. A procedure file for NASTRAN, TRBUCKL predicts both impact induced buckling in composite laminates with initial delaminations and the strain energy release rate due to extension of the delamination. In addition, the file is useful in calculating the dynamic delamination strain energy release rate for a composite laminate under impact loading. This procedure simplifies the simulation of progressive crack extension. TRBUCKL has been incorporated into COSMIC NASTRAN. TRBUCKL is a DMAP Alter for NASTRAN. It is intended for use only with the COSMIC NASTRAN Direct Transient Analysis (RF 9) solution sequence. The program is available as a listing only. TRBUCKL was developed in 1987.
NASA Technical Reports Server (NTRS)
McGowan, David M.
1999-01-01
The analytical formulation of curved-plate non-linear equilibrium equations including transverse-shear-deformation effects is presented. A unified set of non-linear strains that contains terms from both physical and tensorial strain measures is used. Linearized, perturbed equilibrium equations (stability equations) that describe the response of the plate just after buckling occurs are derived. These equations are then modified to allow the plate reference surface to be located a distance z(sub c) from the centroidal surface. The implementation of the new theory into the VICONOPT exact buckling and vibration analysis and optimum design computer program is described. The terms of the plate stiffness matrix using both classical plate theory (CPT) and first-order shear-deformation plate theory (SDPT) are presented. The effects of in-plane transverse and in-plane shear loads are included in the in-plane stability equations. Numerical results for several example problems with different loading states are presented. Comparisons of analyses using both physical and tensorial strain measures as well as CPT and SDPT are made. The computational effort required by the new analysis is compared to that of the analysis currently in the VICONOPT program. The effects of including terms related to in-plane transverse and in-plane shear loadings in the in-plane stability equations are also examined. Finally, results of a design-optimization study of two different cylindrical shells subject to uniform axial compression are presented.
NASA Technical Reports Server (NTRS)
Viswanathan, A. V.; Tamekuni, M.
1973-01-01
Analytical methods based on linear theory are presented for predicting the thermal stresses in and the buckling of heated structures with arbitrary uniform cross section. The structure is idealized as an assemblage of laminated plate-strip elements, curved and planar, and beam elements. Uniaxially stiffened plates and shells of arbitrary cross section are typical examples. For the buckling analysis the structure or selected elements may be subjected to mechanical loads, in additional to thermal loads, in any desired combination of inplane transverse load and axial compression load. The analysis is also applicable to stiffened structures under inplane loads varying through the cross section, as in stiffened shells under bending. The buckling analysis is general and covers all modes of instability. The analysis has been applied to a limited number of problems and the results are presented. These while showing the validity and the applicability of the method do not reflect its full capability.
Stochastic behavior of nanoscale dielectric wall buckling
NASA Astrophysics Data System (ADS)
Friedman, Lawrence H.; Levin, Igor; Cook, Robert F.
2016-03-01
The random buckling patterns of nanoscale dielectric walls are analyzed using a nonlinear multi-scale stochastic method that combines experimental measurements with simulations. The dielectric walls, approximately 200 nm tall and 20 nm wide, consist of compliant, low dielectric constant (low-k) fins capped with stiff, compressively stressed TiN lines that provide the driving force for buckling. The deflections of the buckled lines exhibit sinusoidal pseudoperiodicity with amplitude fluctuation and phase decorrelation arising from stochastic variations in wall geometry, properties, and stress state at length scales shorter than the characteristic deflection wavelength of about 1000 nm. The buckling patterns are analyzed and modeled at two length scales: a longer scale (up to 5000 nm) that treats randomness as a longer-scale measurable quantity, and a shorter-scale (down to 20 nm) that treats buckling as a deterministic phenomenon. Statistical simulation is used to join the two length scales. Through this approach, the buckling model is validated and material properties and stress states are inferred. In particular, the stress state of TiN lines in three different systems is determined, along with the elastic moduli of low-k fins and the amplitudes of the small-scale random fluctuations in wall properties—all in the as-processed state. The important case of stochastic effects giving rise to buckling in a deterministically sub-critical buckling state is demonstrated. The nonlinear multiscale stochastic analysis provides guidance for design of low-k structures with acceptable buckling behavior and serves as a template for how randomness that is common to nanoscale phenomena might be measured and analyzed in other contexts.
Stochastic behavior of nanoscale dielectric wall buckling
Friedman, Lawrence H.; Levin, Igor; Cook, Robert F.
2016-01-01
The random buckling patterns of nanoscale dielectric walls are analyzed using a nonlinear multi-scale stochastic method that combines experimental measurements with simulations. The dielectric walls, approximately 200 nm tall and 20 nm wide, consist of compliant, low dielectric constant (low-k) fins capped with stiff, compressively stressed TiN lines that provide the driving force for buckling. The deflections of the buckled lines exhibit sinusoidal pseudoperiodicity with amplitude fluctuation and phase decorrelation arising from stochastic variations in wall geometry, properties, and stress state at length scales shorter than the characteristic deflection wavelength of about 1000 nm. The buckling patterns are analyzed and modeled at two length scales: a longer scale (up to 5000 nm) that treats randomness as a longer-scale measurable quantity, and a shorter-scale (down to 20 nm) that treats buckling as a deterministic phenomenon. Statistical simulation is used to join the two length scales. Through this approach, the buckling model is validated and material properties and stress states are inferred. In particular, the stress state of TiN lines in three different systems is determined, along with the elastic moduli of low-k fins and the amplitudes of the small-scale random fluctuations in wall properties—all in the as-processed state. The important case of stochastic effects giving rise to buckling in a deterministically sub-critical buckling state is demonstrated. The nonlinear multiscale stochastic analysis provides guidance for design of low-k structures with acceptable buckling behavior and serves as a template for how randomness that is common to nanoscale phenomena might be measured and analyzed in other contexts. PMID:27330220
Nonlinear rotordynamics analysis
NASA Technical Reports Server (NTRS)
Day, W. B.
1985-01-01
The special nonlinearities of the Jeffcott equations in rotordynamics are examined. The immediate application of this analysis is directed toward understanding the excessive vibrations recorded in the LOX pump of the SSME during hot firing ground testing. Deadband, side force and rubbing are three possible sources of inducing nonlinearity in the Jeffcott equations. The present analysis initially reduces these problems to the same mathematical description. A special frequency, named the nonlinear natural frequency is defined and used to develop the solutions of the nonlinear Jeffcott equations as asympotic expansions. This nonlinear natural frequency which is the ratio of the cross-stiffness and the damping, plays a major role in determining response frequencies. Numerical solutions are included for comparison with the analysis. Also, nonlinear frequency-response tables are made for a typical range of values.
Buckling and postbuckling analysis of stiffened composite panels in axial compression
NASA Astrophysics Data System (ADS)
Park, Oung
The major objective of this study is to analyze buckling and delamination behavior of composite stiffened panels subjected to axial compression. First, a combined analytical and experimental study of a blade stiffened composite panel subjected to axial compression was conducted. The effects of the differences between a simple model used to design the panel and the actual experimental conditions were examined. It was found that in spite of many simplifying assumptions the design model did reasonably well in that the experimental failure load was only 10% higher than the design load. Several structural analysis programs, including PANDA2, STAGS, and ABAQUS, were used to obtain high fidelity analysis results. The buckling loads from STAGS agreed well with the experimental failure loads. However, substantial differences were found in the out-of-plane displacements of the panel. Efforts were made to identify the source of these differences. Implementing non-uniform load introduction with general contact definition in the STAGS finite element model improved correlation between the measured and predicted out-of-plane deformations. Next, a new method called Crack Tip Force Method (CTFM) is derived for computing point-wise energy release rate along the delamination front in delaminated plates. The CTFM is computationally simple as the G is computed using the forces transmitted at the crack-tip between the top and bottom sub-laminates and the sub-laminate properties. Finally, buckling and postbuckling of a blade-stiffened composite panel under axial compression with a partial skin-stiffener debond are investigated. Two different finite element models, where nodes of the panel skin and the stiffener flange are located on the mid-plane or at the interface between skin and flange, are used. Linear buckling analysis is conducted using both STAGS and ABAQUS. Postbuckling analysis is conducted with STAGS. Comparison between the present results and previous buckling analysis
Post-Buckling Analysis of Curved Honeycomb Sandwich Panels Containing Interfacial Disbonds
NASA Technical Reports Server (NTRS)
Pineda, Evan J.; Bednarcyk, Brett A.; Krivanek, Thomas K.
2016-01-01
A numerical study on the effect of facesheet-core disbonds on the post-buckling response of curved honeycomb sandwich panels is presented herein. This work was conducted as part of the development of a damage tolerance plan for the next-generation Space Launch System heavy lift launch vehicle payload fairing. As such, the study utilized full-scale fairing barrel segments as the structure of interest. The panels were composed of carbon fiber reinforced polymer facesheets and aluminum honeycomb core. The panels were analyzed numerically using the finite element method incorporating geometric nonlinearity. In a predetermined circular region, facesheet and core nodes were detached to simulate a disbond, between the outer mold line facesheet and honeycomb core, induced via low-speed impact. Surface-to-surface contact in the disbonded region was invoked to prevent interpenetration of the facesheet and core elements and obtain realistic stresses in the core. The diameter of this disbonded region was varied and the effect of the size of the disbond on the post-buckling response was observed. Significant changes in the slope of the edge load-deflection response were used to determine the onset of global buckling and corresponding buckling load. Finally, several studies were conducted to determine the sensitivity of the numerical predictions to refinement in the finite element mesh.
A digital computer study of the buckling of shallow spherical caps and truncated hemispheres
NASA Technical Reports Server (NTRS)
Stilwell, W. C.; Ball, R. E.
1972-01-01
A study of the buckling of thin shells was conducted using a digital computer program for the geometrically nonlinear analysis of arbitrarily loaded shells of revolution. The objective was an evaluation of the program's applicability to bifurcation buckling and imperfection sensitivity analysis. Clamped spherical caps under pressure loading and clamped truncated hemispheres under axial tension were investigated. Buckling loads were determined for axisymmetric and nearly axisymmetric loads and are compared with previously published analytical results based on geometric imperfections.
Post-Buckling and Ultimate Strength Analysis of Stiffened Composite Panel Base on Progressive Damage
NASA Astrophysics Data System (ADS)
Zhang, Guofan; Sun, Xiasheng; Sun, Zhonglei
Stiffened composite panel is the typical thin wall structure applied in aerospace industry, and its main failure mode is buckling subjected to compressive loading. In this paper, the development of an analysis approach using Finite Element Method on post-buckling behavior of stiffened composite structures under compression was presented. Then, the numerical results of stiffened panel are obtained by FE simulations. A thorough comparison were accomplished by comparing the load carrying capacity and key position strains of the specimen with test. The comparison indicates that the FEM results which adopted developed methodology could meet the demand of engineering application in predicting the post-buckling behavior of intact stiffened structures in aircraft design stage.
NASA Technical Reports Server (NTRS)
Ko, William L.
1996-01-01
Mechanical and thermal buckling behavior of monolithic and metal-matrix composite hat-stiffened panels were investigated. The panels have three types of face-sheet geometry: Flat face sheet, microdented face sheet, and microbulged face sheet. The metal-matrix composite panels have three types of face-sheet layups, each of which is combined with various types of hat composite layups. Finite-element method was used in the eigenvalue extractions for both mechanical and thermal buckling. The thermal buckling analysis required both eigenvalue and material property iterations. Graphical methods of the dual iterations are shown. The mechanical and thermal buckling strengths of the hat-stiffened panels with different face-sheet geometry are compared. It was found that by just microdenting or microbulging of the face sheet, the axial, shear, and thermal buckling strengths of both types of hat-stiffened panels could be enhanced considerably. This effect is more conspicuous for the monolithic panels. For the metal-matrix composite panels, the effect of fiber orientations on the panel buckling strengths was investigated in great detail, and various composite layup combinations offering, high panel buckling strengths are presented. The axial buckling strength of the metal-matrix panel was sensitive to the change of hat fiber orientation. However, the lateral, shear, and thermal buckling strengths were insensitive to the change of hat fiber orientation.
A Simple Buckling Analysis Method for Airframe Composite Stiffened Panel by Finite Strip Method
NASA Astrophysics Data System (ADS)
Tanoue, Yoshitsugu
Carbon fiber reinforced plastics (CFRP) have been used in structural components for newly developed aircraft and spacecraft. The main structures of an airframe, such as the fuselage and wings, are essentially composed of stiffened panels. Therefore, in the structural design of airframes, it is important to evaluate the buckling strength of the composite stiffened panels. Widely used finite element method (FEM) can analyzed any stiffened panel shape with various boundary conditions. However, in the early phase of airframe development, many studies are required in structural design prior to carrying out detail drawing. In this phase, performing structural analysis using only FEM may not be very efficient. This paper describes a simple buckling analysis method for composite stiffened panels, which is based on finite strip method. This method can deal with isotropic and anisotropic laminated plates and shells with several boundary conditions. The accuracy of this method was verified by comparing it with theoretical analysis and FEM analysis (NASTRAN). It has been observed that the buckling coefficients calculated via the present method are in agreement with results found by detail analysis methods. Consequently, this method is designed to be an effective calculation tool for the buckling analysis in the early phases of airframe design.
Buckling analysis of fully anisotropic plates containing cutouts and elastically restrained edges
NASA Technical Reports Server (NTRS)
Jones, Kevin M.; Klang, Eric C.
1992-01-01
An analysis is developed which combines the Ritz and collocation methods for the stability solution of an anisotropic plate with a cutout and elastically restrained edges. Results are presented which agree closely with experiment for isotropic and orthotropic materials. Results are also given for restrained anisotropic plates with circular holes loaded in compression and shear. Difference is noted in the critical buckling loads between displacement and stress loaded panels as hole size is increased. Clamping is also seen to affect the trends in buckling associated with hole size.
Limit Load and Buckling Analysis for Assessing Hanford Single-Shell Tank Dome Structural Integrity
Johnson, Kenneth I.; Deibler, John E.; Julyk, Larry J.; Karri, Naveen K.; Pilli, Siva Prasad
2012-12-07
The U.S. Department of Energy, Office of River Protection has commissioned a structural analysis of record (AOR) for the Hanford single shell tanks (SSTs) to assess their structural integrity. The analysis used finite element techniques to predict the tank response to the historical thermal and operating loads. The analysis also addressed the potential tank response to a postulated design basis earthquake. The combined response to static and seismic loads was then evaluated against the design requirements of American Concrete Institute (ACI) standard, ACI-349-06, for nuclear safety-related concrete structures. Further analysis was conducted to estimate the plastic limit load and the elastic-plastic buckling capacity of the tanks. The limit load and buckling analyses estimate the margin between the applied loads and the limiting load capacities of the tank structure. The potential for additional dome loads from waste retrieval equipment and the addition of large dome penetrations to accommodate retrieval equipment has generated additional interest in the limit load and buckling analyses. This paper summarizes the structural analysis methods that were used to evaluate the limit load and buckling of the single shell tanks.
Numerical analysis of pulse signal restoration by stochastic resonance in a buckled microcavity.
Sun, Heng; Liu, Hongjun; Sun, Qibing; Huang, Nan; Wang, Zhaolu; Han, Jing
2016-04-20
A novel scheme is proposed to restore weak pulse signals immersed in noise by stochastic resonance based on photothermal-effect-induced optical bistability in a buckled dome microcavity. The bistable properties of the dome microcavity are analyzed with different initial detuning wavelengths and effective cavity lengths, and bistable transmission can be obtained for input powers in submilliwatt range. A theoretical model is derived to interpret the nonlinear process of pulse signal recovery through double-well potential theory. The cross-correlation coefficient between output signals and pure input pulses is calculated to quantitatively analyze the influence of noise intensity on stochastic resonance. A cross-correlation gain of 7 is obtained, and the noise-hidden signal can be recovered effectively though the buckled dome microcavity with negligible distortion. The simulation results show the potential of using this structure to restore low-level or noise-hidden pulse signals in all-optical integrated systems. PMID:27140110
NASA Technical Reports Server (NTRS)
1984-01-01
Nonlinear structural analysis techniques for engine structures and components are addressed. The finite element method and boundary element method are discussed in terms of stress and structural analyses of shells, plates, and laminates.
Bending and buckling behavior analysis of foamed metal circular plate.
Fan, Jian Ling; Ma, Lian Sheng; Zhang, Lu; De Su, Hou
2016-01-01
This paper establishes a density gradient model along the thickness direction of a circular plate made of foamed material. Based on the first shear deformation plate theory, the result is deduced that the foamed metal circular plate with graded density along thickness direction yields axisymmetric bending problem under the action of uniformly distributed load, and the analytical solution is obtained by solving the governing equation directly. The analyses on two constraint conditions of edge radial clamping and simply supported show that the density gradient index and external load may affect the axisymmetric bending behavior of the plate. Then, based on the classical plate theory, the paper analyzes the behavior of axisymmetric buckling under radial pressure applied on the circular plate. Shooting method is used to obtain the critical load, and the effects of gradient nature of material properties and boundary conditions on the critical load of the plate are analyzed. PMID:27339281
A buckling analysis for rectangular orthotropic plates with centrally located cutouts
NASA Technical Reports Server (NTRS)
Nemeth, M. P.
1984-01-01
An analysis to obtain the buckling loads of a rectangular orthotropic plate with a centrally located cutout is described. Cutout shapes can be elliptical, circular, rectangular, or square. The boundary conditions considered in the analysis are simply supported unloaded edges and either clamped or simply supported loaded edges. The plate is loaded in uniaxial compression by either uniform edge displacement or uniform edge stress. A computer program that implements this analysis is described, and the program use is demonstrated by sample problems.
Rigorous buckling analysis of size-dependent functionally graded cylindrical nanoshells
NASA Astrophysics Data System (ADS)
Sun, Jiabin; Lim, C. W.; Zhou, Zhenhuan; Xu, Xinsheng; Sun, Wei
2016-06-01
This paper presents new analytical solutions for buckling of carbon nanotubes (CNTs) and functionally graded (FG) cylindrical nanoshells subjected to compressive and thermal loads. The model applies Eringen's nonlocal differential constitutive relation to describe the size-dependence of nanoshells. Based on Reddy's higher-order shear deformation theory, governing equations are established and solved by separating the variables. The analysis first re-examines the classical buckling of single-walled CNTs. Accurate solutions are established, and it is found that the buckling stress decreases drastically when the nonlocal parameter reaches a certain value. For CNTs with constant wall-thickness, the buckling stress eventually decreases with enhanced size effect. By comparing with CNTs molecular dynamic simulations, the obtained nonlocal parameters are much smaller than those proposed previously. Subsequently, FG cylindrical nanoshells are analyzed, and it is concluded that similar behavior that has been observed for CNTs is also valid for FG cylindrical nanoshells. The paper further discusses in detail the effects of different geometric parameters, material distribution, and temperature field.
Design guide for predicting nonlinear random response (including snap-through) of buckled plates
NASA Technical Reports Server (NTRS)
Ng, Chung Fai
1989-01-01
This design guide describes a method for predicting the random response of flat and curved plates which is based on theoretical analyses and experimental results. The plate curvature can be due to postbuckling, in-plane mechanical or thermal stresses. Based on a single mode formula, root mean square values of the strain response to broadband excitation are evaluated for different static buckled configurations using the equivalent linearization technique. The effects on the overall strain response due to instability motion of snap-through are included. Panel parameters include clamped and simply-supported boundaries, aspect ratio, thickness and length. Analytical results are compared with experimental results from tests with 12 in. x 15 in. aluminum plates under thermal loading in a progressive wave facility. Comparisons are also made with results from tests with a 2 in. x 15 in. x 0.032 in. aluminum beam under base mechanical excitation. The comparisons help to assess the accuracy of the theory and the conditions under which deviations from the theory due to effects of imperfection and higher modes are significant.
NASA Astrophysics Data System (ADS)
Borovkov, Alexei I.; Avdeev, Ilya V.; Artemyev, A.
1999-05-01
In present work, the stress, vibration and buckling finite element analysis of laminated beams is performed. Review of the equivalent single-layer (ESL) laminate theories is done. Finite element algorithms and procedures integrated into the original FEA program system and based on the classical laminated plate theory (CLPT), first-order shear deformation theory (FSDT), third-order theory of Reddy (TSDT-R) and third- order theory of Kant (TSDT-K) with the use of the Lanczos method for solving of the eigenproblem are developed. Several numerical tests and examples of bending, free vibration and buckling of multilayered and sandwich beams with various material, geometry properties and boundary conditions are solved. New effective higher-order hierarchical element for the accurate calculation of transverse shear stress is proposed. The comparative analysis of results obtained by the considered models and solutions of 2D problems of the heterogeneous anisotropic elasticity is fulfilled.
Effects of Imperfections on the Buckling Response of Compression-Loaded Composite Shells
NASA Technical Reports Server (NTRS)
Hilburger, Mark W.; Starnes, James H., Jr.
2000-01-01
The results of an experimental and numerical study of the effects of imperfections on the buckling response of unstiffened thin-walled composite cylindrical shells are presented. Results that identify the individual and combined effects of traditional initial geometric shell-wall imperfections and non-traditional shell-wall thickness variations, shell-end geometric imperfections and variations in loads applied to the ends of the shells on the shell buckling response are included. In addition, results illustrating the effects of manufacturing flaws in the form of gaps between adjacent pieces of graphite-epoxy tape in some of the laminate plies are presented in detail. The shells have been analyzed with a nonlinear finite-element analysis code that accurately accounts for these effects on the buckling and nonlinear responses of the shells. The numerical results indicate that traditional and nontraditional initial imperfections can cause a significant reduction in the buckling load of a compression-loaded composite shell. Furthermore, the results indicate that the imperfections couple in a nonlinear manner. The numerical results correlate well with the experimental results. The nonlinear analysis results are also compared to the results from a traditional linear bifurcation buckling analysis. The results suggest that the nonlinear analysis procedure can be used for determining accurate, high-fidelity design knockdown factors for shell buckling and collapse. The results can also be used to determine the effects of manufacturing tolerances on the buckling response of composite shells.
Free vibrations and buckling analysis of laminated plates by oscillatory radial basis functions
NASA Astrophysics Data System (ADS)
Neves, A. M. A.; Ferreira, A. J. M.
2015-12-01
In this paper the free vibrations and buckling analysis of laminated plates is performed using a global meshless method. A refined version of Kant's theorie which accounts for transverse normal stress and through-the-thickness deformation is used. The innovation is the use of oscillatory radial basis functions. Numerical examples are performed and results are presented and compared to available references. Such functions proved to be an alternative to the tradicional nonoscillatory radial basis functions.
NASA Technical Reports Server (NTRS)
Stoll, Frederick; Gurdal, Zafer; Starnes, James H., Jr.
1991-01-01
A method was developed for the geometrically nonlinear analysis of the static response of thin-walled stiffened composite structures loaded in uniaxial or biaxial compression. The method is applicable to arbitrary prismatic configurations composed of linked plate strips, such as stiffened panels and thin-walled columns. The longitudinal ends of the structure are assumed to be simply supported, and geometric shape imperfections can be modeled. The method can predict the nonlinear phenomena of postbuckling strength and imperfection sensitivity which are exhibited by some buckling-dominated structures. The method is computer-based and is semi-analytic in nature, making it computationally economical in comparison to finite element methods. The method uses a perturbation approach based on the use of a series of buckling mode shapes to represent displacement contributions associated with nonlinear response. Displacement contributions which are of second order in the model amplitudes are incorported in addition to the buckling mode shapes. The principle of virtual work is applied using a finite basis of buckling modes, and terms through the third order in the model amplitudes are retained. A set of cubic nonlinear algebraic equations are obtained, from which approximate equilibrium solutions are determined. Buckling mode shapes for the general class of structure are obtained using the VIPASA analysis code within the PASCO stiffened-panel design code. Thus, subject to some additional restrictions in loading and plate anisotropy, structures which can be modeled with respect to buckling behavior by VIPASA can be analyzed with respect to nonlinear response using the new method. Results obtained using the method are compared with both experimental and analytical results in the literature. The configurations investigated include several different unstiffened and blade-stiffening panel configurations, featuring both homogeneous, isotropic materials, and laminated composite
Thermal Buckling Analysis of Rectangular Panels Subjected to Humped Temperature Profile Heating
NASA Technical Reports Server (NTRS)
Ko, William I.
2004-01-01
This research investigates thermal buckling characteristics of rectangular panels subjected to different types of humped temperature profile heating. Minimum potential energy and finite-element methods are used to calculate the panel buckling temperatures. The two methods give fairly close thermal buckling solutions. 'Buckling temperature magnification factor of the first kind, eta' is established for the fixed panel edges to scale up the buckling solution of uniform temperature loading case to give the buckling solution of the humped temperature profile loading cases. Also, 'buckling temperature magnification factor of the second kind, xi' is established for the free panel edges to scale up the buckling solution of humped temperature profile loading cases with unheated boundary heat sinks to give the buckling solutions when the boundary heat sinks are heated up.
The thermal effect on buckling analysis of a DWCNT embedded on the Pasternak foundation
NASA Astrophysics Data System (ADS)
Ghorbanpour Arani, A.; Zarei, M. S.; Mohammadimehr, M.; Arefmanesh, A.; Mozdianfard, M. R.
2011-07-01
In this article, the thermal effect on the buckling analysis of a double-walled carbon nanotube (DWCNT) embedded in an elastic medium subjected to a uniform external pressure is investigated. Based on the nonlocal continuum cylindrical shell theory, the following effects are studied: small scale effect, van der Waals (vdW) forces between inner and outer tubes, surrounding elastic medium, and influence of temperature change in high-temperature environment. The interaction between matrix and the outer tube is modeled as a Pasternak foundation. The obtained results of numerical simulation indicate that for any specific circumferential wave number ( n), the nonlocal critical buckling pressure ( pcrit) is related directly to the axial half wave number ( m). Furthermore, the effect of temperature change on the critical buckling pressure is negligible, especially for stiff elastic medium; however, this is not the case if the elastic medium is soft. The strength of the DWCNT is directly related to the Winkler and shear moduli; hence, increase in the latter leads to enhanced pcrit.
An enriched 1D finite element for the buckling analysis of sandwich beam-columns
NASA Astrophysics Data System (ADS)
Sad Saoud, Kahina; Le Grognec, Philippe
2016-06-01
Sandwich constructions have been widely used during the last few decades in various practical applications, especially thanks to the attractive compromise between a lightweight and high mechanical properties. Nevertheless, despite the advances achieved to date, buckling still remains a major failure mode for sandwich materials which often fatally leads to collapse. Recently, one of the authors derived closed-form analytical solutions for the buckling analysis of sandwich beam-columns under compression or pure bending. These solutions are based on a specific hybrid formulation where the faces are represented by Euler-Bernoulli beams and the core layer is described as a 2D continuous medium. When considering more complex loadings or non-trivial boundary conditions, closed-form solutions are no more available and one must resort to numerical models. Instead of using a 2D computationally expensive model, the present paper aims at developing an original enriched beam finite element. It is based on the previous analytical formulation, insofar as the skin layers are modeled by Timoshenko beams whereas the displacement fields in the core layer are described by means of hyperbolic functions, in accordance with the modal displacement fields obtained analytically. By using this 1D finite element, linearized buckling analyses are performed for various loading cases, whose results are confronted to either analytical or numerical reference solutions, for validation purposes.
Buckling analysis and test correlation of hat stiffened panels for hypersonic vehicles
NASA Technical Reports Server (NTRS)
Percy, Wendy C.; Fields, Roger A.
1990-01-01
The paper discusses the design, analysis, and test of hat stiffened panels subjected to a variety of thermal and mechanical load conditions. The panels were designed using data from structural optimization computer codes and finite element analysis. Test methods included the grid shadow moire method and a single gage force stiffness method. The agreement between the test data and analysis provides confidence in the methods that are currently being used to design structures for hypersonic vehicles. The agreement also indicates that post buckled strength may potentially be used to reduce the vehicle weight.
On Critical Buckling Loads of Columns under End Load Dependent on Direction
Başbük, Musa; Eryılmaz, Aytekin; Atay, M. Tarık
2014-01-01
Most of the phenomena of various fields of applied sciences are nonlinear problems. Recently, various types of analytical approximate solution techniques were introduced and successfully applied to the nonlinear differential equations. One of the aforementioned techniques is the Homotopy analysis method (HAM). In this study, we applied HAM to find critical buckling load of a column under end load dependent on direction. We obtained the critical buckling loads and compared them with the exact analytic solutions in the literature. PMID:27379303
NASA Technical Reports Server (NTRS)
Simitses, G. J.; Carlson, R. L.; Riff, R.
1985-01-01
The objective of the present research is to develop a general mathematical model and solution methodologies for analyzing the structural response of thin, metallic shell structures under large transient, cyclic, or static thermomechanical loads. Among the system responses associated with these loads and conditions are thermal buckling, creep buckling, and ratcheting. Thus geometric and material nonlinearities (of high order) can be anticipated and must be considered in developing the mathematical model. A complete, true ab-initio rate theory of kinematics and kinetics for continuum and curved thin structures, without any restriction on the magnitude of the strains or the deformations, was formulated. The time dependence and large strain behavior are incorporated through the introduction of the time rates of metric and curvature in two coordinate systems: fixed (spatial) and convected (material). The relations between the time derivative and the covariant derivative (gradient) were developed for curved space and motion, so the velocity components supply the connection between the equations of motion and the time rates of change of the metric and curvature tensors.
NASA Technical Reports Server (NTRS)
Farrokh, Babak; Segal, Kenneth N.; Akkerman, Michael; Glenn, Ronald L.; Rodini, Benjamin T.; Fan, Wei-Ming; Kellas, Sortiris; Pineda, Evan J.
2014-01-01
In this work, an all-bonded out-of-autoclave (OoA) curved longitudinal composite joint concept, intended for use in the next generation of composite heavy lift launch vehicles, was evaluated and verified through finite element (FE) analysis, fabrication, testing, and post-test inspection. The joint was used to connect two curved, segmented, honeycomb sandwich panels representative of a Space Launch System (SLS) fairing design. The overall size of the resultant panel was 1.37 m by 0.74 m (54 in by 29 in), of which the joint comprised a 10.2 cm (4 in) wide longitudinal strip at the center. NASTRAN and ABAQUS were used to perform linear and non-linear analyses of the buckling and strength performance of the jointed panel. Geometric non-uniformities (i.e., surface contour imperfections) were measured and incorporated into the FE model and analysis. In addition, a sensitivity study of the specimens end condition showed that bonding face-sheet doublers to the panel's end, coupled with some stress relief features at corner-edges, can significantly reduce the stress concentrations near the load application points. Ultimately, the jointed panel was subjected to a compressive load. Load application was interrupted at the onset of buckling (at 356 kN 80 kips). A post-test non-destructive evaluation (NDE) showed that, as designed, buckling occurred without introducing any damage into the panel or the joint. The jointed panel was further capable of tolerating an impact damage to the same buckling load with no evidence of damage propagation. The OoA cured all-composite joint shows promise as a low mass factory joint for segmented barrels.
Cap buckling as a potential mechanism of atherosclerotic plaque vulnerability.
Abdelali, Maria; Reiter, Steven; Mongrain, Rosaire; Bertrand, Michel; L'Allier, Philippe L; Kritikou, Ekaterini A; Tardif, Jean-Claude
2014-04-01
Plaque rupture in atherosclerosis is the primary cause of potentially deadly coronary events, yet about 40% of ruptures occur away from the plaque cap shoulders and cannot be fully explained with the current biomechanical theories. Here, cap buckling is considered as a potential destabilizing factor which increases the propensity of the atherosclerotic plaque to rupture and which may also explain plaque failure away from the cap shoulders. To investigate this phenomenon, quasistatic 2D finite element simulations are performed, considering the salient geometrical and nonlinear material properties of diverse atherosclerotic plaques over the range of physiological loads. The numerical results indicate that buckling may displace the location of the peak von Mises stresses in the deflected caps. Plaque buckling, together with its deleterious effects is further observed experimentally in plaque caps using a physical model of deformable mock coronary arteries with fibroatheroma. Moreover, an analytical approach combining quasistatic equilibrium equations with the Navier-Bresse formulas is used to demonstrate the buckling potential of a simplified arched slender cap under intraluminal pressure and supported by foundations. This analysis shows that plaque caps - calcified, fibrotic or cellular - may buckle in specific undulated shapes once submitted to critical loads. Finally, a preliminary analysis of intravascular ultrasonography recordings of patients with atherosclerotic coronary arteries corroborates the numerical, experimental and theoretical findings and shows that various plaque caps buckle in vivo. By displacing the sites of high stresses in the plaque cap, buckling may explain the atherosclerotic plaque cap rupture at various locations, including cap shoulders. PMID:24491969
Stress analysis and buckling of J-stiffened graphite-epoxy panel
NASA Technical Reports Server (NTRS)
Davis, R. C.
1980-01-01
A graphite epoxy shear panel with bonded on J stiffeners was investigated. The panel, loaded to buckling in a picture frame shear test is described. Two finite element models, each of which included the doubler material bonded to the panel skin under the stiffeners and at the panel edges, were used to make a stress analysis of the panel. The shear load distributions in the panel from two commonly used boundary conditions, applied shear load and applied displacement, were compared with the results from one of the finite element models that included the picture frame test fixture.
Current research on shear buckling and thermal loads with PASCO: Panel Analysis and Sizing Code
NASA Technical Reports Server (NTRS)
Stroud, W. J.; Greene, W. H.; Anderson, M. S.
1981-01-01
The PASCO computer program to obtain the detailed dimensions of optimum stiffened composite structural panels is described. Design requirements in terms of inequality constraints can be placed on buckling loads or vibration frequencies, lamina stresses and strains, and overall panel stiffness for each of many load conditions. General panel cross sections can be treated. An analysis procedure involving a smeared orthotropic solution was investigated. The conservatism in the VIPASA solution and the danger in a smeared orthotropic solution is explored. PASCO's capability to design for thermal loadings is also described. It is emphasized that design studies illustrate the importance of the multiple load condition capability when thermal loads are present.
NASA Technical Reports Server (NTRS)
Ko, William L.
1994-01-01
The combined load (mechanical or thermal load) buckling equations were established for orthotropic rectangular sandwich panels under four different edge conditions by using the Rayleigh-Ritz method of minimizing the total potential energy of a structural system. Two-dimensional buckling interaction curves and three-dimensional buckling interaction surfaces were constructed for high-temperature honeycomb-core sandwich panels supported under four different edge conditions. The interaction surfaces provide overall comparison of the panel buckling strengths and the domains of symmetrical and antisymmetrical buckling associated with the different edge conditions. In addition, thermal buckling curves of these sandwich panels are presented. The thermal buckling conditions for the cases with and without thermal moments were found to be identical for the small deformation theory.
Instability signature for detecting snap-through buckling of dome structures
NASA Astrophysics Data System (ADS)
Yan, Guirong; Duan, Qiuhua; Hua, Xugang
2016-04-01
Dome structures have been built as roofs for venues where many people convene. Failure of this type of structure may jeopardize the safety of hundreds or even thousands people. For this type of structure, snap-through buckling may occur in a local area and gradually expand to the entire structure, leading to a failure of the overall structure. Although numerous structural health monitoring techniques and damage detection approaches have been developed, no research on the detection of a snap-through buckling has been reported. The objective of this study is to find a signature that is sensitive to snap-through buckling in dome structures and can be used to detect snap-through buckling. Considering that a snap-through buckling results in a significant deformation in a local area, which can be reflected by the change in tilting angles of members in that local area, the change in tilting angles of members will be proposed to be a signature to detect snap-through buckling. To verify the proposed instability signature, a reticulated dome structure will be investigated. Both an eigenvalue buckling analysis and a nonlinear buckling analysis will be conducted. The significant changes in tilting angles of members in the buckled regions have demonstrated the efficacy of the proposed instability signature. This research will bridge the research gap between structural health monitoring and structural stability research.
Analysis of Potential for Titanium Liner Buckling after Proof in a Large Kevlar/Epoxy COPV
NASA Technical Reports Server (NTRS)
Phoenix, S. Leigh; Kezirian, Michael T.
2009-01-01
We analyze the potential for liner buckling in a 40-in Kevlar49/epoxy overwrapped spherical pressure vessel (COPV) due to long, local depressions or valleys in the titanium liner, which appeared after proof testing (autofrettage). We begin by presenting the geometric characteristics of approximately 20 mil (0.02 in.) deep depressions measured by laser profilometry in several vessels. While such depths were more typical, depths of more than 40 mils (0.02 in.) were seen near the equator in one particular vessel. Such depressions are largely the result of overlap of the edges of overwrap bands (with rectangular cross-section prepreg tows) from the first or second wrap patterns particularly where they start and end. We then discuss the physical mechanisms of formation of the depressions during the autofrettage process in terms of uneven void compaction in the overwrap around the tow overlap lines and the resulting 10-fold increase in through-thickness stiffness of the overwrap. We consider the effects of liner plastic yielding mechanisms in the liner on residual bending moments and interface pressures with the overwrap both at the peak proof pressure (approx.6500 psi) and when reducing the pressure to 0 psi. During depressurization the Bauschinger phenomenon becomes very important whereby extensive yielding in tension reduces the magnitude of the yield threshold in compression by 30 to 40%, compared to the virgin annealed state of the liner titanium. In the absence of a depression, the liner is elastically stable in compression even at liner overwrap interface pressures nominally 6 times the approx. 1000 psi interface pressure that exists at 0 psi. Using a model based on a plate-on-an-elastic-foundation, we develop an extensive analysis of the possible destabilizing effects of a frozen-in valley. The analysis treats the modifying effects of the residual bending moments and interface pressures remaining after the proof hold as well as the Bauschinger effect on the
Buckling instability in arteries.
Vandiver, Rebecca M
2015-04-21
Arteries can become tortuous in response to abnormal growth stimuli, genetic defects and aging. It is suggested that a buckling instability is a mechanism that might lead to artery tortuosity. Here, the buckling instability in arteries is studied by examining asymmetric modes of bifurcation of two-layer cylindrical structures that are residually stressed. These structures are loaded by an axial force, internal pressure and have nonlinear, anisotropic, hyperelastic responses to stresses. Strain-softening and reduced opening angle are shown to lower the critical internal pressure leading to buckling. In addition, the ratio of the media thickness to the adventitia thickness is shown to have a dramatic impact on arterial instability. PMID:25661070
Buckling Behavior of Compression-Loaded Composite Cylindrical Shells with Reinforced Cutouts
NASA Technical Reports Server (NTRS)
Hilburger, Mark W.; Starnes, James H., Jr.
2002-01-01
Results from a numerical study of the response of thin-wall compression-loaded quasi-isotropic laminated composite cylindrical shells with reinforced and unreinforced square cutouts are presented. The effects of cutout reinforcement orthotropy, size, and thickness on the nonlinear response of the shells are described. A high-fidelity nonlinear analysis procedure has been used to predict the nonlinear response of the shells. The analysis procedure includes a nonlinear static analysis that predicts stable response characteristics of the shells and a nonlinear transient analysis that predicts unstable dynamic buckling response characteristics. The results illustrate how a compression-loaded shell with an unreinforced cutout can exhibit a complex nonlinear response. In particular, a local buckling response occurs in the shell near the cutout and is caused by a complex nonlinear coupling between local shell-wall deformations and in-plane destabilizing compression stresses near the cutout. In general, the addition of reinforcement around a cutout in a compression-loaded shell can retard or eliminate the local buckling response near the cutout and increase the buckling load of the shell, as expected. However, results are presented that show how certain reinforcement configurations can actually cause an unexpected increase in the magnitude of local deformations and stresses in the shell and cause a reduction in the buckling load. Specific cases are presented that suggest that the orthotropy, thickness, and size of a cutout reinforcement in a shell can be tailored to achieve improved response characteristics.
NASA Astrophysics Data System (ADS)
Kim, Nam-Il; Fu, Chung C.; Kim, Moon-Young
2007-02-01
Based on the power series method, the static and dynamic stiffness matrices for the flexural-torsional buckling and free vibration analysis of thin-walled beam with non-symmetric cross-section subjected to linearly variable axial force are newly presented. Additionally, the static stiffness matrix for the lateral buckling analysis of non-symmetric beam is presented for the first time. For this, the elastic strain energy, the potential energy considering the second-order terms of finite rotations, and the kinetic energy for thin-walled beam with non-symmetric cross-section are introduced. Then equations of motion and force-deformation relations are derived from the energy principle. Explicit expressions for displacement parameters are derived based on power series expansions of displacement components. Finally, the static and dynamic element stiffness matrices are determined using force-deformation relationships. In order to verify the accuracy of this study, the numerical solutions are presented and compared with the finite element solutions using the Hermitian beam elements and ABAQUS's shell elements.
Combined compressive and shear buckling analysis of hypersonic aircraft structural sandwich panels
NASA Technical Reports Server (NTRS)
Ko, William L.; Jackson, Raymond H.
1991-01-01
The combined-load (compression and shear) buckling equations were established for orthotropic sandwich panels by using the Rayleigh-Ritz method to minimize the panel total potential energy. The resulting combined-load buckling equations were used to generate buckling interaction curves for super-plastically-formed/diffusion-bonded titanium truss-core sandwich panels and titanium honeycomb-core sandwich panels having the same specific weight. The relative combined-load buckling strengths of these two types of sandwich panels are compared with consideration of their sandwich orientations. For square and nearly square panels of both types, the combined load always induces symmetric buckling. As the panel aspect ratios increase, antisymmetric buckling will show up when the loading is shear-dominated combined loading. The square panel (either type) has the highest combined buckling strength, but the combined load buckling strength drops sharply as the panel aspect ratio increases. For square panels, the truss-core sandwich panel has higher compression-dominated combined load buckling strength. However, for shear dominated loading, the square honeycomb-core sandwich panel has higher shear-dominated combined load buckling strength.
NASA Technical Reports Server (NTRS)
Hilburger, Mark W.; Nemeth, Michael P.; Riddick, Jaret C.; Thornburgh, Robert P.
2004-01-01
A parametric study of the effects of test-fixture-induced initial prestress and elastic edge restraints on the prebuckling and buckling responses of a compression-loaded, quasi-isotropic curved panel is presented. The numerical results were obtained by using a geometrically nonlinear finite element analysis code with high-fidelity models. The results presented show that a wide range of prebuckling and buckling behavior can be obtained by varying parameters that represent circumferential loaded-edge restraint and rotational unloaded-edge restraint provided by a test fixture and that represent the mismatch in specimen and test-fixture radii of curvature. For a certain range of parameters, the panels exhibit substantial nonlinear prebuckling deformations that yield buckling loads nearly twice the corresponding buckling load predicted by a traditional linear bifurcation buckling analysis for shallow curved panels. In contrast, the results show another range of parameters exist for which the nonlinear prebuckling deformations either do not exist or are relatively benign, and the panels exhibit buckling loads that are nearly equal to the corresponding linear bifurcation buckling load. Overall, the results should also be of particular interest to scientists, engineers, and designers involved in simulating flight-hardware boundary conditions in structural verification and certification tests, involved in validating structural analysis tools, and interested in tailoring buckling performance.
Design, Analysis, and On-Sun Evaluation of Reflective Strips Under Controlled Buckling
NASA Technical Reports Server (NTRS)
Jaworske, D. A.; Sechkar, E. A.; Colozza, A. J.
2014-01-01
Solar concentrators are envisioned for use in a variety of space-based applications, including applications involving in situ resource utilization. Identifying solar concentrators that minimize mass and cost are of great interest, especially since launch cost is driven in part by the mass of the payload. Concentrators must also be able to survive the wide temperature excursions on the lunar surface. Identifying smart structures which compensate for changes in concentrator geometry brought about by temperature extremes are of interest. Some applications may benefit from the ability to change the concentrator's focal pattern at will. This paper addresses a method of designing a single reflective strip to produce a desired focal pattern through the use of controlled buckling. Small variations in the cross section over the length of the reflective strip influence the distribution of light in the focal region. A finite element method of analysis is utilized here which calculates the curve produced for a given strip cross section and axial load. Varying axial force and strip cross section over the length of the reflective strip provide a means of optimizing ray convergence in the focal region. Careful selection of a tapered cross section yields a reflective strip that approximates a parabola. An array of reflective strips under controlled buckling produces a light weight concentrator and adjustments in the compression of individual strips provide a means of compensating for temperature excursions or changing the focal pattern at will.
Design, Analysis, and On-Sun Evaluation of Reflective Strips Under Controlled Buckling
NASA Technical Reports Server (NTRS)
Jaworske, Donald A.; Sechkar, Edward A.; Colozza, Anthony J.
2014-01-01
Solar concentrators are envisioned for use in a variety of space-based applications, including applications involving in situ resource utilization. Identifying solar concentrators that minimize mass and cost are of great interest, especially since launch cost is driven in part by the mass of the payload. Concentrators must also be able to survive the wide temperature excursions on the lunar surface. Identifying smart structures which compensate for changes in concentrator geometry brought about by temperature extremes are of interest. Some applications may benefit from the ability to change the concentrators focal pattern at will. This paper addresses a method of designing a single reflective strip to produce a desired focal pattern through the use of controlled buckling. Small variations in the cross section over the length of the reflective strip influence the distribution of light in the focal region. A finite element method of analysis is utilized here which calculates the curve produced for a given strip cross section and axial load. Varying axial force and strip cross section over the length of the reflective strip provide a means of optimizing ray convergence in the focal region. Careful selection of a tapered cross section yields a reflective strip that approximates a parabola. An array of reflective strips under controlled buckling produces a light weight concentrator and adjustments in the compression of individual strips provide a means of compensating for temperature excursions or changing the focal pattern at will.
Mechanical and thermal buckling analysis of sandwich panels under different edge conditions
NASA Technical Reports Server (NTRS)
Ko, William L.
1993-01-01
By using the Rayleigh-Ritz method of minimizing the total potential energy of a structural system, combined load (mechanical or thermal load) buckling equations are established for orthotropic rectangular sandwich panels supported under four different edge conditions. Two-dimensional buckling interaction curves and three dimensional buckling interaction surfaces are constructed for high-temperature honeycomb-core sandwich panels supported under four different edge conditions. The interaction surfaces provide easy comparison of the panel buckling strengths and the domains of symmetrical and antisymmetrical buckling associated with the different edge conditions. Thermal buckling curves of the sandwich panels also are presented. The thermal buckling conditions for the cases with and without thermal moments were found to be identical for the small deformation theory. In sandwich panels, the effect of transverse shear is quite large, and by neglecting the transverse shear effect, the buckling loads could be overpredicted considerably. Clamping of the edges could greatly increase buckling strength more in compression than in shear.
NASA Technical Reports Server (NTRS)
Stein, M.; Housner, J. D.
1978-01-01
A numerical analysis developed for the buckling of rectangular orthotropic layered panels under combined shear and compression is described. This analysis uses a central finite difference procedure based on trigonometric functions instead of using the conventional finite differences which are based on polynomial functions. Inasmuch as the buckle mode shape is usually trigonometric in nature, the analysis using trigonometric finite differences can be made to exhibit a much faster convergence rate than that using conventional differences. Also, the trigonometric finite difference procedure leads to difference equations having the same form as conventional finite differences; thereby allowing available conventional finite difference formulations to be converted readily to trigonometric form. For two-dimensional problems, the procedure introduces two numerical parameters into the analysis. Engineering approaches for the selection of these parameters are presented and the analysis procedure is demonstrated by application to several isotropic and orthotropic panel buckling problems. Among these problems is the shear buckling of stiffened isotropic and filamentary composite panels in which the stiffener is broken. Results indicate that a break may degrade the effect of the stiffener to the extent that the panel will not carry much more load than if the stiffener were absent.
High-Fidelity Nonlinear Analysis of Compression-Loaded Composite Shells
NASA Technical Reports Server (NTRS)
Hilburger, Mark W.; Starnes, James H., Jr.
2001-01-01
The results of an experimental and analytical study of the effects of initial imperfections on the buckling and postbuckling response of unstiffened thin-walled compression-loaded graphite-epoxy cylindrical shells are presented. The shells considered in the study have four different shell-wall laminates and two different shell-radius-to-thickness ratios. The shell-wall laminates include two different orthotropic laminates and two different quasi-isotropic laminates. The shell-radius-to-thickness ratios include shell-radius-to-thickness ratios equal to 100 and 200. The results identify the effects of traditional and nontraditional initial imperfections on the nonlinear response characteristics and buckling loads of the shells. The traditional imperfections include the geometric shell-wall mid-surface imperfections that are commonly discussed in the literature on thin shell buckling. The nontraditional imperfections include shell-wall thickness variations, local shell-wall ply-gaps associated with the fabrication process, shell-end geometric imperfections, nonuniform applied end loads, and variations in the boundary conditions including the effects of elastic boundary conditions. A high-fidelity nonlinear shell analysis procedure that accurately accounts for the effects of these traditional and nontraditional imperfections on the nonlinear response characteristics and buckling loads of the shells is described. The analysis procedure includes a nonlinear static analysis that predicts the stable response characteristics of the shells, and a nonlinear transient analysis that predicts the unstable response characteristics. The results of a local shell-wall stress analysis used to estimate failure stresses are also described.
Dynamic buckling analysis of delaminated composite plates using semi-analytical finite strip method
NASA Astrophysics Data System (ADS)
Ovesy, H. R.; Totounferoush, A.; Ghannadpour, S. A. M.
2015-05-01
The delamination phenomena can become of paramount importance when the design of the composite plates is concerned. In the current study, the effect of through-the-width delamination on dynamic buckling behavior of a composite plate is studied by implementing semi-analytical finite strip method. In this method, the energy and work integrations are computed analytically due to the implementation of trigonometric functions. Moreover, the method can lead to converged results with comparatively small number of degrees of freedom. These features have made the method quite efficient. To account for delamination effects, displacement field is enriched by adding appropriate terms. Also, the penetration of the delamination surfaces is prevented by incorporating an appropriate contact scheme into the time response analysis. Some selected results are validated against those available in the literature.
Analyses of Buckling and Stable Tearing in Thin-Sheet Materials
NASA Technical Reports Server (NTRS)
Seshadri, B. R.; Newman, J. C., Jr.
1998-01-01
This paper was to verify the STAGS (general shell, geometric and material nonlinear) code and the critical crack tip opening angle (CTOA) fracture criterion for predicting stable tearing in cracked panels that fail with severe out of plane buckling. Materials considered ranged from brittle to ductile behavior. Test data used in this study are reported elsewhere. The STAGS code was used to model stable tearing using a critical CTOA value that was determined from a cracked panel that was 'restrained' from buckling. ne analysis methodology was then used to predict the influence of buckling on stable tearing and failure loads. Parameters like crack length to specimen width ratio, crack configuration, thickness, and material tensile properties had a significant influence on the buckling behavior of cracked thin sheet materials. Experimental and predicted results showed a varied buckling response for different crack length to sheet thickness ratios because different buckling modes were activated. Effects of material tensile properties and fracture toughness on buckling response were presented. The STAGS code and the CTOA fracture criterion were able to predict the influence of buckling on stable tearing behavior and failure loads on a variety of materials and crack configurations.
Artery buckling analysis using a two-layered wall model with collagen dispersion.
Mottahedi, Mohammad; Han, Hai-Chao
2016-07-01
Artery buckling has been proposed as a possible cause for artery tortuosity associated with various vascular diseases. Since microstructure of arterial wall changes with aging and diseases, it is essential to establish the relationship between microscopic wall structure and artery buckling behavior. The objective of this study was to developed arterial buckling equations to incorporate the two-layered wall structure with dispersed collagen fiber distribution. Seven porcine carotid arteries were tested for buckling to determine their critical buckling pressures at different axial stretch ratios. The mechanical properties of these intact arteries and their intima-media layer were determined via pressurized inflation test. Collagen alignment was measured from histological sections and modeled by a modified von-Mises distribution. Buckling equations were developed accordingly using microstructure-motivated strain energy function. Our results demonstrated that collagen fibers disperse around two mean orientations symmetrically to the circumferential direction (39.02°±3.04°) in the adventitia layer; while aligning closely in the circumferential direction (2.06°±3.88°) in the media layer. The microstructure based two-layered model with collagen fiber dispersion described the buckling behavior of arteries well with the model predicted critical pressures match well with the experimental measurement. Parametric studies showed that with increasing fiber dispersion parameter, the predicted critical buckling pressure increases. These results validate the microstructure-based model equations for artery buckling and set a base for further studies to predict the stability of arteries due to microstructural changes associated with vascular diseases and aging. PMID:27031686
Shell Buckling Design Criteria Based on Manufacturing Imperfection Signatures
NASA Technical Reports Server (NTRS)
Hilburger, Mark W.; Nemeth, Michael P.; Starnes, James H., Jr.
2004-01-01
An analysis-based approach .for developing shell-buckling design criteria for laminated-composite cylindrical shells that accurately accounts for the effects of initial geometric imperfections is presented. With this approach, measured initial geometric imperfection data from six graphite-epoxy shells are used to determine a manufacturing-process-specific imperfection signature for these shells. This imperfection signature is then used as input into nonlinear finite-element analyses. The imperfection signature represents a "first-approximation" mean imperfection shape that is suitable for developing preliminary-design data. Comparisons of test data and analytical results obtained by using several different imperfection shapes are presented for selected shells. Overall, the results indicate that the analysis-based approach presented for developing reliable preliminary-design criteria has the potential to provide improved, less conservative buckling-load estimates, and to reduce the weight and cost of developing buckling-resistant shell structures.
The secondary buckling transition: wrinkling of buckled spherical shells.
Knoche, Sebastian; Kierfeld, Jan
2014-07-01
We theoretically explain the complete sequence of shapes of deflated spherical shells. Decreasing the volume, the shell remains spherical initially, then undergoes the classical buckling instability, where an axisymmetric dimple appears, and, finally, loses its axisymmetry by wrinkles developing in the vicinity of the dimple edge in a secondary buckling transition. We describe the first axisymmetric buckling transition by numerical integration of the complete set of shape equations and an approximate analytic model due to Pogorelov. In the buckled shape, both approaches exhibit a locally compressive hoop stress in a region where experiments and simulations show the development of polygonal wrinkles, along the dimple edge. In a simplified model based on the stability equations of shallow shells, a critical value for the compressive hoop stress is derived, for which the compressed circumferential fibres will buckle out of their circular shape in order to release the compression. By applying this wrinkling criterion to the solutions of the axisymmetric models, we can calculate the critical volume for the secondary buckling transition. Using the Pogorelov approach, we also obtain an analytical expression for the critical volume at the secondary buckling transition: The critical volume difference scales linearly with the bending stiffness, whereas the critical volume reduction at the classical axisymmetric buckling transition scales with the square root of the bending stiffness. These results are confirmed by another stability analysis in the framework of Donnel, Mushtari and Vlasov (DMV) shell theory, and by numerical simulations available in the literature. PMID:25039007
NASA Technical Reports Server (NTRS)
Hilburger, Mark W.; Lovejoy, Andrew E.; Thornburgh, Robert P.; Rankin, Charles
2012-01-01
NASA s Shell Buckling Knockdown Factor (SBKF) project has the goal of developing new analysis-based shell buckling design factors (knockdown factors) and design and analysis technologies for launch vehicle structures. Preliminary design studies indicate that implementation of these new knockdown factors can enable significant reductions in mass and mass-growth in these vehicles. However, in order to validate any new analysis-based design data or methods, a series of carefully designed and executed structural tests are required at both the subscale and full-scale levels. This paper describes the design and analysis of three different orthogrid-stiffeNed metallic cylindrical-shell test articles. Two of the test articles are 8-ft-diameter, 6-ft-long test articles, and one test article is a 27.5-ft-diameter, 20-ft-long Space Shuttle External Tank-derived test article.
Probabilistic progressive buckling of trusses
NASA Technical Reports Server (NTRS)
Pai, Shantaram S.; Chamis, Christos C.
1991-01-01
A three-bay, space, cantilever truss is probabilistically evaluated to describe progressive buckling and truss collapse in view of the numerous uncertainties associated with the structural, material, and load variables (primitive variables) that describe the truss. Initially, the truss is deterministically analyzed for member forces, and member(s) in which the axial force exceeds the Euler buckling load are identified. These member(s) are then discretized with several intermediate nodes and a probabilistic buckling analysis is performed on the truss to obtain its probabilistic buckling loads and respective mode shapes. Furthermore, sensitivities associated with the uncertainties in the primitive variables are investigated, margin of safety values for the truss are determined, and truss end node displacements are noted. These steps are repeated by sequentially removing the buckled member(s) until onset of truss collapse is reached. Results show that this procedure yields an optimum truss configuration for a given loading and for a specified reliability.
NASA Technical Reports Server (NTRS)
Housner, J. M.; Stein, M.
1975-01-01
A computer program is presented which was developed for the combined compression and shear of stiffened variable thickness orthotropic composite panels on discrete springs: boundary conditions are general and include elastic boundary restraints. Buckling solutions are obtained by using a newly developed trigonometric finite difference procedure which improves the solution convergence rate over conventional finite difference methods. The classical general shear buckling results which exist only for simply supported panels over a limited range of orthotropic properties, were extended to the complete range of these properties for simply supported panels and, in addition, to the complete range of orthotropic properties for clamped panels. The program was also applied to parametric studies which examine the effect of filament orientation upon the buckling of graphite-epoxy panels. These studies included an examination of the filament orientations which yield maximum shear or compressive buckling strength for panels having all four edges simply supported or clamped over a wide range of aspect ratios. Panels with such orientations had higher buckling loads than comparable, equal weight, thin skinned aluminum panels. Also included among the parameter studies were examinations of combined axial compression and shear buckling and examinations of panels with rotational elastic edge restraints.
Investigations on Buckling Behaviour of Laminated Curved Composite Stiffened Panels
NASA Astrophysics Data System (ADS)
Kumar, N. Jeevan; Babu, P. Ramesh; Pandu, Ratnakar
2014-04-01
In Industrial applications structural efficiency is primary concern, this brings about the need of strong and lightweight materials. Due to their high specific strength, fibre reinforced polymers find wide application in these areas. Panels made of composite materials are widely used in aerospace structures, automobile, civil, marine and biomedical industries because of their good mechanical properties, impact resistance, excellent damage tolerance and also low fabrication cost. In this Paper, buckling and post-buckling analysis was performed on composite stiffened panel to obtain the critical load and modes of failures, with different parameters like ply-orientation, different composite materials, and stiffeners and by changing the number of stiffeners was derived. To analyze the post buckling behaviour of composite stiffened panels the nonlinear finite element analysis is employed and substantial investigations are undertaken using finite element (FE) model. Effect of critical parameters on buckling behaviour is studied and parametric studies were conducted with analytical tool to understand the structural behaviour in the post buckling range.
Buckling failures in insect exoskeletons.
Parle, Eoin; Herbaj, Simona; Sheils, Fiona; Larmon, Hannah; Taylor, David
2016-02-01
Thin walled tubes are often used for load-bearing structures, in nature and in engineering, because they offer good resistance to bending and torsion at relatively low weight. However, when loaded in bending they are prone to failure by buckling. It is difficult to predict the loading conditions which cause buckling, especially for tubes whose cross sections are not simple shapes. Insights into buckling prevention might be gained by studying this phenomenon in the exoskeletons of insects and other arthropods. We investigated the leg segments (tibiae) of five different insects: the locust (Schistocerca gergaria), American cockroach (Periplaneta americana), death's head cockroach (Blaberus discoidalis), stick insect (Parapachymorpha zomproi) and bumblebee (Bombus terrestris audax). These were tested to failure in cantilever bending and modelled using finite element analysis (FEA). The tibiae of the locust and the cockroaches were found to be approximately circular in shape. Their buckling loads were well predicted by linear elastic FEA, and also by one of the analytical solutions available in the literature for elastic buckling. The legs of the stick insect are also circular in cross section but have several prominent longitudinal ridges. We hypothesised that these ridges might protect the legs against buckling but we found that this was not the case: the loads necessary for elastic buckling were not reached in practice because yield occurred in the material, causing plastic buckling. The legs of bees have a non-circular cross section due to a pollen-carrying feature (the corbicula). We found that this did not significantly affect their resistance to buckling. Our results imply that buckling is the dominant failure mode in the tibia of insects; it likely to be a significant consideration for other arthropods and any organisms with stiff exoskeletons. The interactions displayed here between material properties and cross sectional geometry may provide insights for the
Buckle driven delamination in thin hard film compliant substrate systems.
Cordill, Megan J.; Adams, David Price; Moody, Neville Reid; Corona, Edmundo; Kennedy, Marian S.; Bahr, David F.; Reedy, Earl David, Jr.
2010-06-01
rigid elastic solutions. To address this issue we developed a finite element analysis technique that employed a cohesive zone model to simulate interfacial crack growth. Specifying the traction-separation relationship, cohesive strength, and work of separation along with film thickness, film stress, and film and substrate properties, buckle width and height were determined as a function of interfacial toughness. The simulations indicate that an analysis based on rigid substrate solutions significantly underestimate toughness for prescribed buckle widths: a result consistent with an analysis by Yu and Hutchinson that pieced together a solution based on non-linear plate theory with a solution for the linear film on substrate problem. More importantly, the results defined a lower limiting bound to seemingly disparate buckle deflection data. The variance from linear elastic behavior, especially for the small buckles, indicates more than substrate compliance is controlling behavior. Comparison of the experimental results with cohesive zone simulations suggests that the two buckle behaviors are associated with different levels of substrate yielding. In this presentation we will use the results to show how substrate compliance and deformation affect delamination and buckling of films on compliant substrates and provide a means to predict device performance.
Non-isothermal buckling behavior of viscoplastic shell structures
NASA Technical Reports Server (NTRS)
Riff, Richard; Simitses, G. J.
1988-01-01
Described are the mathematical model and solution methodologies for analyzing the structural response of thin, metallic elasto-viscoplastic shell structures under large thermomechanical loads and their non-isothermal buckling behavior. Among the system responses associated with these loads and conditions are snap-through, buckling, thermal buckling, and creep buckling. This geometric and material nonlinearities (of high order) can be anticipated and are considered in the model and the numerical treatment.
Pre-Test Analysis Predictions for the Shell Buckling Knockdown Factor Checkout Tests - TA01 and TA02
NASA Technical Reports Server (NTRS)
Thornburgh, Robert P.; Hilburger, Mark W.
2011-01-01
This report summarizes the pre-test analysis predictions for the SBKF-P2-CYL-TA01 and SBKF-P2-CYL-TA02 shell buckling tests conducted at the Marshall Space Flight Center (MSFC) in support of the Shell Buckling Knockdown Factor (SBKF) Project, NASA Engineering and Safety Center (NESC) Assessment. The test article (TA) is an 8-foot-diameter aluminum-lithium (Al-Li) orthogrid cylindrical shell with similar design features as that of the proposed Ares-I and Ares-V barrel structures. In support of the testing effort, detailed structural analyses were conducted and the results were used to monitor the behavior of the TA during the testing. A summary of predicted results for each of the five load sequences is presented herein.
Analysis of bending and buckling of pre-twisted beams: A bioinspired study
NASA Astrophysics Data System (ADS)
Zhao, Zi-Long; Zhao, Hong-Ping; Chang, Zheng; Feng, Xi-Qiao
2014-08-01
Twisting chirality is widely observed in artificial and natural materials and structures at different length scales. In this paper, we theoretically investigate the effect of twisting chiral morphology on the mechanical properties of elastic beams by using the Timoshenko beam model. Particular attention is paid to the transverse bending and axial buckling of a pre-twisted rectangular beam. The analytical solution is first derived for the deflection of a clamped-free beam under a uniformly or periodically distributed transverse force. The critical buckling condition of the beam subjected to its self-weight and an axial compressive force is further solved. The results show that the twisting morphology can significantly improve the resistance of beams to both transverse bending and axial buckling. This study helps understand some phenomena associated with twisting chirality in nature and provides inspirations for the design of novel devices and structures.
Buckling Analysis of Anisotropic Curved Panels and Shells with Variable Curvature
NASA Technical Reports Server (NTRS)
Jaunky, Navin; Knight, Norman F., Jr.; Ambur, Damodar R.
1998-01-01
A buckling formulation for anisotropic curved panels with variable curvature is presented in this paper. The variable curvature panel is assumed to consists of two or more panels of constant but different curvatures. Bezier functions are used as Ritz functions Displacement (C(sup 0)), and slope (C(sup 1)) continuities between segments are imposed by manipulation of the Bezier control points. A first-order shear-deformation theory is used in the buckling formulation. Results obtained from the present formulation are compared with those from finite element simulations and are found to be in good agreement.
Buckling Behavior of Compression-Loaded Composite Cylindrical Shells With Reinforced Cutouts
NASA Technical Reports Server (NTRS)
Hilburger, Mark W.; Sarnes, James H., Jr.
2004-01-01
Results from a numerical study of the response of thin-walled compression-loaded quasi-isotropic laminated composite cylindrical shells with unreinforced and reinforced square cutouts are presented. The effects of cutout reinforcement orthotropy, size, and thickness on the nonlinear response of the shells are described. A nonlinear analysis procedure has been used to predict the nonlinear response of the shells. The results indicate that a local buckling response occurs in the shell near the cutout when subjected to load and is caused by a nonlinear coupling between local shell-wall deformations and in-plane destabilizing compression stresses near the cutout. In general, reinforcement around a cutout in a compression-loaded shell is shown to retard or eliminate the local buckling response near the cutout and increase the buckling load of the shell. However, some results show that certain reinforcement configurations can cause an unexpected increase in the magnitude of local deformations and stresses in the shell and cause a reduction in the buckling load. Specific cases are presented that suggest that the orthotropy, thickness, and size of a cutout reinforcement in a shell can be tailored to achieve improved buckling response characteristics.
Nonlinear analysis of pupillary dynamics.
Onorati, Francesco; Mainardi, Luca Tommaso; Sirca, Fabiola; Russo, Vincenzo; Barbieri, Riccardo
2016-02-01
Pupil size reflects autonomic response to different environmental and behavioral stimuli, and its dynamics have been linked to other autonomic correlates such as cardiac and respiratory rhythms. The aim of this study is to assess the nonlinear characteristics of pupil size of 25 normal subjects who participated in a psychophysiological experimental protocol with four experimental conditions, namely “baseline”, “anger”, “joy”, and “sadness”. Nonlinear measures, such as sample entropy, correlation dimension, and largest Lyapunov exponent, were computed on reconstructed signals of spontaneous fluctuations of pupil dilation. Nonparametric statistical tests were performed on surrogate data to verify that the nonlinear measures are an intrinsic characteristic of the signals. We then developed and applied a piecewise linear regression model to detrended fluctuation analysis (DFA). Two joinpoints and three scaling intervals were identified: slope α0, at slow time scales, represents a persistent nonstationary long-range correlation, whereas α1 and α2, at middle and fast time scales, respectively, represent long-range power-law correlations, similarly to DFA applied to heart rate variability signals. Of the computed complexity measures, α0 showed statistically significant differences among experimental conditions (p<0.001). Our results suggest that (a) pupil size at constant light condition is characterized by nonlinear dynamics, (b) three well-defined and distinct long-memory processes exist at different time scales, and (c) autonomic stimulation is partially reflected in nonlinear dynamics. PMID:26351899
A novel method for studying the buckling of nanotubes considering geometrical imperfections
NASA Astrophysics Data System (ADS)
Anoop Krishnan, N. M.; Ghosh, Debraj
2014-05-01
Buckling of nanotubes has been studied using many methods such as molecular dynamics (MD), molecular mechanics, and continuum-based shell theories. In MD, motion of the individual atoms is tracked under applied temperature and pressure, ensuring a reliable estimate of the material response. The response thus simulated varies for individual nanotubes and is only as accurate as the force field used to model the atomic interactions. On the other hand, there exists a rich literature on the understanding of continuum mechanics-based shell theories. Based on the observations on the behavior of nanotubes, there have been a number of shell theory-based approaches to study the buckling of nanotubes. Although some of these methods yield a reasonable estimate of the buckling stress, investigation and comparison of buckled mode shapes obtained from continuum analysis and MD are sparse. Previous studies show that the direct application of shell theories to study nanotube buckling often leads to erroneous results. The present study reveals that a major source of this error can be attributed to the departure of the shape of the nanotube from a perfect cylindrical shell. Analogous to the shell buckling in the macro-scale, in this work, the nanotube is modeled as a thin-shell with initial imperfection. Then, a nonlinear buckling analysis is carried out using the Riks method. It is observed that this proposed approach yields significantly improved estimate of the buckling stress and mode shapes. It is also shown that the present method can account for the variation of buckling stress as a function of the temperature considered. Hence, this can prove to be a robust method for a continuum analysis of nanosystems taking in the effect of variation of temperature as well.
Effects of Imperfections on the Buckling Response of Compression-Loaded Composite Shells
NASA Technical Reports Server (NTRS)
Hilburger, Mark W.; Starnes, James H., Jr.
2002-01-01
The results of an experimental and analytical study of the effects of initial imperfections on the buckling and postbuckling response of three unstiffened thin-walled compression-loaded graphite-epoxy cylindrical shells with different orthotropic and quasi-isotropic shell-wall laminates are presented. The results identify the effects of traditional and non-traditional initial imperfections on the non-linear response and buckling loads of the shells. The traditional imperfections include the geometric shell-wall mid-surface imperfect ions that are commonly discussed in the literature on thin shell buckling. The non-traditional imperfections include shell-wall thickness variations local shell-wall ply-gaps associated with the fabrication process, sheltered geometric imperfections, non-uniform applied end loads, and variations in the boundary conditions including the effects of elastic boundary conditions. A high-fidelity non-linear shell analysis procedure that accurately accounts for the effects of these traditional and non-traditional imperfections on the nonlinear response, and buckling loads of the shells is described. The analysis procedure includes a non-linear static analysis that predicts stable response characteristics of the shells and a non-linear transient analysis that predicts unstable response characteristics.
Thermal-structural panel buckling tests
NASA Technical Reports Server (NTRS)
Thompson, Randolph C.; Richards, W. Lance
1991-01-01
The buckling characteristics of a titanium matrix composite hat-stiffened panel were experimentally examined for various combinations of thermal and mechanical loads. Panel failure was prevented by maintaining the applied loads below real-time critical buckling predictions. The test techniques used to apply the loads, minimize boundary were shown to compare well with a finite-element buckling analysis for previous panels. Comparisons between test predictions and analysis for this panel are ongoing.
Mechanics of precisely controlled thin film buckling on Elastomeric substrate.
Sun, Y.; Jiang, H.; Rogers, J.; Huang, Y.; Arizone State Univ.; Beckman Inst.; University of Illinois Urbana-Champaign
2007-01-01
Stretchable electronics has many important and emerging applications. Sun et al. [Nature Nanotech. 1, 201 (2006)] recently demonstrated stretchable electronics based on precisely controlled buckle geometries in GaAs and Si nanoribbons on elastomeric substrates. A nonlinear buckling model is presented in this letter to study the mechanics of this type of thin film/substrate system. An analytical solution is obtained for the buckling geometry (wavelength and amplitude) and the maximum strain in buckled thin film. This solution agrees very well with the experiments, and shows explicitly how buckling can significantly reduce the thin film strain to achieve the system stretchability.
Experimental analysis of buckling in aircraft skin panels by fibre optic sensors
NASA Astrophysics Data System (ADS)
Güemes, J. A.; Menendez, J. M.; Frövel, M.; Fernandez, I.; Pintado, J. M.
2001-06-01
Three blade-stiffened CFRP panels with co-cured stiffener webs, manufactured by means of an elastomeric mould, have been tested under compressive load. Several Bragg grating sensors have been surface bonded on two of the stiffened panels and have been embedded into the stiffener webs of the third panel. The Bragg grating sensors measured the strain distribution in the stiffener web and in the skin panels. The bucking onset was clearly detected in every case, the post-buckling behaviour can be tracked, but the information is heavily dependent on the right choice of the sensor position and the buckling mode. To calibrate the system, and to evaluate the influence of different curing pressures, and the use of unidirectional or fabric prepreg material, tensile test specimens were made on flat panels. The strain measurements provided by the optical fibre sensors in tensile tests were compared with the strain measurements provided by conventional clamp extensometers.
NASA Astrophysics Data System (ADS)
Lai, Changliang; Wang, Junbiao; Liu, Chuang
2014-10-01
Six typical composite grid cylindrical shells are constructed by superimposing three basic types of ribs. Then buckling behavior and structural efficiency of these shells are analyzed under axial compression, pure bending, torsion and transverse bending by finite element (FE) models. The FE models are created by a parametrical FE modeling approach that defines FE models with original natural twisted geometry and orients cross-sections of beam elements exactly. And the approach is parameterized and coded by Patran Command Language (PCL). The demonstrations of FE modeling indicate the program enables efficient generation of FE models and facilitates parametric studies and design of grid shells. Using the program, the effects of helical angles on the buckling behavior of six typical grid cylindrical shells are determined. The results of these studies indicate that the triangle grid and rotated triangle grid cylindrical shell are more efficient than others under axial compression and pure bending, whereas under torsion and transverse bending, the hexagon grid cylindrical shell is most efficient. Additionally, buckling mode shapes are compared and provide an understanding of composite grid cylindrical shells that is useful in preliminary design of such structures.
Buckling of conical shell with local imperfections
NASA Technical Reports Server (NTRS)
Cooper, P. A.; Dexter, C. B.
1974-01-01
Small geometric imperfections in thin-walled shell structures can cause large reductions in buckling strength. Most imperfections found in structures are neither axisymmetric nor have the shape of buckling modes but rather occur locally. This report presents the results of a study of the effect of local imperfections on the critical buckling load of a specific axially compressed thin-walled conical shell. The buckling calculations were performed by using a two-dimensional shell analysis program referred to as the STAGS (Structural Analysis of General Shells) computer code, which has no axisymmetry restrictions. Results show that the buckling load found from a bifurcation buckling analysis is highly dependent on the circumferential arc length of the imperfection type studied. As the circumferential arc length of the imperfection is increased, a reduction of up to 50 percent of the critical load of the perfect shell can occur. The buckling load of the cone with an axisymmetric imperfections is nearly equal to the buckling load of imperfections which extended 60 deg or more around the circumference, but would give a highly conservative estimate of the buckling load of a shell with an imperfection of a more local nature.
Simplified dynamic buckling assessment of steel containments
Farrar, C.R.; Duffey, T.A.; Renick, D.H.
1993-02-01
A simplified, three-degree-of-freedom analytical procedure for performing a response spectrum buckling analysis of a thin containment shell is developed. Two numerical examples with R/t values which bound many existing steel containments are used to illustrate the procedure. The role of damping on incipient buckling acceleration level is evaluated for a regulatory seismic spectrum using the two numerical examples. The zero-period acceleration level that causes incipient buckling in either of the two containments increases 31% when damping is increased from 1% to 4% of critical. Comparisons with finite element results on incipient buckling levels are favorable.
Nonlinear Principal Components Analysis: Introduction and Application
ERIC Educational Resources Information Center
Linting, Marielle; Meulman, Jacqueline J.; Groenen, Patrick J. F.; van der Koojj, Anita J.
2007-01-01
The authors provide a didactic treatment of nonlinear (categorical) principal components analysis (PCA). This method is the nonlinear equivalent of standard PCA and reduces the observed variables to a number of uncorrelated principal components. The most important advantages of nonlinear over linear PCA are that it incorporates nominal and ordinal…
NASA Technical Reports Server (NTRS)
Anderson, Melvin S.; Kennedy, David
1993-01-01
The problem considered is the development of the necessary plate stiffnesses for use in the general purpose program VICONOPT for buckling and vibration of composite plate assemblies. The required stiffnesses include the effects of transverse shear deformation and are for sinusoidal response along the plate length as required in VICONOPT. The method is based on the exact solution of the plate differential equations for a composite laminate having fully populated A, B, and D stiffness matrices which leads to an ordinary differential equation of tenth order.
NASA Technical Reports Server (NTRS)
Jaunky, Navin; Knight, Norman F., Jr.; Ambur, Damodar R.
1995-01-01
A smeared stiffener theory for stiffened panels is presented that includes skin-stiffener interaction effects. The neutral surface profile of the skin-stiffener combination is developed analytically using the minimum potential energy principle and statics conditions. The skin-stiffener interaction is accounted for by computing the stiffness due to the stiffener and the skin in the skin-stiffener region about the neutral axis at the stiffener. Buckling load results for axially stiffened, orthogrid, and general grid-stiffened panels are obtained using the smeared stiffness combined with a Rayleigh-Ritz method and are compared with results from detailed finite element analyses.
Initial post-buckling of variable-stiffness curved panels
NASA Astrophysics Data System (ADS)
White, S. C.; Raju, G.; Weaver, P. M.
2014-11-01
Variable-stiffness shells are curved composite structures in which the fibre-reinforcement follow curvilinear paths in space. Having a wider design space than traditional composite shells, they have the potential to improve a wide variety of weight-critical structures. In this paper, a new method for computing the initial post-buckling response of variable-stiffness cylindrical panels is presented, based on the differential quadrature method. Integro-differential governing and boundary equations governing the problem, derived with Koiter's theory (Koiter, 1945), are solved using a mixed generalised differential quadrature (GDQ) and integral quadrature (GIQ) approach. The post-buckling behaviour is determined on the basis of a quadratic expansion of the displacement fields. Orthogonality of the mode-shapes in the expansion series is ensured by a novel use of the Moore-Penrose generalised matrix inverse for solving the GDQ-GIQ equations. The new formulation is validated against benchmark analytical post-buckling results for constant stiffness plates and shells, and compared with non-linear finite-element (FE) analysis for variable-stiffness shells. Stability estimates are found to be in good agreement with incremental FE results in the vicinity of the buckling load, requiring only a fraction of the number of variables used by the current method.
Buckling analysis of moderately thick rectangular plates using coupled displacement field method
NASA Astrophysics Data System (ADS)
Meera Saheb, K.; Aruna, K.
2015-12-01
A simple and efficient coupled displacement field method is developed to study the buckling load parameters of the moderately thick rectangular plates. This method has been successfully applied to study the same for the Timoshenko beams. A single term trigonometric admissible displacement field is assumed for one of the variables, say, the total rotations (in both X, Y directions). Making use of the coupling equations, the spatial variation for the remaining lateral displacement field is derived in terms of the total rotations. The coupled displacement field method makes the energy formulation to contains half the number of unknown independent coefficients, in the case of a rectangular plate, contrary to the conventional Rayleigh-Ritz method. The expressions for the non-dimensional buckling load parameters of the moderately thick rectangular plates with all the edges simply supported are derived. The numerical values of these parameters obtained using the coupled displacement field method match very well with open literature demonstrating the effectiveness of the coupled displacement field method.
NASA Astrophysics Data System (ADS)
Rahmani, O.; Jandaghian, A. A.
2015-06-01
In this paper, a general third-order beam theory that accounts for nanostructure-dependent size effects and two-constituent material variation through the nanobeam thickness, i.e., functionally graded material (FGM) beam is presented. The material properties of FG nanobeams are assumed to vary through the thickness according to the power law. A detailed derivation of the equations of motion based on Eringen nonlocal theory using Hamilton's principle is presented, and a closed-form solution is derived for buckling behavior of the new model with various boundary conditions. The nonlocal elasticity theory includes a material length scale parameter that can capture the size effect in a functionally graded material. The proposed model is efficient in predicting the shear effect in FG nanobeams by applying third-order shear deformation theory. The proposed approach is validated by comparing the obtained results with benchmark results available in the literature. In the following, a parametric study is conducted to investigate the influences of the length scale parameter, gradient index, and length-to-thickness ratio on the buckling of FG nanobeams and the improvement on nonlocal third-order shear deformation theory comparing with the classical (local) beam model has been shown. It is found out that length scale parameter is crucial in studying the stability behavior of the nanobeams.
NASA Technical Reports Server (NTRS)
Shuart, M. J.
1985-01-01
The short-wavelength buckling (or the microbuckling) and the interlaminar and inplane shear failures of multi-directional composite laminates loaded in uniaxial compression are investigated. A laminate model is presented that idealizes each lamina. The fibers in the lamina are modeled as a plate, and the matrix in the lamina is modeled as an elastic foundation. The out-of-plane w displacement for each plate is expressed as a trigonometric series in the half-wavelength of the mode shape for laminate short-wavelength buckling. Nonlinear strain-displacement relations are used. The model is applied to symmetric laminates having linear material behavior. The laminates are loaded in uniform end shortening and are simply supported. A linear analysis is used to determine the laminate stress, strain, and mode shape when short-wavelength buckling occurs. The equations for the laminate compressive stress at short-wavelength buckling are dominated by matrix contributions.
Nonlinear principal component analysis of climate data
Boyle, J.; Sengupta, S.
1995-06-01
This paper presents the details of the nonlinear principal component analysis of climate data. Topic discussed include: connection with principal component analysis; network architecture; analysis of the standard routine (PRINC); and results.
Buckling of Multiwall Carbon Nanotubes under Axial Compression
NASA Astrophysics Data System (ADS)
Akita, Seiji; Nishio, Mitsumasa; Nakayama, Yoshikazu
2006-06-01
We have investigated the axial buckling of multiwall nanotubes under the axial compression using nanomanipulation experiments and molecular dynamics (MD) simulations. Experimentally, Young’s moduli of nanotubes with different inner hollow diameters for the same outer diameters are consistent with the Eulers buckling model based on the continuum analysis. The MD simulations for the buckling behavior of triple- and double-walled nanotubes are also consistent with the continuum analysis. This good agreement indicates that Euler’s buckling model is applicable to the analysis of the axial buckling behavior of the multiwall nanotubes.
Nonlinear Analysis and Preliminary Testing Results of a Hybrid Wing Body Center Section Test Article
NASA Technical Reports Server (NTRS)
Przekop, Adam; Jegley, Dawn C.; Rouse, Marshall; Lovejoy, Andrew E.; Wu, Hsi-Yung T.
2015-01-01
A large test article was recently designed, analyzed, fabricated, and successfully tested up to the representative design ultimate loads to demonstrate that stiffened composite panels with through-the-thickness reinforcement are a viable option for the next generation large transport category aircraft, including non-conventional configurations such as the hybrid wing body. This paper focuses on finite element analysis and test data correlation of the hybrid wing body center section test article under mechanical, pressure and combined load conditions. Good agreement between predictive nonlinear finite element analysis and test data is found. Results indicate that a geometrically nonlinear analysis is needed to accurately capture the behavior of the non-circular pressurized and highly-stressed structure when the design approach permits local buckling.
Probabilistic Dynamic Buckling of Smart Composite Shells
NASA Technical Reports Server (NTRS)
Chamis, Christos C.; Abumeri, Galib H.
2007-01-01
A computational simulation method is presented to evaluate the deterministic and nondeterministic dynamic buckling of smart composite shells. The combined use of intraply hybrid composite mechanics, finite element computer codes, and probabilistic analysis enable the effective assessment of the dynamic buckling load of smart composite shells. A universal plot is generated to estimate the dynamic buckling load of composite shells at various load rates and probabilities. The shell structure is also evaluated with smart fibers embedded in the plies right next to the outer plies. The results show that, on the average, the use of smart fibers improved the shell buckling resistance by about 10% at different probabilities and delayed the buckling occurrence time. The probabilistic sensitivities results indicate that uncertainties in the fiber volume ratio and ply thickness have major effects on the buckling load while uncertainties in the electric field strength and smart material volume fraction have moderate effects. For the specific shell considered in this evaluation, the use of smart composite material is not recommended because the shell buckling resistance can be improved by simply re-arranging the orientation of the outer plies, as shown in the dynamic buckling analysis results presented in this report.
Probabilistic Dynamic Buckling of Smart Composite Shells
NASA Technical Reports Server (NTRS)
Abumeri, Galib H.; Chamis, Christos C.
2003-01-01
A computational simulation method is presented to evaluate the deterministic and nondeterministic dynamic buckling of smart composite shells. The combined use of composite mechanics, finite element computer codes, and probabilistic analysis enable the effective assessment of the dynamic buckling load of smart composite shells. A universal plot is generated to estimate the dynamic buckling load of composite shells at various load rates and probabilities. The shell structure is also evaluated with smart fibers embedded in the plies right below the outer plies. The results show that, on the average, the use of smart fibers improved the shell buckling resistance by about 10 percent at different probabilities and delayed the buckling occurrence time. The probabilistic sensitivities results indicate that uncertainties in the fiber volume ratio and ply thickness have major effects on the buckling load while uncertainties in the electric field strength and smart material volume fraction have moderate effects. For the specific shell considered in this evaluation, the use of smart composite material is not recommended because the shell buckling resistance can be improved by simply re-arranging the orientation of the outer plies, as shown in the dynamic buckling analysis results presented in this report.
NASA Technical Reports Server (NTRS)
Stoll, Frederick
1993-01-01
The NLPAN computer code uses a finite-strip approach to the analysis of thin-walled prismatic composite structures such as stiffened panels. The code can model in-plane axial loading, transverse pressure loading, and constant through-the-thickness thermal loading, and can account for shape imperfections. The NLPAN code represents an attempt to extend the buckling analysis of the VIPASA computer code into the geometrically nonlinear regime. Buckling mode shapes generated using VIPASA are used in NLPAN as global functions for representing displacements in the nonlinear regime. While the NLPAN analysis is approximate in nature, it is computationally economical in comparison with finite-element analysis, and is thus suitable for use in preliminary design and design optimization. A comprehensive description of the theoretical approach of NLPAN is provided. A discussion of some operational considerations for the NLPAN code is included. NLPAN is applied to several test problems in order to demonstrate new program capabilities, and to assess the accuracy of the code in modeling various types of loading and response. User instructions for the NLPAN computer program are provided, including a detailed description of the input requirements and example input files for two stiffened-panel configurations.
Nonlinear Finite Element Analysis of Shells with Large Aspect Ratio
NASA Technical Reports Server (NTRS)
Chang, T. Y.; Sawamiphakdi, K.
1984-01-01
A higher order degenerated shell element with nine nodes was selected for large deformation and post-buckling analysis of thick or thin shells. Elastic-plastic material properties are also included. The post-buckling analysis algorithm is given. Using a square plate, it was demonstrated that the none-node element does not have shear locking effect even if its aspect ratio was increased to the order 10 to the 8th power. Two sample problems are given to illustrate the analysis capability of the shell element.
NASA Technical Reports Server (NTRS)
Lovejoy, Andrew E.; Hilburger, Mark W.
2013-01-01
This document outlines a Modeling and Analysis Plan (MAP) to be followed by the SBKF analysts. It includes instructions on modeling and analysis formulation and execution, model verification and validation, identifying sources of error and uncertainty, and documentation. The goal of this MAP is to provide a standardized procedure that ensures uniformity and quality of the results produced by the project and corresponding documentation.
Design sensitivity analysis of nonlinear structural response
NASA Technical Reports Server (NTRS)
Cardoso, J. B.; Arora, J. S.
1987-01-01
A unified theory is described of design sensitivity analysis of linear and nonlinear structures for shape, nonshape and material selection problems. The concepts of reference volume and adjoint structure are used to develop the unified viewpoint. A general formula for design sensitivity analysis is derived. Simple analytical linear and nonlinear examples are used to interpret various terms of the formula and demonstrate its use.
Nonlinear Analysis of the Space Shuttle Superlightweight External Fuel Tank
NASA Technical Reports Server (NTRS)
Nemeth, Michael P.; Britt, Vicki O.; Collins, Timothy J.; Starnes, James H., Jr.
1996-01-01
Results of buckling and nonlinear analyses of the Space Shuttle external tank superlightweight liquid-oxygen (LO2) tank are presented. Modeling details and results are presented for two prelaunch loading conditions and for two full-scale structural tests that were conducted on the original external tank. The results illustrate three distinctly different types of nonlinear response for thin-walled shells subjected to combined mechanical and thermal loads. The nonlinear response phenomena consist of bifurcation-type buckling, short-wavelength nonlinear bending, and nonlinear collapse associated with a limit point. For each case, the results show that accurate predictions of non- linear behavior generally require a large-scale, high-fidelity finite-element model. Results are also presented that show that a fluid-filled launch-vehicle shell can be highly sensitive to initial geometric imperfections. In addition, results presented for two full-scale structural tests of the original standard-weight external tank suggest that the finite-element modeling approach used in the present study is sufficient for representing the nonlinear behavior of the superlightweight LO2 tank.
Geometrically Nonlinear Static Analysis of 3D Trusses Using the Arc-Length Method
NASA Technical Reports Server (NTRS)
Hrinda, Glenn A.
2006-01-01
Rigorous analysis of geometrically nonlinear structures demands creating mathematical models that accurately include loading and support conditions and, more importantly, model the stiffness and response of the structure. Nonlinear geometric structures often contain critical points with snap-through behavior during the response to large loads. Studying the post buckling behavior during a portion of a structure's unstable load history may be necessary. Primary structures made from ductile materials will stretch enough prior to failure for loads to redistribute producing sudden and often catastrophic collapses that are difficult to predict. The responses and redistribution of the internal loads during collapses and possible sharp snap-back of structures have frequently caused numerical difficulties in analysis procedures. The presence of critical stability points and unstable equilibrium paths are major difficulties that numerical solutions must pass to fully capture the nonlinear response. Some hurdles still exist in finding nonlinear responses of structures under large geometric changes. Predicting snap-through and snap-back of certain structures has been difficult and time consuming. Also difficult is finding how much load a structure may still carry safely. Highly geometrically nonlinear responses of structures exhibiting complex snap-back behavior are presented and analyzed with a finite element approach. The arc-length method will be reviewed and shown to predict the proper response and follow the nonlinear equilibrium path through limit points.
Buckling and vibration of a rotating beam†
NASA Astrophysics Data System (ADS)
Nachman, A.
1986-09-01
The equations for the vibration of a rotating beam, such as a helicopter blade, are exhibited. The beam is elastic (in general non-linearly so), the description is geometrically exact, the axis of rotation does not necessarily pass through the beam's clamped end (precession) and cross-sectional shearing is accounted for by using a director theory. Particular attention is paid to the impossibility of vibration (or buckling) confined to a plane making an angle β to the axis of rotation unless β=π/2 (orπ/2 or 0) or rotatory inertia is neglected. For purposed of illustration the analysis is specialized to describe Euler-Bernoulli and Timoshenko beams.
Buckling instability of self-assembled colloidal columns.
Swan, James W; Vasquez, Paula A; Furst, Eric M
2014-09-26
Suspended, slender self-assembled domains of magnetically responsive colloids are observed to buckle in microgravity. Upon cessation of the magnetic field that drives their assembly, these columns expand axially and buckle laterally. This phenomenon resembles the buckling of long beams due to thermal expansion; however, linear stability analysis predicts that the colloidal columns are inherently susceptible to buckling because they are freely suspended in a Newtonian fluid. The dominant buckling wavelength increases linearly with column thickness and is quantitatively described using an elastohydrodynamic model and the suspension thermodynamic equation of state. PMID:25302919
Buckling Instability of Self-Assembled Colloidal Columns
NASA Astrophysics Data System (ADS)
Swan, James W.; Vasquez, Paula A.; Furst, Eric M.
2014-09-01
Suspended, slender self-assembled domains of magnetically responsive colloids are observed to buckle in microgravity. Upon cessation of the magnetic field that drives their assembly, these columns expand axially and buckle laterally. This phenomenon resembles the buckling of long beams due to thermal expansion; however, linear stability analysis predicts that the colloidal columns are inherently susceptible to buckling because they are freely suspended in a Newtonian fluid. The dominant buckling wavelength increases linearly with column thickness and is quantitatively described using an elastohydrodynamic model and the suspension thermodynamic equation of state.
Computer aided nonlinear electrical networks analysis
NASA Technical Reports Server (NTRS)
Slapnicar, P.
1977-01-01
Techniques used in simulating an electrical circuit with nonlinear elements for use in computer-aided circuit analysis programs are described. Elements of the circuit include capacitors, resistors, inductors, transistors, diodes, and voltage and current sources (constant or time varying). Simulation features are discussed for dc, ac, and/or transient circuit analysis. Calculations are based on the model approach of formulating the circuit equations. A particular solution of transient analysis for nonlinear storage elements is described.
Nonlinear Analysis of Surface EMG Time Series
NASA Astrophysics Data System (ADS)
Zurcher, Ulrich; Kaufman, Miron; Sung, Paul
2004-04-01
Applications of nonlinear analysis of surface electromyography time series of patients with and without low back pain are presented. Limitations of the standard methods based on the power spectrum are discussed.
Macro stress mapping on thin film buckling
Goudeau, P.; Villain, P.; Renault, P.-O.; Tamura, N.; Celestre, R.S.; Padmore, H.A.
2002-11-06
Thin films deposited by Physical Vapour Deposition techniques on substrates generally exhibit large residual stresses which may be responsible of thin film buckling in the case of compressive stresses. Since the 80's, a lot of theoretical work has been done to develop mechanical models but only a few experimental work has been done on this subject to support these theoretical approaches and nothing concerning local stress measurement mainly because of the small dimension of the buckling (few 10th mm). This paper deals with the application of micro beam X-ray diffraction available on synchrotron radiation sources for stress mapping analysis of gold thin film buckling.
Static Nonlinear Analysis In Concrete Structures
Hemmati, Ali
2008-07-08
Push-over analysis is a simple and applied approach which can be used for estimation of demand responses influenced by earthquake stimulations. The analysis is non-linear static analysis of the structure affected under increasing lateral loads and specifying the displacement--load diagram or structure capacity curve, draw the curve the base shear values and lateral deflection on the roof level of the building will be used. However, for estimation of the real behavior of the structure against earthquake, the non-linear dynamic analysis approaches and various accelerographs should be applied. Of course it should be noted that this approach especially in relation with tall buildings is complex and time consuming. In the article, the different patterns of lateral loading in push-over analysis have been compared with non-linear dynamic analysis approach so that the results represented accordingly. The researches indicated the uniformly--distributed loading is closer to real status.
Buckling of graded coatings: A continuum model
NASA Astrophysics Data System (ADS)
Chiu, Tz-Cheng
2000-12-01
Requirements for the protection of hot section components in many high temperature applications such as earth-to-orbit winged planes and advanced turbine systems have led to the application of thermal barrier coatings (TBCs) that utilize ceramic coatings on metal substrates. An alternative concept to homogeneous ceramic coatings is the functionally graded materials (FGM) in which the composition of the coating is intentionally graded to improve the bonding strength and to reduce the magnitude of the residual and thermal stresses. A widely observed failure mode in such layered systems is known to be interface cracking that leads to spallation fracture. In most cases, the final stage of the failure process for a thin coating appears to be due to buckling instability under thermally or mechanically induced compressive stress. The objective of this study is to develop a solution to the buckling instability problem by using continuum elasticity rather than a structural mechanics approach. The emphasis in the solution will be on the investigation of the effect of material inhomogeneity in graded coatings on the instability load, the postbuckling behavior, and fracture mechanics parameters such as the stress intensity factors and strain energy release rate. In this analysis, a nonlinear continuum theory is employed to examine the interface crack problem. The analytical solution of the instability problem permits the study of the effect of material inhomogeneity upon the inception of buckling and establishes benchmark results for the numerical solutions of related problems. To study the postbuckling behavior and to calculate the stress intensity factors and strain energy release rate a geometrically nonlinear finite element procedure with enriched crack-tip element is developed. Both plane strain and axisymmetric interface crack problems in TBCs with either homogeneous or graded coating are then considered by using the finite element procedure. It is assumed that the
Geometrically nonlinear analysis of adhesively bonded joints
NASA Technical Reports Server (NTRS)
Dattaguru, B.; Everett, R. A., Jr.; Whitcomb, J. D.; Johnson, W. S.
1982-01-01
A geometrically nonlinear finite element analysis of cohesive failure in typical joints is presented. Cracked-lap-shear joints were chosen for analysis. Results obtained from linear and nonlinear analysis show that nonlinear effects, due to large rotations, significantly affect the calculated mode 1, crack opening, and mode 2, inplane shear, strain-energy-release rates. The ratio of the mode 1 to mode 2 strain-energy-relase rates (G1/G2) was found to be strongly affected by he adhesive modulus and the adherend thickness. The ratios between 0.2 and 0.8 can be obtained by varying adherend thickness and using either a single or double cracked-lap-shear specimen configuration. Debond growth rate data, together with the analysis, indicate that mode 1 strain-energy-release rate governs debond growth. Results from the present analysis agree well with experimentally measured joint opening displacements.
Seismic analysis of piping with nonlinear supports
Barta, D.A.; Huang, S.N.; Severud, L.K.
1980-01-01
The modeling and results of nonlinear time-history seismic analyses for three sizes of pipelines restrained by mechanical snubbes are presented. Numerous parametric analyses were conducted to obtain sensitivity information which identifies relative importance of the model and analysis ingredients. Special considerations for modeling the pipe clamps and the mechanical snubbers based on experimental characterization data are discussed. Comparisions are also given of seismic responses, loads and pipe stresses predicted by standard response spectra methods and the nonlinear time-history methods.
Nonlinear transient analysis via energy minimization
NASA Technical Reports Server (NTRS)
Kamat, M. P.; Knight, N. F., Jr.
1978-01-01
The formulation basis for nonlinear transient analysis of finite element models of structures using energy minimization is provided. Geometric and material nonlinearities are included. The development is restricted to simple one and two dimensional finite elements which are regarded as being the basic elements for modeling full aircraft-like structures under crash conditions. The results indicate the effectiveness of the technique as a viable tool for this purpose.
On a High-Fidelity Hierarchical Approach to Buckling Load Calculations
NASA Technical Reports Server (NTRS)
Arbocz, Johann; Starnes, James H.; Nemeth, Michael P.
2001-01-01
As a step towards developing a new design philosophy, one that moves away from the traditional empirical approach used today in design towards a science-based design technology approach, a recent test series of 5 composite shells carried out by Waters at NASA Langley Research Center is used. It is shown how the hierarchical approach to buckling load calculations proposed by Arbocz et al can be used to perform an approach often called "high fidelity analysis", where the uncertainties involved in a design are simulated by refined and accurate numerical methods. The Delft Interactive Shell DEsign COde (short, DISDECO) is employed for this hierarchical analysis to provide an accurate prediction of the critical buckling load of the given shell structure. This value is used later as a reference to establish the accuracy of the Level-3 buckling load predictions. As a final step in the hierarchical analysis approach, the critical buckling load and the estimated imperfection sensitivity of the shell are verified by conducting an analysis using a sufficiently refined finite element model with one of the current generation two-dimensional shell analysis codes with the advanced capabilities needed to represent both geometric and material nonlinearities.
Buckling Load Calculations of the Isotropic Shell A-8 Using a High-Fidelity Hierarchical Approach
NASA Technical Reports Server (NTRS)
Arbocz, Johann; Starnes, James H.
2002-01-01
As a step towards developing a new design philosophy, one that moves away from the traditional empirical approach used today in design towards a science-based design technology approach, a test series of 7 isotropic shells carried out by Aristocrat and Babcock at Caltech is used. It is shown how the hierarchical approach to buckling load calculations proposed by Arbocz et al can be used to perform an approach often called 'high fidelity analysis', where the uncertainties involved in a design are simulated by refined and accurate numerical methods. The Delft Interactive Shell DEsign COde (short, DISDECO) is employed for this hierarchical analysis to provide an accurate prediction of the critical buckling load of the given shell structure. This value is used later as a reference to establish the accuracy of the Level-3 buckling load predictions. As a final step in the hierarchical analysis approach, the critical buckling load and the estimated imperfection sensitivity of the shell are verified by conducting an analysis using a sufficiently refined finite element model with one of the current generation two-dimensional shell analysis codes with the advanced capabilities needed to represent both geometric and material nonlinearities.
Nonlinear Analysis Of Rotor Dynamics
NASA Technical Reports Server (NTRS)
Day, William B.; Zalik, Richard
1988-01-01
Study explores analytical consequences of nonlinear Jeffcott equations of rotor dynamics. Section 1: Summary of previous studies. Section 2: Jeffcott Equations. Section 3: Proves two theorems that provide inequalities on coefficients of differential equations and magnitude of forcing function in absence of side force. Section 4: Numerical investigation of multiple-forcing-function problem by introducing both side force and mass imbalance. Section 5: Examples of numberical solutions of complex generalized Jeffcott equation with two forcing functions of different frequencies f1 and f2. Section 6: Boundedness and stability of solutions.Section 7: Concludes report reviewing analytical results and significance.
Stable Tearing and Buckling Responses of Unstiffened Aluminum Shells with Long Cracks
NASA Technical Reports Server (NTRS)
Starnes, James H., Jr.; Rose, Cheryl A.
1999-01-01
The results of an analytical and experimental study of the nonlinear response of thin, unstiffened, aluminum cylindrical shells with a long longitudinal crack are presented. The shells are analyzed with a nonlinear shell analysis code that accurately accounts for global and local structural response phenomena. Results are presented for internal pressure and for axial compression loads. The effect of initial crack length on the initiation of stable crack growth and unstable crack growth in typical shells subjected to internal pressure loads is predicted using geometrically nonlinear elastic-plastic finite element analyses and the crack-tip-opening angle (CTOA) fracture criterion. The results of these analyses and of the experiments indicate that the pressure required to initiate stable crack growth and unstable crack growth in a shell subjected to internal pressure loads decreases as the initial crack length increases. The effects of crack length on the prebuckling, buckling and postbuckling responses of typical shells subjected to axial compression loads are also described. For this loading condition, the crack length was not allowed to increase as the load was increased. The results of the analyses and of the experiments indicate that the initial buckling load and collapse load for a shell subjected to axial compression loads decrease as the initial crack length increases. Initial buckling causes general instability or collapse of a shell for shorter initial crack lengths. Initial buckling is a stable local response mode for longer initial crack lengths. This stable local buckling response is followed by a stable postbuckling response, which is followed by general or overall instability of the shell.
Stable Tearing and Buckling Responses of Unstiffened Aluminum Shells with Long Cracks
NASA Technical Reports Server (NTRS)
Starnes, James H., Jr.; Rose, Cheryl A.
1998-01-01
The results of an analytical and experimental study of the nonlinear response of thin, unstiffened, aluminum cylindrical shells with a long longitudinal crack are presented. The shells are analyzed with a nonlinear shell analysis code that accurately accounts for global and local structural response phenomena. Results are presented for internal pressure and for axial compression loads. The effect of initial crack length on the initiation of stable crack growth and unstable crack growth in typical shells subjected to internal pressure loads is predicted using geometrically nonlinear elastic-plastic finite element analyses and the crack-tip-opening angle (CTOA) fracture criterion. The results of these analyses and of the experiments indicate that the pressure required to initiate stable crack growth and unstable crack growth in a shell subjected to internal pressure loads decreases as the initial crack length increases. The effects of crack length on the prebuckling, buckling and postbuckling responses of typical shells subjected to axial compression loads are also described. For this loading condition, the crack length was not allowed to increase as the load was increased. The results of the analyses and of the experiments indicate that the initial buckling load and collapse load for a shell subjected to axial compression loads decrease as the initial crack length increases. Initial buckling causes general instability or collapse of a shell for shorter initial crack lengths. Initial buckling is a stable local response mode for longer initial crack lengths. This stable local buckling response is followed by a stable postbuckling response, which is followed by general or overall instability of the shell.
Statistical energy analysis of nonlinear vibrating systems.
Spelman, G M; Langley, R S
2015-09-28
Nonlinearities in practical systems can arise in contacts between components, possibly from friction or impacts. However, it is also known that quadratic and cubic nonlinearity can occur in the stiffness of structural elements undergoing large amplitude vibration, without the need for local contacts. Nonlinearity due purely to large amplitude vibration can then result in significant energy being found in frequency bands other than those being driven by external forces. To analyse this phenomenon, a method is developed here in which the response of the structure in the frequency domain is divided into frequency bands, and the energy flow between the frequency bands is calculated. The frequency bands are assigned an energy variable to describe the mean response and the nonlinear coupling between bands is described in terms of weighted summations of the convolutions of linear modal transfer functions. This represents a nonlinear extension to an established linear theory known as statistical energy analysis (SEA). The nonlinear extension to SEA theory is presented for the case of a plate structure with quadratic and cubic nonlinearity. PMID:26303923
NASA Astrophysics Data System (ADS)
Achong, A.
1999-05-01
This paper presents a non-linear analysis of the dome-shaped notes on the steelpan under compressive and thermal stresses. Equations are derived for the static and dynamic response of symmetrically distorted notes. Analytical results are obtained for modal frequencies, non-linear coupling coefficients and the buckling parameter. Experimental results demonstrate the vibration characteristics and their dependence on temperature. Experimental results were also obtained for the effects of stress relaxation which follows the shaping and tuning process of these notes by hammer peening. The results of the analysis are applicable to other shell-like structures not necessarily designed for musical purposes.
Simplified method for nonlinear structural analysis
NASA Technical Reports Server (NTRS)
Kaufman, A.
1983-01-01
A simplified inelastic analysis computer program was developed for predicting the stress-strain history of a thermomechanically cycled structure from an elastic solution. The program uses an iterative and incremental procedure to estimate the plastic strains from the material stress-strain properties and a simulated plasticity hardening model. The simplified method was exercised on a number of problems involving uniaxial and multiaxial loading, isothermal and nonisothermal conditions, and different materials and plasticity models. Good agreement was found between these analytical results and nonlinear finite element solutions for these problems. The simplified analysis program used less than 1 percent of the CPU time required for a nonlinear finite element analysis.
Functionalization of Buckled Graphene
NASA Astrophysics Data System (ADS)
Nelson, Timothy C.
Buckled graphene produced by the halogen based etching of 6H-SiC provides a new route for the functionalization of the graphene surface. This surface provides an important new stepping off point in the development of molecular electronics and sensors. While the graphene surface is relatively inert, the fluorinated defect sites inherent in the buckled graphene surface yield an excellent location for chemical reactions such as nucleophilic substitution. This thesis shows the utility of the fluorinated defect sites through the well characterized diazonium reaction. Buckled graphene films were prepared on silicon carbide substrates using inductively coupled plasma and reactive ion etching, and annealed at 1000° C to coalesce the BG. The films were reacted with benzene, nitrobenzene, acetonitrile, or a nitrophenyl diazonium salt solution. The diazonium salt was chosen due to its known reaction with graphene produced by other methods. Consequently, reaction of the diazonium with buckled graphene would provide a basis for comparing the reactivity of the surface with these other forums of graphene. The interactions of buckled graphene with the other species were investigated as they represent either constituent parts of the diazonium salt or the solvent. The reacted surfaces were analyzed by X-ray photoelectron spectroscopy, which reveals changes in the surface chemical state due to the functionalization of the buckled graphene by each species. Each reaction yielded significant pi-pi bonding, while the diazonium salt reaction produced additional covalently bonded phenyl groups on the buckled graphene surface. The covalent reaction site was shown to be the surface fluorinated defect site. This observation illustrates the utility of the buckled graphene surface in the functionalization of graphene. Moreover, it provides additional confirmation of the nature of the buckled graphene surface.
Nonlinear analysis of random gust response
NASA Astrophysics Data System (ADS)
Lee, Yan-Nian
In the present research, the nonlinear unsteady aerodynamics is incorporated in the application of Matched Filter Theory to determine the aerodynamic response to random gust. The analysis is focused on the gust response at low Mach numbers. Two airplane configurations, the F-18 HARV and F-16XL, have been tested in forced oscillation to provide the necessary data. The atmospheric turbulence is assumed to be characterized by the von Kármán gust power spectral density function. The nonlinear aerodynamic model is set up through Fourier functional analysis; while the linear aerodynamic model is calculated with the unsteady Quasi-Vortex-Lattice method. Both nonlinear and linear aerodynamic models are used to provide the airplane aerodynamics for comparison. The static results show that nonlinear unsteady aerodynamics produce at least 50% ~ 60% higher maximum lift responses than the linear unsteady aerodynamics. The pitching moment coefficients are more negative for the F-18 HARV and more positive for the F-16XL with the nonlinear aerodynamic models than the linear ones under the prescribed random gust In plunging motion, the dynamic results show that the use of nonlinear unsteady aerodynamics will result in 48.7% ~ 90.1% higher possible maximum gust load factors than with linear unsteady aerodynamics.
NASA Astrophysics Data System (ADS)
Xie, Dan; Xu, Min; Dai, Honghua; Dowell, Earl H.
2015-02-01
The proper orthogonal decomposition (POD) method for analysis of nonlinear panel flutter subjected to supersonic flow is presented. Optimal POD modes are extracted from a chaotic Galerkin mode responses. The aeroelastic equations of motion are constructed using von Karman plate theory, first-order piston theory and quasi-steady thermal stress theory. A simply-supported plate with thermal loads from a uniformly distributed temperature is considered. Many types of panel behaviors, including stable flat, dynamically stable buckled, limit cycle oscillation, nonharmonic periodic motion, quasi-periodic motion and chaotic motion are observed. Our primary focus is on chaos and the route to chaos. It is found that a sudden transition from the buckled state to chaos occurs. Time history, phase portrait, Poincaré map, bifurcation diagram and Lyapunov exponent are employed to study chaos. The POD chaotic results obtained are compared with the traditional Galerkin solutions. It is shown that the POD method can obtain accurate chaotic solutions, using fewer modes and less computational effort than the Galerkin mode approach; additionally, the POD method converges faster in the analysis of chaotic transients. Effects of length-to-width ratios and thermal loads are presented. It is found that a smaller width for fixed length will produce more stable flutter response, while the thermal loads degrade the flutter boundary and result in a more complex evolution of dynamic motions. The numerical simulations show that the robustness of the POD modes depends on the dynamic pressure but not on temperature.
Nonlinear Fourier analysis with cnoidal waves
Osborne, A.R.
1996-12-31
Fourier analysis is one of the most useful tools to the ocean engineer. The approach allows one to analyze wave data and thereby to describe a dynamical motion in terms of a linear superposition of ordinary sine waves. Furthermore, the Fourier technique allows one to compute the response function of a fixed or floating structure: each sine wave in the wave or force spectrum yields a sine wave in the response spectrum. The counting of fatigue cycles is another area where the predictable oscillations of sine waves yield procedures for the estimation of the fatigue life of structures. The ocean environment, however, is a source of a number of nonlinear effects which must also be included in structure design. Nonlinearities in ocean waves deform the sinusoidal shapes into other kinds of waves such as the Stokes wave, cnoidal wave or solitary wave. A key question is: Does there exist a generalization of linear Fourier analysis which uses nonlinear basis functions rather than the familiar sine waves? Herein addresses the dynamics of nonlinear wave motion in shallow water where the basis functions are cnoidal waves and discuss nonlinear Fourier analysis in terms of a linear superposition of cnoidal waves plus their mutual nonlinear interactions. He gives a number of simple examples of nonlinear Fourier wave motion and then analyzes an actual surface-wave time series obtained on an offshore platform in the Adriatic Sea. Finally, he briefly discusses application of the cnoidal wave spectral approach to the computation of the frequency response function of a floating vessel. The results given herein will prove useful in future engineering studies for the design of fixed, floating and complaint offshore structures.
Nonlinear Dynamical Analysis of Fibrillation
NASA Astrophysics Data System (ADS)
Kerin, John A.; Sporrer, Justin M.; Egolf, David A.
2013-03-01
The development of spatiotemporal chaotic behavior in heart tissue, termed fibrillation, is a devastating, life-threatening condition. The chaotic behavior of electrochemical signals, in the form of spiral waves, causes the muscles of the heart to contract in an incoherent manner, hindering the heart's ability to pump blood. We have applied the mathematical tools of nonlinear dynamics to large-scale simulations of a model of fibrillating heart tissue to uncover the dynamical modes driving this chaos. By studying the evolution of Lyapunov vectors and exponents over short times, we have found that the fibrillating tissue is sensitive to electrical perturbations only in narrow regions immediately in front of the leading edges of spiral waves, especially when these waves collide, break apart, or hit the edges of the tissue sample. Using this knowledge, we have applied small stimuli to areas of varying sensitivity. By studying the evolution of the effects of these perturbations, we have made progress toward controlling the electrochemical patterns associated with heart fibrillation. This work was supported by the U.S. National Science Foundation (DMR-0094178) and Research Corporation.
NASA Technical Reports Server (NTRS)
Dose, A
1941-01-01
The present report describes a device for ascertaining the bending and buckling effect in stress measurements on shell structures accessible from one side only. Beginning with a discussion of the relationship between flexural strain and certain parameters, the respective errors of the test method for great or variable skin curvature within the test range are analyzed and illustrated by specimen example.
NASA Technical Reports Server (NTRS)
1991-01-01
After an 800-foot-tall offshore oil recovery platform collapsed, the engineers at Engineering Dynamics, Inc., Kenner, LA, needed to learn the cause of the collapse, and analyze the proposed repairs. They used STAGSC-1, a NASA structural analysis program with geometric and nonlinear buckling analysis. The program allowed engineers to determine the deflected and buckling shapes of the structural elements. They could then view the proposed repairs under the pressure that caused the original collapse.
A method for nonlinear exponential regression analysis
NASA Technical Reports Server (NTRS)
Junkin, B. G.
1971-01-01
A computer-oriented technique is presented for performing a nonlinear exponential regression analysis on decay-type experimental data. The technique involves the least squares procedure wherein the nonlinear problem is linearized by expansion in a Taylor series. A linear curve fitting procedure for determining the initial nominal estimates for the unknown exponential model parameters is included as an integral part of the technique. A correction matrix was derived and then applied to the nominal estimate to produce an improved set of model parameters. The solution cycle is repeated until some predetermined criterion is satisfied.
Theory of buckling and post-buckling behavior of elastic structures
NASA Technical Reports Server (NTRS)
Budiansky, B.
1974-01-01
The present paper provides a unified, general presentation of the basic theory of the buckling and post-buckling behavior of elastic structures in a form suitable for application to a wide variety of special problems. The notation of functional analysis is used for this purpose. Before the general analysis, simple conceptual models are used to elucidate the basic concepts of bifurcation buckling, snap buckling, imperfection sensitivity, load-shortening relations, and stability. The energy approach, the virtual-work approach, and mode interaction are discussed. The derivations and results are applicable to continua and finite-dimensional systems. The virtual-work and energy approaches are given separate treatments, but their equivalence is made explicit. The basic concepts of stability occupy a secondary position in the present approach.
NASA Technical Reports Server (NTRS)
Pineda, Evan J.; Myers, David E.; Kosareo, Daniel N.; Kellas, Sotiris
2014-01-01
Four honeycomb sandwich panels, representing 1/16th arc segments of a 10 m diameter barrel section of the heavy lift launch vehicle, were manufactured under the NASA Composites for Exploration program and the NASA Constellation Ares V program. Two configurations were chosen for the panels: 6-ply facesheets with 1.125 in. honeycomb core and 8-ply facesheets with 1.000 in. honeycomb core. Additionally, two separate carbon fiber/epoxy material systems were chosen for the facesheets: inautoclave IM7/977-3 and out-of-autoclave T40-800B/5320-1. Smaller 3- by 5-ft panels were cut from the 1/16th barrel sections. These panels were tested under compressive loading at the NASA Langley Research Center. Furthermore, linear eigenvalue and geometrically nonlinear finite element analyses were performed to predict the compressive response of the 3- by 5-ft panels. This manuscript summarizes the experimental and analytical modeling efforts pertaining to the panel composed of 8-ply, T40-800B/5320-1 facesheets (referred to as Panel C). To improve the robustness of the geometrically nonlinear finite element model, measured surface imperfections were included in the geometry of the model. Both the linear and nonlinear, two-dimensional (2-D) and three-dimensional (3-D), models yield good qualitative and quantitative predictions. Additionally, it was predicted correctly that the panel would fail in buckling prior to failing in strength.
NASA Technical Reports Server (NTRS)
Pineda, Evan Jorge; Myers, David E.; Kosareo, Daniel N.; Zalewski, Bart F.; Kellas, Sotiris; Dixon, Genevieve D.; Krivanek, Thomas M.; Gyekenyesi, Thomas G.
2014-01-01
Four honeycomb sandwich panels, representing 1/16th arc segments of a 10-m diameter barrel section of the Heavy Lift Launch Vehicle, were manufactured and tested under the NASA Composites for Exploration and the NASA Constellation Ares V programs. Two configurations were chosen for the panels: 6-ply facesheets with 1.125 in. honeycomb core and 8-ply facesheets with 1.0 in. honeycomb core. Additionally, two separate carbon fiber/epoxy material systems were chosen for the facesheets: in-autoclave IM7/977-3 and out-of-autoclave T40-800b/5320-1. Smaller 3 ft. by 5 ft. panels were cut from the 1/16th barrel sections and tested under compressive loading. Furthermore, linear eigenvalue and geometrically nonlinear finite element analyses were performed to predict the compressive response of each 3 ft. by 5 ft. panel. To improve the robustness of the geometrically nonlinear finite element model, measured surface imperfections were included in the geometry of the model. Both the linear and nonlinear models yielded good qualitative and quantitative predictions. Additionally, it was correctly predicted that the panel would fail in buckling prior to failing in strength. Furthermore, several imperfection studies were performed to investigate the influence of geometric imperfections, fiber angle misalignments, and three-dimensional effects on the compressive response of the panel.
NASA Astrophysics Data System (ADS)
Cherniaev, Aleksandr; Komarov, Valeriy
2014-09-01
Composite drive shafts are extensively used in automotive and aeronautical applications due to lightweight combined with exceptional strength and stiffness. Complexity of the drive shaft design problem associated with the need to determine rational values for multiple parameters characterizing composite material (fiber orientation angles, stacking sequence and ply thicknesses), as well as with the fact that multiple conflicting design constraints should be considered simultaneously. In this paper we approach this problem considering carbon/epoxy drive shaft design as a multistep optimization process. It includes the following steps: 1) determination of fiber orientation angles and laminate stacking sequence based on analysis of loading conditions and analytical expressions predicting buckling load and minimal natural frequency of idealized drive shaft; 2) finding rational ply thicknesses using formal optimization procedure utilizing response surface approximations and gradient-based optimization algorithm; and 3) verification analysis of the optimized configuration with the use of nonlinear buckling analysis to ensure satisfaction of stability constraint.
NASA Astrophysics Data System (ADS)
Cherniaev, Aleksandr; Komarov, Valeriy
2015-10-01
Composite drive shafts are extensively used in automotive and aeronautical applications due to lightweight combined with exceptional strength and stiffness. Complexity of the drive shaft design problem associated with the need to determine rational values for multiple parameters characterizing composite material (fiber orientation angles, stacking sequence and ply thicknesses), as well as with the fact that multiple conflicting design constraints should be considered simultaneously. In this paper we approach this problem considering carbon/epoxy drive shaft design as a multistep optimization process. It includes the following steps: 1) determination of fiber orientation angles and laminate stacking sequence based on analysis of loading conditions and analytical expressions predicting buckling load and minimal natural frequency of idealized drive shaft; 2) finding rational ply thicknesses using formal optimization procedure utilizing response surface approximations and gradient-based optimization algorithm; and 3) verification analysis of the optimized configuration with the use of nonlinear buckling analysis to ensure satisfaction of stability constraint.
NASA Technical Reports Server (NTRS)
Librescu, L.; Khdeir, A. A.; Frederick, D.
1989-01-01
This paper deals with the substantiation of a shear deformable theory of cross-ply laminated composite shallow shells. While the developed theory preserves all the advantages of the first order transverse shear deformation theory it succeeds in eliminating some of its basic shortcomings. The theory is further employed in the analysis of the eigenvibration and static buckling problems of doubly curved shallow panels. In this context, the state space concept is used in conjunction with the Levy method, allowing one to analyze these problems in a unified manner, for a variety of boundary conditions. Numerical results are presented and some pertinent conclusions are formulated.
On a compressed elastic-plastic column optimized for post-buckling behaviour
NASA Astrophysics Data System (ADS)
Bielski, Jan; Bochenek, Bogdan
2008-12-01
A model of a column is proposed in order to analyse the post-buckling behaviour of a structural element in the elastic-plastic deformation range. The ideal two point I-section applied here simplifies the deformation analysis, that is, the problem of development of plastic zones in a section is eliminated, but still gives the possibility for qualitative analysis and optimization of the post-critical equilibrium paths. The coefficients of linear or parabolic variability of thickness of the flanges and their distance (web width) are accepted as model parameters and hence could be used for design variables in the optimization procedure. Moreover, the stiffness of an additional elastic support of the free end of the beam is also included as a parameter or design variable. A material model is employed with non-linear asymptotic isotropic hardening without the Bauschinger effect. Change of the tangent modulus is continuous and smooth during the transition from the elastic to plastic deformation range. The main goal of the analysis is to determine the values of the design variables for which the post-critical equilibrium paths are stable at least in the specified range of a generalized displacement. The constraints for the constant volume of the flanges and web material are applied. The inequality constraints are imposed on the flange thickness and web width. Various formulations of the optimization problem are proposed for all types of non-linear behaviour, including elastic or plastic buckling and elastic or elastic-plastic post-buckling deformation.
Probabilistic seismic demand analysis of nonlinear structures
NASA Astrophysics Data System (ADS)
Shome, Nilesh
Recent earthquakes in California have initiated improvement in current design philosophy and at present the civil engineering community is working towards development of performance-based earthquake engineering of structures. The objective of this study is to develop efficient, but accurate procedures for probabilistic analysis of nonlinear seismic behavior of structures. The proposed procedures help the near-term development of seismic-building assessments which require an estimation of seismic demand at a given intensity level. We also develop procedures to estimate the probability of exceedance of any specified nonlinear response level due to future ground motions at a specific site. This is referred as Probabilistic Seismic Demand Analysis (PSDA). The latter procedure prepares the way for the next stage development of seismic assessment that consider the uncertainties in nonlinear response and capacity. The proposed procedures require structure-specific nonlinear analyses for a relatively small set of recorded accelerograms and (site-specific or USGS-map-like) seismic hazard analyses. We have addressed some of the important issues of nonlinear seismic demand analysis, which are selection of records for structural analysis, the number of records to be used, scaling of records, etc. Initially these issues are studied through nonlinear analysis of structures for a number of magnitude-distance bins of records. Subsequently we introduce regression analysis of response results against spectral acceleration, magnitude, duration, etc., which helps to resolve these issues more systematically. We illustrate the demand-hazard calculations through two major example problems: a 5story and a 20-story SMRF building. Several simple, but quite accurate closed-form solutions have also been proposed to expedite the demand-hazard calculations. We find that vector-valued (e.g., 2-D) PSDA estimates demand hazard more accurately. This procedure, however, requires information about 2
NASA Astrophysics Data System (ADS)
Andrews, Blake M.; Song, Junho; Fahnestock, Larry A.
2009-09-01
Buckling-restrained braces (BRBs) have recently become popular in the United States for use as primary members of seismic lateral-force-resisting systems. A BRB is a steel brace that does not buckle in compression but instead yields in both tension and compression. Although design guidelines for BRB applications have been developed, systematic procedures for assessing performance and quantifying reliability are still needed. This paper presents an analytical framework for assessing buckling-restrained braced frame (BRBF) reliability when subjected to seismic loads. This framework efficiently quantifies the risk of BRB failure due to low-cycle fatigue fracture of the BRB core. The procedure includes a series of components that: (1) quantify BRB demand in terms of BRB core deformation histories generated through stochastic dynamic analyses; (2) quantify the limit-state of a BRB in terms of its remaining cumulative plastic ductility capacity based on an experimental database; and (3) evaluate the probability of BRB failure, given the quantified demand and capacity, through structural reliability analyses. Parametric studies were conducted to investigate the effects of the seismic load, and characteristics of the BRB and BRBF on the probability of brace failure. In addition, fragility curves (i.e., conditional probabilities of brace failure given ground shaking intensity parameters) were created by the proposed framework. While the framework presented in this paper is applied to the assessment of BRBFs, the modular nature of the framework components allows for application to other structural components and systems.
Nonlinear laminate analysis for metal matrix fiber composites
NASA Technical Reports Server (NTRS)
Chamis, C. C.; Sinclair, J. H.
1981-01-01
A nonlinear laminate analysis is described for predicting the mechanical behavior (stress-strain relationships) of angle-ply laminates in which the matrix is strained nonlinearly by both the residual stress and the mechanical load and in which additional nonlinearities are induced due to progressive fiber fractures and ply relative rotations. The nonlinear laminate analysis is based on linear composite mechanics and a piece-wise linear laminate analysis to handle the nonlinear responses. Results obtained by using this nonlinear analysis on boron-fiber/aluminum-matrix angle-ply laminates agree well with experimental data. The results shown illustrate the in situ ply stress-strain behavior and synergistic strength enhancement.
Nonlinear laminate analysis for metal matrix fiber composites
NASA Technical Reports Server (NTRS)
Chamis, C. C.; Sinclair, J. H.
1981-01-01
A nonlinear laminate analysis is described for predicting the mechanical behavior (stress-strain relationships) of angleplied laminates in which the matrix is strained nonlinearly by both the residual stress and the mechanical load and in which additional nonlinearities are induced due to progressive fiber fractures and ply relative rotations. The nonlinear laminate analysis (NLA) is based on linear composite mechanics and a piece wise linear laminate analysis to handle the nonlinear responses. Results obtained by using this nonlinear analysis on boron fiber/aluminum matrix angleplied laminates agree well with experimental data. The results shown illustrate the in situ ply stress-strain behavior and synergistic strength enhancement.
Nonlinear time-series analysis revisited
NASA Astrophysics Data System (ADS)
Bradley, Elizabeth; Kantz, Holger
2015-09-01
In 1980 and 1981, two pioneering papers laid the foundation for what became known as nonlinear time-series analysis: the analysis of observed data—typically univariate—via dynamical systems theory. Based on the concept of state-space reconstruction, this set of methods allows us to compute characteristic quantities such as Lyapunov exponents and fractal dimensions, to predict the future course of the time series, and even to reconstruct the equations of motion in some cases. In practice, however, there are a number of issues that restrict the power of this approach: whether the signal accurately and thoroughly samples the dynamics, for instance, and whether it contains noise. Moreover, the numerical algorithms that we use to instantiate these ideas are not perfect; they involve approximations, scale parameters, and finite-precision arithmetic, among other things. Even so, nonlinear time-series analysis has been used to great advantage on thousands of real and synthetic data sets from a wide variety of systems ranging from roulette wheels to lasers to the human heart. Even in cases where the data do not meet the mathematical or algorithmic requirements to assure full topological conjugacy, the results of nonlinear time-series analysis can be helpful in understanding, characterizing, and predicting dynamical systems.
Nonlinear time-series analysis revisited.
Bradley, Elizabeth; Kantz, Holger
2015-09-01
In 1980 and 1981, two pioneering papers laid the foundation for what became known as nonlinear time-series analysis: the analysis of observed data-typically univariate-via dynamical systems theory. Based on the concept of state-space reconstruction, this set of methods allows us to compute characteristic quantities such as Lyapunov exponents and fractal dimensions, to predict the future course of the time series, and even to reconstruct the equations of motion in some cases. In practice, however, there are a number of issues that restrict the power of this approach: whether the signal accurately and thoroughly samples the dynamics, for instance, and whether it contains noise. Moreover, the numerical algorithms that we use to instantiate these ideas are not perfect; they involve approximations, scale parameters, and finite-precision arithmetic, among other things. Even so, nonlinear time-series analysis has been used to great advantage on thousands of real and synthetic data sets from a wide variety of systems ranging from roulette wheels to lasers to the human heart. Even in cases where the data do not meet the mathematical or algorithmic requirements to assure full topological conjugacy, the results of nonlinear time-series analysis can be helpful in understanding, characterizing, and predicting dynamical systems. PMID:26428563
Probabilistic analysis of a materially nonlinear structure
NASA Technical Reports Server (NTRS)
Millwater, H. R.; Wu, Y.-T.; Fossum, A. F.
1990-01-01
A probabilistic finite element program is used to perform probabilistic analysis of a materially nonlinear structure. The program used in this study is NESSUS (Numerical Evaluation of Stochastic Structure Under Stress), under development at Southwest Research Institute. The cumulative distribution function (CDF) of the radial stress of a thick-walled cylinder under internal pressure is computed and compared with the analytical solution. In addition, sensitivity factors showing the relative importance of the input random variables are calculated. Significant plasticity is present in this problem and has a pronounced effect on the probabilistic results. The random input variables are the material yield stress and internal pressure with Weibull and normal distributions, respectively. The results verify the ability of NESSUS to compute the CDF and sensitivity factors of a materially nonlinear structure. In addition, the ability of the Advanced Mean Value (AMV) procedure to assess the probabilistic behavior of structures which exhibit a highly nonlinear response is shown. Thus, the AMV procedure can be applied with confidence to other structures which exhibit nonlinear behavior.
Analysis of nonlinear structures via mode synthesis
NASA Technical Reports Server (NTRS)
Gieseke, R. K.
1975-01-01
An effective procedure for NASTRAN was developed that permits any number of substructures of any size to be synthesized for the purpose of developing normal modes of vibration of the complete structural system. The technique is extended to permit modal transient analysis of the subdivided system. This latter procedure permits the use of NASTRAN's ability to include nonlinear forces in the problem. The five-phase process is accomplished using standard NASTRAN rigid formats with problem-independent alter packages and DMAP sequences.
Dynamic Snap-Through of Thermally Buckled Structures by a Reduced Order Method
NASA Technical Reports Server (NTRS)
Przekop, Adam; Rizzi, Stephen A.
2007-01-01
The goal of this investigation is to further develop nonlinear modal numerical simulation methods for application to geometrically nonlinear response of structures exposed to combined high intensity random pressure fluctuations and thermal loadings. The study is conducted on a flat aluminum beam, which permits a comparison of results obtained by a reduced-order analysis with those obtained from a numerically intensive simulation in physical degrees-of-freedom. A uniformly distributed thermal loading is first applied to investigate the dynamic instability associated with thermal buckling. A uniformly distributed random loading is added to investigate the combined thermal-acoustic response. In the latter case, three types of response characteristics are considered, namely: (i) small amplitude vibration around one of the two stable buckling equilibrium positions, (ii) intermittent snap-through response between the two equilibrium positions, and (iii) persistent snap-through response between the two equilibrium positions. For the reduced-order analysis, four categories of modal basis functions are identified including those having symmetric transverse, anti-symmetric transverse, symmetric in-plane, and anti-symmetric in-plane displacements. The effect of basis selection on the quality of results is investigated for the dynamic thermal buckling and combined thermal-acoustic response. It is found that despite symmetric geometry, loading, and boundary conditions, the anti-symmetric transverse and symmetric in-plane modes must be included in the basis as they participate in the snap-through behavior.
NASA Technical Reports Server (NTRS)
Myers, David E.; Pineda, Evan J.; Zalewski, Bart F.; Kosareo, Daniel N.; Kellas, Sotiris
2013-01-01
Four honeycomb sandwich panels, representing 1/16th arc segments of a 10-m diameter barrel section of the heavy lift launch vehicle, were manufactured under the NASA Composites for Exploration program and the NASA Space Launch Systems program. Two configurations were chosen for the panels: 6-ply facesheets with 1.125 in. honeycomb core and 8-ply facesheets with 1.000 in. honeycomb core. Additionally, two separate carbon fiber/epoxy material systems were chosen for the facesheets: inautoclave IM7/977-3 and out-of-autoclave T40-800b/5320-1. Smaller 3.00- by 5.00-ft panels were cut from the 1/16th barrel sections. These panels were tested under compressive loading at the NASA Langley Research Center. Furthermore, linear eigenvalue and geometrically nonlinear finite element analysis was performed to predict the compressive response of the 3.00- by 5.00-ft panels. This manuscript summarizes the experimental and analytical modeling efforts pertaining to the panel composed of 8-ply, IM7/977-3 facesheets (referred to Panel A). To improve the robustness of the geometrically nonlinear finite element model, measured surface imperfections were included in the geometry of the model. Both the linear and nonlinear models yield good qualitative and quantitative predictions. Additionally, it was predicted correctly that the panel would fail in buckling prior to failing in strength. Furthermore, several imperfection studies were performed to investigate the influence of geometric imperfections, fiber misalignments, and three-dimensional (3 D) effects on the compressive response of the panel.
A Biomechanical Model of Artery Buckling
Han, Hai-Chao
2010-01-01
The stability of arteries under blood pressure load is essential to the maintenance of normal arterial function and the loss of stability can lead to tortuosity and kinking that are associated with significant clinical complications. However, mechanical analysis of arterial bent buckling is lacking. To address this issue, this paper presents a biomechanical model of arterial buckling. Using a linear elastic cylindrical arterial model, the mechanical equations for arterial buckling were developed and the critical buckling pressure was found to be a function of the wall stiffness (Young’s modulus), arterial radius, length, wall thickness, and the axial strain. Both the model equations and experimental results demonstrated that the critical pressure is related to the axial strain. Arteries may buckle and become tortuous due to reduced (sub-physiological) axial strain, hypertensive pressure, and a weakened wall. These results are in accordance with, and provide a possible explanation to the clinical observations that these changes are the risk factors for arterial tortuosity and kinking. The current model is also applicable to veins and ureters. PMID:17689541
Nonlinear analysis of EEG for epileptic seizures
Hively, L.M.; Clapp, N.E.; Daw, C.S.; Lawkins, W.F.; Eisenstadt, M.L.
1995-04-01
We apply chaotic time series analysis (CTSA) to human electroencephalogram (EEG) data. Three epoches were examined: epileptic seizure, non-seizure, and transition from non-seizure to seizure. The CTSA tools were applied to four forms of these data: raw EEG data (e-data), artifact data (f-data) via application of a quadratic zero-phase filter of the raw data, artifact-filtered data (g- data) and that was the residual after subtracting f-data from e-data, and a low-pass-filtered version (h-data) of g-data. Two different seizures were analyzed for the same patient. Several nonlinear measures uniquely indicate an epileptic seizure in both cases, including an abrupt decrease in the time per wave cycle in f-data, an abrupt increase in the Kolmogorov entropy and in the correlation dimension for e-h data, and an abrupt increase in the correlation dimension for e-h data. The transition from normal to seizure state also is characterized by distinctly different trends in the nonlinear measures for each seizure and may be potential seizure predictors for this patient. Surrogate analysis of e-data shows that statistically significant nonlinear structure is present during the non-seizure, transition , and seizure epoches.
Generic element processor (application to nonlinear analysis)
NASA Technical Reports Server (NTRS)
Stanley, Gary
1989-01-01
The focus here is on one aspect of the Computational Structural Mechanics (CSM) Testbed: finite element technology. The approach involves a Generic Element Processor: a command-driven, database-oriented software shell that facilitates introduction of new elements into the testbed. This shell features an element-independent corotational capability that upgrades linear elements to geometrically nonlinear analysis, and corrects the rigid-body errors that plague many contemporary plate and shell elements. Specific elements that have been implemented in the Testbed via this mechanism include the Assumed Natural-Coordinate Strain (ANS) shell elements, developed with Professor K. C. Park (University of Colorado, Boulder), a new class of curved hybrid shell elements, developed by Dr. David Kang of LPARL (formerly a student of Professor T. Pian), other shell and solid hybrid elements developed by NASA personnel, and recently a repackaged version of the workhorse shell element used in the traditional STAGS nonlinear shell analysis code. The presentation covers: (1) user and developer interfaces to the generic element processor, (2) an explanation of the built-in corotational option, (3) a description of some of the shell-elements currently implemented, and (4) application to sample nonlinear shell postbuckling problems.
NASA Astrophysics Data System (ADS)
Wiggins, Andrew D.
Bow seals are critical components on advanced marine vehicles that rely on aerostatic support to reduce drag. They consist of a series of open-ended fabric cylinders ("fingers") that contact the free surface and, when inflated, form a compliant pressure barrier. Bow seals are unique in that, unlike a majority of structures in civil and mechanical engineering, bow seals operate in a buckled state. The response characteristics of these structures are of practical interest due to unacceptable wear rates on seal components and difficulties in predicting seal performance. Despite this, the hydroelastic response of the seal system, particularly basic information on seal vibration modes and the mechanisms responsible for seal wear, remains largely unknown. Similarly, estimates of the hydrodynamic loads on the seal system are inaccurate and based on heuristic scaling of data from small-scale experiments, where similitude is challenging to maintain. Thus, a large-scale test system is necessary to obtain accurate estimates of bow seal response. The work is comprised of three parts. Part one presents detailed observations of bow seal response acquired using a large-scale test platform developed as part of the present study. These high-resolution observations, the first of their kind, show bow seal response to be characterized by complex post-buckling behavior. Part two proposes an analytical framework for interpreting the wide range of behavior observed at large scale. Using this framework, key parameters driving seal conformation and stability are identified. It is found that, due to their buckled state, bow seals are highly susceptible to a mode switching instability, which may be a potential mechanism responsible for the damaging vibrations. In part three, a benchtop experiment is used to demonstrate that the scalings identified in this study hold across a wide range of bending rigidities. This work has implications for improving drag and wear characteristics in future bow
Scleral Buckling with Chandelier Illumination
Seider, Michael I.; Nomides, Riikka E. K.; Hahn, Paul; Mruthyunjaya, Prithvi; Mahmoud, Tamer H.
2016-01-01
Scleral buckling is a highly successful technique for the repair of rhegmatogenous retinal detachment that requires intra-operative examination of the retina and treatment of retinal breaks via indirect ophthalmoscopy. Data suggest that scleral buckling likely results in improved outcomes for many patients but is declining in popularity, perhaps because of significant advances in vitrectomy instrumentation and visualization systems. Emerging data suggest that chandelier-assisted scleral buckling is safe and has many potential advantages over traditional buckling techniques. By combining traditional scleral buckling with contemporary vitreoretinal visualization techniques, chandelier-assistance may increase the popularity of scleral buckling to treat primary rhegmatogenous retinal detachment for surgeons of the next generation, maintaining buckling as an option for appropriate patients in the future. PMID:27621789
NASA Technical Reports Server (NTRS)
Hilburger, Mark W.; Starnes, James H., Jr.
2004-01-01
The results of an experimental and numerical study of the effects of initial imperfections on the buckling response and failure of unstiffened thin-walled compression-loaded graphite-epoxy cylindrical shells are presented. The shells considered in the study have six different orthotropic or quasi-isotropic shell-wall laminates and two different shell-radius-to-thickness ratios. The numerical results include the effects of geometric shell-wall mid-surface imperfections, shell-wall thickness variations, local shell-wall ply-gaps associated with the fabrication process, shell-end geometric imperfections, nonuniform end loads, and the effects of elastic boundary conditions. Selected cylinder parameter uncertainties were also considered. Results that illustrate the effects of imperfections and uncertainties on the nonlinear response characteristics, buckling loads and failure the shells are presented. In addition, a common failure analysis is used to predict material failures in the shells.
Effect of boundary conditions on piezoelectric buckled beams for vibrational noise harvesting
NASA Astrophysics Data System (ADS)
Cottone, F.; Mattarelli, M.; Vocca, H.; Gammaitoni, L.
2015-11-01
Nonlinear bistable systems have proven to be advantageous for energy harvesting of random and real ambient vibrations. One simple way of implementing a bistable transducer is setting a piezoelectric beam in a post-buckled configuration by axial compression. Besides, hinged or clamped-clamped type of boundary conditions correspond to two different post-buckled shape functions. Here we study, through theoretical analysis and numerical simulations, the efficiency of a hinged and clamped-clamped piezoelectric bridge under band-limited random noise with progressive axial load. Clamped configuration results to harvest 26% more power than hinged around an optimal axial load of 0.05%, while, in the intra-well trapped situation, above 0.1%, the two configurations present no substantial difference. Nevertheless, simulations confirm the advantage of exploiting inter-well oscillations in bistable regime.
NASA Technical Reports Server (NTRS)
Pineda, Evan J.; Meyers, David E.; Kosareo, Daniel N.; Zalewski, Bart F.; Dixon, Genevieve D.
2013-01-01
Four honeycomb sandwich panel types, representing 1/16th arc segments of a 10-m diameter barrel section of the Heavy Lift Launch Vehicle (HLLV), were manufactured and tested under the NASA Composites for Exploration program and the NASA Constellation Ares V program. Two configurations were chosen for the panels: 6-ply facesheets with 1.125 in. honeycomb core and 8-ply facesheets with 1.000 in. honeycomb core. Additionally, two separate carbon fiber/epoxy material systems were chosen for the facesheets: in-autoclave IM7/977-3 and out-of-autoclave T40-800b/5320-1. Smaller 3- by 5-ft panels were cut from the 1/16th barrel sections. These panels were tested under compressive loading at the NASA Langley Research Center (LaRC). Furthermore, linear eigenvalue and geometrically nonlinear finite element analyses were performed to predict the compressive response of each 3- by 5-ft panel. This manuscript summarizes the experimental and analytical modeling efforts pertaining to the panels composed of 6-ply, IM7/977-3 facesheets (referred to as Panels B-1 and B-2). To improve the robustness of the geometrically nonlinear finite element model, measured surface imperfections were included in the geometry of the model. Both the linear and nonlinear models yield good qualitative and quantitative predictions. Additionally, it was correctly predicted that the panel would fail in buckling prior to failing in strength. Furthermore, several imperfection studies were performed to investigate the influence of geometric imperfections, fiber angle misalignments, and three-dimensional (3-D) effects on the compressive response of the panel.
Parry, G.; Coupeau, C.; Colin, J.; Cimetiere, A.; Grilhe, J
2004-08-02
The transition from a straight-sided wrinkle to a periodic distribution of bubbles has been experimentally studied by atomic force microscopy for a stressed thin film relying on a substrate. A non-linear numerical analysis has been carried out and the different steps of the wrinkle evolution have been characterized. Different parameters of the buckling structure such as the shape parameter of the blisters and the stress relaxation have been determined and compared to the experimental data. The comparison of elastic strain energies has highlighted the possible coexistence of structures with different wavelengths.
Buckling of hybrid nanocomposites with embedded graphene and carbon nanotubes
NASA Astrophysics Data System (ADS)
Chandra, Y.; Saavedra Flores, E. I.; Scarpa, F.; Adhikari, S.
2016-09-01
With the aid of atomistic multiscale modelling and analytical approaches, buckling strength has been determined for carbon nanofibres/epoxy composite systems. Various nanofibres configurations considered are single walled carbon nano tube (SWCNT) and single layer graphene sheet (SLGS) and SLGS/SWCNT hybrid systems. Computationally, both eigen-value and non-linear large deformation-based methods have been employed to calculate the buckling strength. The non-linear computational model generated here takes into account of complex features such as debonding between polymer and filler (delamination under compression), nonlinearity in the polymer, strain-based damage criteria for the matrix, contact between fillers and interlocking of distorted filler surfaces with polymer. The effect of bridging nanofibres with an interlinking compound on the buckling strength of nano-composites has also been presented here. Computed enhancement in buckling strength of the polymer system due to nano reinforcement is found to be in the range of experimental and molecular dynamics based results available in open literature. The findings of this work indicate that carbon based nanofillers enhance the buckling strength of host polymers through various local failure mechanisms.
NASA Technical Reports Server (NTRS)
Svalbonas, V.
1973-01-01
The User's manual for the shell theory automated for rotational structures (STARS) 2B and 2V (buckling, vibrations) is presented. Several features of the program are: (1) arbitrary branching of the shell meridians, (2) arbitrary boundary conditions, (3) minimum input requirements to describe a complex, practical shell of revolution structure, and (4) accurate analysis capability using a minimum number of degrees of freedom.
Buckling Capacity Curves for Steel Spherical Shells Loaded by the External Pressure
NASA Astrophysics Data System (ADS)
Błażejewski, Paweł; Marcinowski, Jakub
2015-03-01
Assessment of buckling resistance of pressurised spherical cap is not an easy task. There exist two different approaches which allow to achieve this goal. The first approach involves performing advanced numerical analyses in which material and geometrical nonlinearities would be taken into account as well as considering the worst imperfections of the defined amplitude. This kind of analysis is customarily called GMNIA and is carried out by means of the computer software based on FEM. The other, comparatively easier approach, relies on the utilisation of earlier prepared procedures which enable determination of the critical resistance pRcr, the plastic resistance pRpl and buckling parameters a, b, h, l 0 needed to the definition of the standard buckling resistance curve. The determination of the buckling capacity curve for the particular class of spherical caps is the principal goal of this work. The method of determination of the critical pressure and the plastic resistance were described by the authors in [1] whereas the worst imperfection mode for the considered class of spherical shells was found in [2]. The determination of buckling parameters defining the buckling capacity curve for the whole class of shells is more complicated task. For this reason the authors focused their attention on spherical steel caps with the radius to thickness ratio of R/t = 500, the semi angle j = 30o and the boundary condition BC2 (the clamped supporting edge). Taking into account all imperfection forms considered in [2] and different amplitudes expressed by the multiple of the shell thickness, sets of buckling parameters defining the capacity curve were determined. These parameters were determined by the methods proposed by Rotter in [3] and [4] where the method of determination of the exponent h by means of additional parameter k was presented. As a result of the performed analyses the standard capacity curves for all considered imperfection modes and amplitudes 0.5t, 1.0t, 1.5t
Turbine blade nonlinear structural and life analysis
NASA Technical Reports Server (NTRS)
Mcknight, R. L.; Laflen, J. H.; Halford, G. R.; Kaufman, A.
1982-01-01
The utility of advanced structural analysis and life prediction techniques was evaluated for the life assessment of a commercial air-cooled turbine blade with a history of tip cracking. Three dimensional, nonlinear finite element structural analyses were performed for the blade tip region. The computed strain-temperature history of the critical location was imposed on a uniaxial strain controlled test specimen to evaluate the validity of the structural analysis method. Experimental results indicated higher peak stresses and greater stress relaxation than the analytical predictions. Life predictions using the Strainrange Partitioning and Frequency Modified approaches predicted 1200 to 4420 cycles and 2700 cycles to crack initiation, respectively, compared to an observed life of 3000 cycles.
Pihler-Puzović, D; Hazel, A L; Mullin, T
2016-09-14
We report the results from a combined experimental and numerical investigation of buckling in a novel variant of an elastic column under axial load. We find that including a regular line of centred holes in the column can prevent conventional, global, lateral buckling. Instead, the local microstructure introduced by the holes allows the column to buckle in an entirely different, internal, mode in which the holes are compressed in alternate directions, but the column maintains the lateral reflection symmetry about its centreline. The internal buckling mode can be accommodated within a smaller external space than the global one; and it is the preferred buckling mode over an intermediate range of column lengths for sufficiently large holes. For very short or sufficiently long columns a modification of the classical, global, lateral buckling is dominant. PMID:27501288
Buckling behavior and structural efficiency of open-section stiffened composite compression panels
NASA Technical Reports Server (NTRS)
Williams, J. G.; Stein, M.
1976-01-01
Several experiments with J- and blade-stiffened graphite/epoxy panels were conducted to obtain insight into how well experimental data could be correlated with analysis for the buckling behavior of open-section stiffened composite compression panels. Although some nonlinear behavior was observed during the experiments, adequate correlation with analysis was obtained to justify the use of linear, thin-plate buckling analysis in a minimum-weight design synthesis program for J- and blade-configurations. Results from two design studies using this program are presented. In the first study the minimum weights of Jand blade-configurations for two different material systems (graphite/epoxy and aluminum) are determined subject to buckling and strength constraints for a wide range of the compressive load index. In the second study the minimum weights required for graphite/epoxy blade-stiffened panels to satisfy additional stiffness constraints typical of medium-size commercial aircraft wing structures are determined. Both minimum-weight studies indicate that graphite/epoxy open-section stiffened panels can be designed so that weight savings of 30 to 50% are possible compared with the most efficient aluminum designs.
Numerical Simulation Of Buckling In Waffle Plants
NASA Technical Reports Server (NTRS)
Yin, Dah N.; Tran, Vu M.
1990-01-01
Accurate results obtained when fillet radii considered. Two reports describe numerical and experimental study of application of PASCO and WAFFLE computer programs to analysis of buckling in integrally machined, biaxially stiffened panel. PASCO (Panal Analysis and Sizing Code) is finite-element stress-and-strain code written for analysis and sizing of uniaxially stiffened panels. WAFFLE program provides comprehensive stress analysis of waffle panel, used to determine bending moments at interfaces.
Nonlinear and Failure Analysis of Composite Structures
NASA Technical Reports Server (NTRS)
Noor, Ahmed K.; Starnes, James H. (Technical Monitor)
2002-01-01
The overall goal of this research is to assess the effect of discontinuities and uncertainties on the nonlinear response and failure of stiffened composite panels subjected to combined mechanical and thermal loads. The key elements of the study are: (a) study of the effects of stiffener geometry and of transverse stresses on the response, damage initiation and propagation in stiffened composite panels; (b) use of hierarchical sensitivity coefficients to identify the major parameters that affect the response and damage in each of the different levels in the hierarchy (micromechanical, layer, panel, subcomponent and component levels); and, (c) application of fuzzy set techniques to identify the range and variation of possible responses. The computational models developed are used in conjunction with experiments to understand the physical phenomena associated with the nonlinear response and failure of stiffened composite panels. A toolkit is developed for use in conjunction with deterministic analysis programs to help the designer in assessing the effect of uncertainties in the different computational model parameters on the variability of the response quantities.
Nonlinear Analysis of the Space Shuttle Super-Lightweight External Fuel Tank
NASA Technical Reports Server (NTRS)
Nemeth, Michael P.; Britt, Vicki O.; Collins, Timothy J.; Starnes, James H., Jr.
1996-01-01
The results of buckling and nonlinear analyses of the Space Shuttle External Tank super-lightweight liquid oxygen (LOX) tank are presented. Modeling details and results are presented for two prelaunch loading conditions and for two full-scale structural tests conducted on the original external tank. These results illustrate three distinctly different types of nonlinear responses for thin-walled shells subjected to combined mechanical and thermal loads. These nonlinear response phenomena consist of bifurcation-type buckling, short-wavelength nonlinear bending, and nonlinear collapse associated with a limit point. For each case, the results show that accurate predictions of nonlinear behavior generally require a large scale high-fidelity finite element model. Results are also presented that show that a fluid filled launch vehicle shell can be highly sensitive to initial geometric imperfections. In addition, results presented for two full scale structural tests of the original standard weight external tank suggest that the finite element modeling approach used in the present study is sufficient for representing the nonlinear behavior of the super lightweight LOX tank.
NASA Astrophysics Data System (ADS)
Patil, Mayuri Suresh
Plates or members containing plate elements have been used in the offshore, aerospace and construction industry. Cutouts are often located to lighten the weight of the structure, but these cutouts reduce the ultimate strength of the plate. A number of studies have taken place for determining the buckling strength of a perforated plated but few discuss the effect of material strain hardening on the buckling strength of a perforated plate. Buckling strength is often considered as an important criterial to determine the serviceable limit of the perforated plate in the offshore structure. The aim of the present study is to investigate the effect of material strain hardening on the strength characteristic of a perforated plate under uniaxial loading. This load at some point could lead to a possibility of instability. A square plate with perforation is considered here. The plate is considered to be simply supported at all four edges and has been kept straight. The perforation is located at the center of the plate. A number of ANSYS static nonlinear analysis are undertaken with different strain hardening material properties for AL7075. The Ramberg-Osgood method is used to determine the stress-strain curve for different strain hardening values. The plate thickness and the cutout size of the perforation are varied to determine the effect on the strength. The study covers the behavior of the system in the elastic buckling and the elastic-plastic region.
Fujita, Katsuhisa; Nakamura, Kazuhiro; Ito, Tomohiro; Iwamoto, Yoichi
1996-12-01
In the Great Hanshin Earthquake which occurred in January 1995, extremely serious damages to the elevated expressways were found. Some of those piers are made of steel and many of them buckled and revealed plastic deformations. One of them revealed the circumferentially uniform outward bulge at the middle portion in the axial direction, though the buckling of a long circular cylinder will occur at it`s bottom end accompanied by more complicated deformation patterns typical to the bending buckling. In this study, simple reduced scale models of the pier were fabricated and the dynamic and static buckling tests were performed. The effect of the girder weight or vertical excitation on the buckling phenomena were investigated. In addition to the tests, static buckling analysis using FEM was also performed in order to clarify the causes for this specified buckling phenomena.
Elastic torsional buckling of thin-walled composite cylinders
NASA Technical Reports Server (NTRS)
Marlowe, D. E.; Sushinsky, G. F.; Dexter, H. B.
1974-01-01
The elastic torsional buckling strength has been determined experimentally for thin-walled cylinders fabricated with glass/epoxy, boron/epoxy, and graphite/epoxy composite materials and composite-reinforced aluminum and titanium. Cylinders have been tested with several unidirectional-ply orientations and several cross-ply layups. Specimens were designed with diameter-to-thickness ratios of approximately 150 and 300 and in two lengths of 10 in. and 20 in. The results of these tests were compared with the buckling strengths predicted by the torsional buckling analysis of Chao.
On lateral buckling of end-loaded cantilevers, including the effect of warping stiffness
NASA Astrophysics Data System (ADS)
Reissner, E.; Reissner, J. E.; Wan, F. Y. M.
1987-06-01
We investigate the numerical consequences of the presence of certain non-linear terms in the expressions for the components of transverse shearing strain which occur in the derivation of one-dimensional equations for small finite deflections of straight beams from three-dimensional finite elasticity through use of the principle of minimum potential energy. While particular emphasis is placed on the effect of warping stiffness, the paper also includes results of interest in connection with the classical Michell-Prandtl-analysis of lateral buckling of endloaded cantilevers. Comprehensive numerical results are obtained for the entire range of the relevant dimensionless parameters, using power series, asymptotic expansion and modern numerical methods procedures.
Development of solution techniques for nonlinear structural analysis
NASA Technical Reports Server (NTRS)
Vos, R. G.; Andrews, J. S.
1974-01-01
Nonlinear structural solution methods in the current research literature are classified according to order of the solution scheme, and it is shown that the analytical tools for these methods are uniformly derivable by perturbation techniques. A new perturbation formulation is developed for treating an arbitrary nonlinear material, in terms of a finite-difference generated stress-strain expansion. Nonlinear geometric effects are included in an explicit manner by appropriate definition of an applicable strain tensor. A new finite-element pilot computer program PANES (Program for Analysis of Nonlinear Equilibrium and Stability) is presented for treatment of problems involving material and geometric nonlinearities, as well as certain forms on nonconservative loading.
Nonlinear, finite deformation, finite element analysis
NASA Astrophysics Data System (ADS)
Nguyen, Nhung; Waas, Anthony M.
2016-06-01
with energy conservation and work-conjugacy due to the use of the Jaumann objective stress rate in ABAQUS nonlinear incremental analysis is viewed as a consequence of the implementation of a constitutive model that violates these requirements.
Buckling testing of composite columns
NASA Astrophysics Data System (ADS)
Barbero, Ever; Tomblin, John
1992-11-01
Euler buckling test results are presented for large composite columns relevant to the mass production of composite structural members by pultrusion. The experimental procedure employed yields highly reproducible and accurate results. All percentage differences between theory and experiment are below 6.2 percent; the theoretically predicted long-column buckling load is accurate even in the case of the most complex composite materials.
Osmotic buckling of spherical capsules.
Knoche, Sebastian; Kierfeld, Jan
2014-11-01
We study the buckling of elastic spherical shells under osmotic pressure with the osmolyte concentration of the exterior solution as a control parameter. We compare our results for the bifurcation behavior with results for buckling under mechanical pressure control, that is, with an empty capsule interior. We find striking differences for the buckling states between osmotic and mechanical buckling. Mechanical pressure control always leads to fully collapsed states with opposite sides in contact, whereas uncollapsed states with a single finite dimple are generic for osmotic pressure control. For sufficiently large interior osmolyte concentrations, osmotic pressure control is qualitatively similar to buckling under volume control with the volume prescribed by the osmolyte concentrations inside and outside the shell. We present a quantitative theory which also captures the influence of shell elasticity on the relationship between osmotic pressure and volume. These findings are relevant for the control of buckled shapes in applications. We show how the osmolyte concentration can be used to control the volume of buckled shells. An accurate analytical formula is derived for the relationship between the osmotic pressure, the elastic moduli and the volume of buckled capsules. This also allows use of elastic capsules as osmotic pressure sensors or deduction of elastic properties and the internal osmolyte concentration from shape changes in response to osmotic pressure changes. We apply our findings to published experimental data on polyelectrolyte capsules. PMID:25209240
Buckling and Damage Resistance of Transversely-Loaded Composite Shells
NASA Technical Reports Server (NTRS)
Wardle, Brian L.
1998-01-01
Experimental and numerical work was conducted to better understand composite shell response to transverse loadings which simulate damage-causing impact events. The quasi-static, centered, transverse loading response of laminated graphite/epoxy shells in a [+/-45(sub n)/O(sub n)](sub s) layup having geometric characteristics of a commercial fuselage are studied. The singly-curved composite shell structures are hinged along the straight circumferential edges and are either free or simply supported along the curved axial edges. Key components of the shell response are response instabilities due to limit-point and/or bifurcation buckling. Experimentally, deflection-controlled shell response is characterized via load-deflection data, deformation-shape evolutions, and the resulting damage state. Finite element models are used to study the kinematically nonlinear shell response, including bifurcation, limit-points, and postbuckling. A novel technique is developed for evaluating bifurcation from nonlinear prebuckling states utilizing asymmetric spatial discretization to introduce numerical perturbations. Advantages of the asymmetric meshing technique (AMT) over traditional techniques include efficiency, robustness, ease of application, and solution of the actual (not modified) problems. The AMT is validated by comparison to traditional numerical analysis of a benchmark problem and verified by comparison to experimental data. Applying the technique, bifurcation in a benchmark shell-buckling problem is correctly identified. Excellent agreement between the numerical and experimental results are obtained for a number of composite shells although predictive capability decreases for stiffer (thicker) specimens which is attributed to compliance of the test fixture. Restraining the axial edge (simple support) has the effect of creating a more complex response which involves unstable bifurcation, limit-point buckling, and dynamic collapse. Such shells were noted to bifurcate into
Early detection of local buckling in structural members
NASA Astrophysics Data System (ADS)
Ali, Bashir; Sundaresan, Mannur J.; Schulz, Mark J.; Hughes, Derke
2005-05-01
Most structural health monitoring analyses to date have focused on the determination of damage in the form of crack growth in metallic materials or delamination or other types of damage growth in composite materials. However, in many applications, local instability in the form of buckling can be the precursor to more extensive damage and unstable failure of the structure. If buckling could be detected in the very early stages, there is a possibility of taking preventive measures to stabilize and save the structure. Relatively few investigations have addressed this type of damage initiation in structures. Recently, during the structural health monitoring of a wind turbine blade, local buckling was identified as the cause of premature failure. A stress wave propagation technique was used in this test to detect the precursor to the buckling failure in the form of early changes in the local curvature of the blade. These conditions have also been replicated in the laboratory and results are reported in this paper. A composite column was subjected to axial compression to induce various levels of buckling deformation. Two different techniques were used to detect the precursors to buckling in this column. The first identifier is the change in the vibration shapes and natural frequencies of the column. The second is the change in the characteristics of diagnostic Lamb waves during the buckling deformation. Experiments indicate that very small changes in curvature during the initial stages of buckling are detectable using the structural health monitoring techniques. The experimental vibration characteristics of the column with slight initial curvatures compared qualitatively with finite element results. The finite element analysis is used to identify the frequencies that are most sensitive to buckling deformation, and to select suitable locations for the placement of sensors that can detect even small changes in the local curvature.
Nonlinear adaptive wavelet analysis of electrocardiogram signals
NASA Astrophysics Data System (ADS)
Yang, H.; Bukkapatnam, S. T.; Komanduri, R.
2007-08-01
Wavelet representation can provide an effective time-frequency analysis for nonstationary signals, such as the electrocardiogram (EKG) signals, which contain both steady and transient parts. In recent years, wavelet representation has been emerging as a powerful time-frequency tool for the analysis and measurement of EKG signals. The EKG signals contain recurring, near-periodic patterns of P , QRS , T , and U waveforms, each of which can have multiple manifestations. Identification and extraction of a compact set of features from these patterns is critical for effective detection and diagnosis of various disorders. This paper presents an approach to extract a fiducial pattern of EKG based on the consideration of the underlying nonlinear dynamics. The pattern, in a nutshell, is a combination of eigenfunctions of the ensembles created from a Poincare section of EKG dynamics. The adaptation of wavelet functions to the fiducial pattern thus extracted yields two orders of magnitude (some 95%) more compact representation (measured in terms of Shannon signal entropy). Such a compact representation can facilitate in the extraction of features that are less sensitive to extraneous noise and other variations. The adaptive wavelet can also lead to more efficient algorithms for beat detection and QRS cancellation as well as for the extraction of multiple classical EKG signal events, such as widths of QRS complexes and QT intervals.
Methods of stability analysis in nonlinear mechanics
Warnock, R.L.; Ruth, R.D.; Gabella, W.; Ecklund, K.
1989-01-01
We review our recent work on methods to study stability in nonlinear mechanics, especially for the problems of particle accelerators, and compare our ideals to those of other authors. We emphasize methods that (1) show promise as practical design tools, (2) are effective when the nonlinearity is large, and (3) have a strong theoretical basis. 24 refs., 2 figs., 2 tabs.
Buckling and failure characteristics of graphite-polyimide shear panels
NASA Technical Reports Server (NTRS)
Shuart, M. J.; Hagaman, J. A.
1983-01-01
The buckling and failure characteristics of unstiffened, blade stiffened, and hat stiffened graphite-polyimide shear panels are described. The picture frame shear test is used to obtain shear stress-strain data at room temperature and at 316 deg C. The experimental results are compared with a linear buckling analysis, and the specimen failure modes are described. The effect of the 316 deg C test temperature on panel behavior are discussed.
Nonlinear analysis of helix traveling wave tubes
Freund, H.P.; Zaidman, E.G.; Vanderplaats, N.R.; Kodis, M.A.
1994-12-31
A nonlinear formulation of the interaction in a helix traveling wave tube (TWT) is presented. The formulation is intended to treat a wide class of helix TWTs including both emission-gated and multi-tone operation. The essential feature of each of these configurations is that multiple waves must be included in the formulation. As a result, a fully time-dependent analysis is required. The numerical procedure for this in a helix TWT is complicated by the fact that the radial profile of the field varies with frequency. This contrasts, for example, with the case of a smooth bore waveguide in which the radial profile for each TE{sub ln} or TM{sub ln} mode is invariant in frequency. Because of this, a complete self-consistent particle-in-cell (PIC) formulation must be three-dimensional. In order to circumvent the computational expense of a 3D PIC formulation, the authors adopt an approach in which the electromagnetic field is represented as a superposition of azimuthally symmetric modes in a vacuum sheath helix. The specific electron distributions are chosen to model either a continuous beam for the multi-tone TWT and a pulsed beam for the emission-gated TWT. Numerical results of the simulation for examples of interest to an emission-gated TWT experiment at NRL will be presented.
Nonlinear Analysis of Pulsating White Dwarf Lightcurves
NASA Astrophysics Data System (ADS)
Provencal, J. L.; Montgomery, M. H.; Shipman, H.; WET TEam
2015-06-01
Convection remains one of the largest sources of theoretical uncertainty in our understanding of stellar physics. For example, Bergeron (1995) show that basic parameters such as flux, line profiles, energy distribution, color indices, and equivalent widths are extremely sensitive to the assumed convective parameterization. This is compelling, since we use our knowledge of these basic parameters to calibrate white dwarf cooling sequences, provide detailed estimates for the ages of individual white dwarfs, and determine the age of the Galactic disk. The Whole Earth Telescope (WET) is engaged in a long term project to empirically calibrate the physical properties of convection in pulsating white dwarfs by combining asteroseismology and analysis of nonlinear light curves. Nonsinusoidal distortions, in the form of narrow peaks and wider valleys, are observed in many pulsating white dwarf light curves. These are a reflection of the local depth of the convection zone, a value which varies during a pulsation cycle. Applying asteroseismology and convective light curve fitting to a wide sample of pulsating white dwarfs provides an empirical map of how the convective response time (the convection zone “depth”) varies as a function of effective temperature, and this can be compared with theoretical models, both MLT and hydrodynamic. This project has resulted in a large database of white dwarf lightcurves and pulsation frequencies. We present current results for DA and DB pulsators, and provide a few examples of interesting pulsation behavior seen along the way.
Nonlinear damage detection in composite structures using bispectral analysis
NASA Astrophysics Data System (ADS)
Ciampa, Francesco; Pickering, Simon; Scarselli, Gennaro; Meo, Michele
2014-03-01
Literature offers a quantitative number of diagnostic methods that can continuously provide detailed information of the material defects and damages in aerospace and civil engineering applications. Indeed, low velocity impact damages can considerably degrade the integrity of structural components and, if not detected, they can result in catastrophic failure conditions. This paper presents a nonlinear Structural Health Monitoring (SHM) method, based on ultrasonic guided waves (GW), for the detection of the nonlinear signature in a damaged composite structure. The proposed technique, based on a bispectral analysis of ultrasonic input waveforms, allows for the evaluation of the nonlinear response due to the presence of cracks and delaminations. Indeed, such a methodology was used to characterize the nonlinear behaviour of the structure, by exploiting the frequency mixing of the original waveform acquired from a sparse array of sensors. The robustness of bispectral analysis was experimentally demonstrated on a damaged carbon fibre reinforce plastic (CFRP) composite panel, and the nonlinear source was retrieved with a high level of accuracy. Unlike other linear and nonlinear ultrasonic methods for damage detection, this methodology does not require any baseline with the undamaged structure for the evaluation of the nonlinear source, nor a priori knowledge of the mechanical properties of the specimen. Moreover, bispectral analysis can be considered as a nonlinear elastic wave spectroscopy (NEWS) technique for materials showing either classical or non-classical nonlinear behaviour.
Nonlinear analysis of structures. [within framework of finite element method
NASA Technical Reports Server (NTRS)
Armen, H., Jr.; Levine, H.; Pifko, A.; Levy, A.
1974-01-01
The development of nonlinear analysis techniques within the framework of the finite-element method is reported. Although the emphasis is concerned with those nonlinearities associated with material behavior, a general treatment of geometric nonlinearity, alone or in combination with plasticity is included, and applications presented for a class of problems categorized as axisymmetric shells of revolution. The scope of the nonlinear analysis capabilities includes: (1) a membrane stress analysis, (2) bending and membrane stress analysis, (3) analysis of thick and thin axisymmetric bodies of revolution, (4) a general three dimensional analysis, and (5) analysis of laminated composites. Applications of the methods are made to a number of sample structures. Correlation with available analytic or experimental data range from good to excellent.
Sutureless scleral buckle in the management of rhegmatogenous retinal detachment
Shanmugam, P Mahesh; Singh, Tajinder Pal; Ramanjulu, Rajesh; Rodrigues, Gladys; Reddy, Srinivasulu
2015-01-01
Purpose: To evaluate the anatomical and functional outcomes of sutureless scleral buckling for the repair of rhegmatogenous retinal detachment (RD). Design: Retrospective interventional case series. Materials and Methods: Retrospective analysis of 50 eyes of 49 patients with rhegmatogenous RD, who underwent sutureless scleral buckling from January 2009 to March 2013. Results: Primary retinal re-attachment rate of 86% was achieved with single surgery, but final anatomical success was 94% with additional interventions in the form of intravitreal gas, buckle revision, and/or pars plana vitrectomy. Best corrected logarithm of minimum angle of resolution visual acuity improved from 1.44 ± 1.01 preoperatively to 0.50 ± 0.40 at a mean follow-up of 6.7 months. Conclusion: Sutureless scleral buckling achieves excellent anatomical and functional success in majority of the patients with rhegmatogenous RD. PMID:26576521
Enhancement of Buckling Load with the Use of Active Materials
NASA Technical Reports Server (NTRS)
Yuan, F. G.
2002-01-01
In this paper, active buckling control of a beam using piezoelectric materials is investigated. Under small deformation, mathematical models are developed to describe the behavior of the beams subjected to an axial compressive load with geometric imperfections and load eccentricities under piezoelectric force. Two types of supports, simply supported and clamped, of the beam with a partially bonded piezoelectric actuator are used to illustrate the concept. For the beam with load eccentricities and initial geometric imperfections, the load- carrying capacity can be significantly enhanced by counteracting moments from the piezoelectric actuator. For the single piezoelectric actuator, using static feedback closed-loop control, the first buckling load can be eliminated. In the case of initially straight beams, analytical solutions of the enhanced first critical buckling load due to the increase of bending stiffness by piezoelectric actuators are derived based on linearized buckling analysis.
Ductility demands on buckling-restrained braced frames under earthquake loading
NASA Astrophysics Data System (ADS)
Fahnestock, Larry A.; Sause, Richard; Ricles, James M.; Lu, Le-Wu
2003-12-01
Accurate estimates of ductility demands on buckling-restrained braced frames (BRBFs) are crucial to performance-based design of BRBFs. An analytical study on the seismic behavior of BRBFs has been conducted at the ATLSS Center, Lehigh University to prepare for an upcoming experimental program. The analysis program DRAIN-2DX was used to model a one-bay, four-story prototype BRBF including material and geometric nonlinearities. The buckling-restrained brace (BRB) model incorporates both isotropic and kinematic hardening. Nonlinear static pushover and time-history analyses were performed on the prototype BRBF. Performance objectives for the BRBs were defined and used to evaluate the time-history analysis results. Particular emphasis was placed on global ductility demands and ductility demands on the BRBs. These demands were compared with anticipated ductility capacities. The analysis results, along with results from similar previous studies, are used to evaluate the BRBF design provisions that have been recommended for codification in the United States. The results show that BRB maximum ductility demands can be as high as 20 to 25. These demands significantly exceed those anticipated by the BRBF recommended provisions. Results from the static pushover and time-history analyses are used to demonstrate why the ductility demands exceed those anticipated by the recommended provisions. The BRB qualification testing protocol contained in the BRBF recommended provisions is shown to be inadequate because it requires only a maximum ductility demand of at most 7.5. Modifications to the testing protocol are recommended.
Nonlinearity Analysis and Parameters Optimization for an Inductive Angle Sensor
Ye, Lin; Yang, Ming; Xu, Liang; Zhuang, Xiaoqi; Dong, Zhaopeng; Li, Shiyang
2014-01-01
Using the finite element method (FEM) and particle swarm optimization (PSO), a nonlinearity analysis based on parameter optimization is proposed to design an inductive angle sensor. Due to the structure complexity of the sensor, understanding the influences of structure parameters on the nonlinearity errors is a critical step in designing an effective sensor. Key parameters are selected for the design based on the parameters' effects on the nonlinearity errors. The finite element method and particle swarm optimization are combined for the sensor design to get the minimal nonlinearity error. In the simulation, the nonlinearity error of the optimized sensor is 0.053% in the angle range from −60° to 60°. A prototype sensor is manufactured and measured experimentally, and the experimental nonlinearity error is 0.081% in the angle range from −60° to 60°. PMID:24590353
Analytical and experimental vibration and buckling characteristics of a pretensioned stayed column
NASA Technical Reports Server (NTRS)
Belvin, W. K.
1982-01-01
Modal vibration tests to determine lateral modes of vibration of a stayed column and static axial compression tests to determine the column's buckling and postbuckling behavior have been performed. Effects of stay tension levels and vibration-load interaction are presented. Two finite element models are used to analyze the column, a three-dimensional frame using NASTRAN and an equivalent two-dimensional frame using an exact dynamic stiffness matrix. Both analyses correlated well with the linear vibration and buckling experimental data. Results indicate premature buckling of the column due to vibration-load interaction and nonlinear oscillations due to stay slackening. Postbuckling behavior of the column is unusual because of stay slackening and results in a postbuckling restoring force of less than the bifurcation buckling load. Guidelines for design of pretensioned structures are presented which consider buckling, postbuckling and vibration behavior.
NASA Technical Reports Server (NTRS)
Haftka, Raphael T.; Cohen, Gerald A.; Mroz, Zenon
1990-01-01
A uniform variational approach to sensitivity analysis of vibration frequencies and bifurcation loads of nonlinear structures is developed. Two methods of calculating the sensitivities of bifurcation buckling loads and vibration frequencies of nonlinear structures, with respect to stiffness and initial strain parameters, are presented. A direct method requires calculation of derivatives of the prebuckling state with respect to these parameters. An adjoint method bypasses the need for these derivatives by using instead the strain field associated with the second-order postbuckling state. An operator notation is used and the derivation is based on the principle of virtual work. The derivative computations are easily implemented in structural analysis programs. This is demonstrated by examples using a general purpose, finite element program and a shell-of-revolution program.
NASA Technical Reports Server (NTRS)
Williams, F. W.; Anderson, M. S.; Kennedy, D.; Butler, R.; Aston, G.
1990-01-01
A computer program which is designed for efficient, accurate buckling and vibration analysis and optimum design of composite panels is described. The capabilities of the program are given along with detailed user instructions. It is written in FORTRAN 77 and is operational on VAX, IBM, and CDC computers and should be readily adapted to others. Several illustrations of the various aspects of the input are given along the example problems illustrating the use and application of the program.
NASA Technical Reports Server (NTRS)
Hoff, N J; Fuchs, S J; Cirillo, Adam J
1944-01-01
This paper is the second part of a series of reports on the inward bulge type buckling of monocoque cylinders. It presents the results of an experimental investigation of buckling in combined bending and compression. In the investigation it was found that the theory developed in part I of the present series predicts the buckling load in combined bending and compression with the same degree of accuracy as the older theory does in pure bending. In the realm covered by the experiments no systematic variation of the parameter N was observed. The analysis of the test results afforded a check on the theories of buckling of a curved panel. The agreement between experiment and theory was reasonably good. In addition, the effect of the end conditions upon the stress distribution under loads and upon initial stresses was investigated.
Buckling of Cracked Laminated Composite Cylindrical Shells Subjected to Combined Loading
NASA Astrophysics Data System (ADS)
Allahbakhsh, Hamidreza; Shariati, Mahmoud
2013-10-01
A series of finite element analysis on the cracked composite cylindrical shells under combined loading is carried out to study the effect of loading condition, crack size and orientation on the buckling behavior of laminated composite cylindrical shells. The interaction buckling curves of cracked laminated composite cylinders subject to different combinations of axial compression, bending, internal pressure and external pressure are obtained, using the finite element method. Results show that the internal pressure increases the critical buckling load of the CFRP cylindrical shells and bending and external pressure decrease it. Numerical analysis show that axial crack has the most detrimental effect on the buckling load of a cylindrical shell and results show that for lower values of the axial compressive load and higher values of the external pressure, the buckling is usually in the global mode and for higher values of axial compressive load and lower levels of external pressure the buckling mode is mostly in the local mode.
Identifying nonlinear biomechanical models by multicriteria analysis
NASA Astrophysics Data System (ADS)
Srdjevic, Zorica; Cveticanin, Livija
2012-02-01
In this study, the methodology developed by Srdjevic and Cveticanin (International Journal of Industrial Ergonomics 34 (2004) 307-318) for the nonbiased (objective) parameter identification of the linear biomechanical model exposed to vertical vibrations is extended to the identification of n-degree of freedom (DOF) nonlinear biomechanical models. The dynamic performance of the n-DOF nonlinear model is described in terms of response functions in the frequency domain, such as the driving-point mechanical impedance and seat-to-head transmissibility function. For randomly generated parameters of the model, nonlinear equations of motion are solved using the Runge-Kutta method. The appropriate data transformation from the time-to-frequency domain is performed by a discrete Fourier transformation. Squared deviations of the response functions from the target values are used as the model performance evaluation criteria, thus shifting the problem into the multicriteria framework. The objective weights of criteria are obtained by applying the Shannon entropy concept. The suggested methodology is programmed in Pascal and tested on a 4-DOF nonlinear lumped parameter biomechanical model. The identification process over the 2000 generated sets of parameters lasts less than 20 s. The model response obtained with the imbedded identified parameters correlates well with the target values, therefore, justifying the use of the underlying concept and the mathematical instruments and numerical tools applied. It should be noted that the identified nonlinear model has an improved accuracy of the biomechanical response compared to the accuracy of a linear model.
Tensile buckling of advanced turboprops
NASA Technical Reports Server (NTRS)
Chamis, C. C.; Aiello, R. A.
1982-01-01
Theoretical studies were conducted to determine analytically the tensile buckling of advanced propeller blades (turboprops) in centrifugal fields, as well as the effects of tensile buckling on other types of structural behavior, such as resonant frequencies and flutter. Theoretical studies were also conducted to establish the advantages of using high performance composite turboprops as compared to titanium. Results show that the vibration frequencies are not affected appreciably prior to 80 percent of the tensile speed. Some frequencies approach zero as the tensile buckling speed is approached. Composites provide a substantial advantage over titanium on a buckling speed to weight basis. Vibration modes change as the rotor speed is increased and substantial geometric coupling is present.
Buckling and structural efficiency of sandwich-blade stiffened composite compression panels
NASA Technical Reports Server (NTRS)
Stein, M.; Williams, J. G.
1978-01-01
The minimum mass structural efficiency curve was determined for sandwich blade stiffened composite compression panels subjected to buckling and strength constraints. High structural efficiencies are attainable for this type of construction. A method of analysis is presented for the buckling of panels of this configuration which shows that buckling of such panels is strongly dependent on the through-the-thickness transverse shearing of the stiffener. Experimental results are presented and compared with theory.
Effects of Stiffening and Mechanical Load on Thermal Buckling of Stiffened Cylindrical Shells
NASA Technical Reports Server (NTRS)
Johnson, Theodore F.; Card, Michael F.
1995-01-01
A study of thermal buckling of stiffened cylindrical shells with the proportions of a preliminary supersonic transport fuselage design (1970) is presented. The buckling analysis is performed using an axisymmetric shell-of-revolution code, BOSOR4. The effects of combined mechanical (axial loading) and thermal loading (heated skins) are investigated. Results indicate that the location of longitudinal eccentric stiffening has a very large effect on the thermal buckling strength of longitudinally stiffened shells, and on longitudinally stiffened shells with rings.
NASA Technical Reports Server (NTRS)
Simitses, George J.; Carlson, Robert L.; Riff, Richard
1991-01-01
The object of the research reported herein was to develop a general mathematical model and solution methodologies for analyzing the structural response of thin, metallic shell structures under large transient, cyclic, or static thermomechanical loads. Among the system responses associated with these loads and conditions are thermal buckling, creep buckling, and ratcheting. Thus geometric and material nonlinearities (of high order) can be anticipated and must be considered in developing the mathematical model. The methodology is demonstrated through different problems of extension, shear, and of planar curved beams. Moreover, importance of the inclusion of large strain is clearly demonstrated, through the chosen applications.
A nonlinear analysis of the EHF booster
Colton, E.P.; Shi, D.
1987-01-01
We have analyzed particle motion at 1.2 GeV with assumption of nonlinearities arising from non-linear space charge forces and from the lattice sextupoles which are tuned to cancel the machine chromaticity. In the first case the motion is as expected and there are no problems as long as the x and y betatron tunes are separated by an integer or more. In the second case the motion is stable so long as the betatron amplitudes do not exceed values corresponding to beam normalized emittance of 100 mm-mr; when this occurs the effects of fifth-order betatron resonances are observed. 3 refs.
Buckling of Branched Cytoskeletal Filaments
NASA Astrophysics Data System (ADS)
Quint, D. A.; Schwarz, J. M.
2011-03-01
In vitro experiments of growing dendritic actin networks demonstrate reversible stress-softening at high loads, above some critical load. The transition to the stress-softening regime has been attributed to the elastic buckling of individual actin filaments. To estimate the critical load above which softening should occur, we extend the elastic theory of buckling of individual filaments embedded in a network to include the buckling of branched filaments, a signature trait of growing dendritic actin networks. Under certain assumptions, there will be approximately a seven-fold increase in the classical critical bucking load, when compared to the unbranched filament, which is entirely due to the presence of a branch. Moreover, we go beyond the classical buckling regime to investigate the effect of entropic fluctuations. The result of compressing the filament in this case leads to an increase in these fluctuations and eventually the harmonic approximation breaks down signifying the onset of the buckling transition. We compute corrections to the classical critical buckling load near this breakdown.
A Bayesian Approach for Multigroup Nonlinear Factor Analysis.
ERIC Educational Resources Information Center
Song, Xin-Yuan; Lee, Sik-Yum
2002-01-01
Developed a Bayesian approach for a general multigroup nonlinear factor analysis model that simultaneously obtains joint Bayesian estimates of the factor scores and the structural parameters subjected to some constraints across different groups. (SLD)
Single-strain-gage force/stiffness buckling prediction techniques on a hat-stiffened panel
NASA Technical Reports Server (NTRS)
Hudson, Larry D.; Thompson, Randolph C.
1991-01-01
Predicting the buckling characteristics of a test panel is necessary to ensure panel integrity during a test program. A single-strain-gage buckling prediction method was developed on a hat-stiffened, monolithic titanium buckling panel. The method is an adaptation of the original force/stiffness method which requires back-to-back gages. The single-gage method was developed because the test panel did not have back-to-back gages. The method was used to predict buckling loads and temperatures under various heating and loading conditions. The results correlated well with a finite element buckling analysis. The single-gage force/stiffness method was a valid real-time and post-test buckling prediction technique.
Nonlinear Robustness Analysis Tools for Flight Control Law Validation & Verification
NASA Astrophysics Data System (ADS)
Chakraborty, Abhijit
Loss of control in flight is among the highest aviation accident categories for both the number of accidents and the number of fatalities. The flight controls community is seeking an improved validation tools for safety critical flight control systems. Current validation tools rely heavily on linear analysis, which ignore the inherent nonlinear nature of the aircraft dynamics and flight control system. Specifically, current practices in validating the flight control system involve gridding the flight envelope and checking various criteria based on linear analysis to ensure safety of the flight control system. The analysis and certification methods currently applied assume the aircrafts' dynamics is linear. In reality, the behavior of the aircraft is always nonlinear due to its aerodynamic characteristics and physical limitations imposed by the actuators. This thesis develops nonlinear analysis tools capable of certifying flight control laws for nonlinear aircraft dynamics. The proposed analysis tools can handle both the aerodynamic nonlinearities and the physical limitations imposed by the actuators in the aircrafts' dynamics. This proposed validation technique will extend and enrich the predictive capability of existing flight control law validation methods to analyze nonlinearities. The objective of this thesis is to provide the flight control community with an advanced set of analysis tools to reduce aviation fatalities and accidents rate.
The dynamic aspects of thermo-elasto-viscoplastic snap-through and creep buckling phenomena
NASA Technical Reports Server (NTRS)
Riff, R.; Simitses, G. J.
1987-01-01
Use of a mathematical model and solution methodology, to examine dynamic buckling and dynamic postbuckling behavior of shallow arches and spherical caps made of a realistic material and undergoing non-isothermal, elasto-viscoplastic deformation was examined. Thus, geometric as well as material type nonlinearities of higher order are included in this analysis. The dynamic stability problem is studied under impulsive loading and suddenly applied loading with loads of constant magnitude and infinite duration. A finite element model was derived directly from the incrementally formulated nonlinear shell equations, by using a tensor-oriented procedure. As an example of the results, the time history of the midspan displacement of a damped shallow circular arch is presented.
Employment of CB models for non-linear dynamic analysis
NASA Technical Reports Server (NTRS)
Klein, M. R. M.; Deloo, P.; Fournier-Sicre, A.
1990-01-01
The non-linear dynamic analysis of large structures is always very time, effort and CPU consuming. Whenever possible the reduction of the size of the mathematical model involved is of main importance to speed up the computational procedures. Such reduction can be performed for the part of the structure which perform linearly. Most of the time, the classical Guyan reduction process is used. For non-linear dynamic process where the non-linearity is present at interfaces between different structures, Craig-Bampton models can provide a very rich information, and allow easy selection of the relevant modes with respect to the phenomenon driving the non-linearity. The paper presents the employment of Craig-Bampton models combined with Newmark direct integration for solving non-linear friction problems appearing at the interface between the Hubble Space Telescope and its solar arrays during in-orbit maneuvers. Theory, implementation in the FEM code ASKA, and practical results are shown.
NASA Technical Reports Server (NTRS)
Ko, William L.; Jackson, Raymond H.
1991-01-01
Combined compressive and shear buckling analysis was conducted on flat rectangular sandwich panels with the consideration of transverse shear effects of the core. The sandwich panel is fabricated with titanium honeycomb core and laminated metal matrix composite face sheets. The results show that the square panel has the highest combined load buckling strength, and that the buckling strength decreases sharply with the increases of both temperature and panel aspect ratio. The effect of layup (fiber orientation) on the buckling strength of the panels was studied in detail. The metal matrix composite sandwich panel was much more efficient than the sandwich panel with nonreinforced face sheets and had the same specific weight.
NASA Technical Reports Server (NTRS)
Li, Yi-Wei; Elishakoff, Isaac; Starnes, James H., Jr.; Bushnell, David
1998-01-01
This study is an extension of a previous investigation of the combined effect of axisymmetric thickness variation and axisymmetric initial geometric imperfection on buckling of isotropic shells under uniform axial compression. Here the anisotropic cylindrical shells are investigated by means of Koiter's energy criterion. An asymptotic formula is derived which can be used to determine the critical buckling load for composite shells with combined initial geometric imperfection and thickness variation. Results are compared with those obtained by the software packages BOSOR4 and PANDA2.
Theoretical and software considerations for nonlinear dynamic analysis
NASA Technical Reports Server (NTRS)
Schmidt, R. J.; Dodds, R. H., Jr.
1983-01-01
In the finite element method for structural analysis, it is generally necessary to discretize the structural model into a very large number of elements to accurately evaluate displacements, strains, and stresses. As the complexity of the model increases, the number of degrees of freedom can easily exceed the capacity of present-day software system. Improvements of structural analysis software including more efficient use of existing hardware and improved structural modeling techniques are discussed. One modeling technique that is used successfully in static linear and nonlinear analysis is multilevel substructuring. This research extends the use of multilevel substructure modeling to include dynamic analysis and defines the requirements for a general purpose software system capable of efficient nonlinear dynamic analysis. The multilevel substructuring technique is presented, the analytical formulations and computational procedures for dynamic analysis and nonlinear mechanics are reviewed, and an approach to the design and implementation of a general purpose structural software system is presented.
Ground motion estimation and nonlinear seismic analysis
McCallen, D.B.; Hutchings, L.J.
1995-08-14
Site specific predictions of the dynamic response of structures to extreme earthquake ground motions are a critical component of seismic design for important structures. With the rapid development of computationally based methodologies and powerful computers over the past few years, engineers and scientists now have the capability to perform numerical simulations of many of the physical processes associated with the generation of earthquake ground motions and dynamic structural response. This paper describes application of a physics based, deterministic, computational approach for estimation of earthquake ground motions which relies on site measurements of frequently occurring small (i.e. M < 3 ) earthquakes. Case studies are presented which illustrate application of this methodology for two different sites, and nonlinear analyses of a typical six story steel frame office building are performed to illustrate the potential sensitivity of nonlinear response to site conditions and proximity to the causative fault.
Nonlinear dynamic analysis for elastic robotic arms
NASA Astrophysics Data System (ADS)
Korayem, M. H.; Rahimi, H. N.
2011-06-01
The aim of the paper is to analyze the nonlinear dynamics of robotic arms with elastic links and joints. The main contribution of the paper is the comparative assessment of assumed modes and finite element methods as more convenient approaches for computing the nonlinear dynamic of robotic systems. Numerical simulations comprising both methods are carried out and results are discussed. Hence, advantages and disadvantages of each method are illustrated. Then, adding the joint flexibility to the system is dealt with and the obtained model is demonstrated. Finally, a brief description of the optimal motion generation is presented and the simulation is carried out to investigate the role of robot dynamic modeling in the control of robots.
Nonlinear analysis of the gradient drift instability
NASA Astrophysics Data System (ADS)
González, Rafael; Vega, Matías de la
An analytical study of the gradient drift instability in the equatorial electrojet of wavelengths in the order of one kilometer is presented. Different mechanisms, linear, non-local and turbulent, are found in the literature to explain the predominance of the 1 km wavelength in the electrojet. In the present work a simplified model is proposed in which the nonlinear evolution of three coupled modes is followed. By considering that one of the modes attains the stationary state, the evolution of the other two is obtained, and it is found that they follow equations of the Lotka-Volterra type. A stable stationary nonlinear solution for these equations is also found, and the conditions under which periodic solutions are possible are analyzed.
Analysis and design of robust decentralized controllers for nonlinear systems
Schoenwald, D.A.
1993-07-01
Decentralized control strategies for nonlinear systems are achieved via feedback linearization techniques. New results on optimization and parameter robustness of non-linear systems are also developed. In addition, parametric uncertainty in large-scale systems is handled by sensitivity analysis and optimal control methods in a completely decentralized framework. This idea is applied to alleviate uncertainty in friction parameters for the gimbal joints on Space Station Freedom. As an example of decentralized nonlinear control, singular perturbation methods and distributed vibration damping are merged into a control strategy for a two-link flexible manipulator.
Pseudosteady-state analysis of nonlinear aircraft maneuvers
NASA Technical Reports Server (NTRS)
Young, J. W.; Schy, A. A.; Johnson, K. G.
1980-01-01
An analytical method was developed for studying the combined effects of rotational coupling and nonlinear aerodynamics on aircraft response for specified control inputs. The method involves the simultaneous solution of two nonlinear equations which are functions of angle attack, roll rate, and control inputs. The method was applied to a number of maneuvers for a fighter-type aircraft. Time history responses verified the usefulness of the analysis for predicting a variety of response characteristics caused by interacting nonlinear aerodynamic and inertial effects, including spin conditions.
Comparative Convergence Analysis of Nonlinear AMLI-Cycle Multigrid
Hu, Xiaozhe; Vassilevski, Panayot S.; Xu, Jinchao
2013-04-30
The purpose of our paper is to provide a comprehensive convergence analysis of the nonlinear algebraic multilevel iteration (AMLI)-cycle multigrid (MG) method for symmetric positive definite problems. We show that the nonlinear AMLI-cycle MG method is uniformly convergent, based on classical assumptions for approximation and smoothing properties. Furthermore, under only the assumption that the smoother is convergent, we show that the nonlinear AMLI-cycle method is always better (or not worse) than the respective V-cycle MG method. Finally, numerical experiments are presented to illustrate the theoretical results.
Nonlinear analysis of capillary instability with heat and mass transfer
NASA Astrophysics Data System (ADS)
Awasthi, Mukesh Kumar; Agrawal, G. S.
2012-06-01
The nonlinear capillary instability of the cylindrical interface between the vapor and liquid phases of a fluid is studied when there is heat and mass transfer across the interface, using viscous potential flow theory. The fluids are considered to be viscous and incompressible with different kinematic viscosities. Both asymmetric and axisymmetric disturbances are considered. The analysis is based on the method of multiple scale perturbation and the nonlinear stability is governed by first-order nonlinear partial differential equation. The stability conditions are obtained and discussed theoretically as well as numerically. Regions of stability and instability have been shown graphically indicating the effect of various parameters. It has been observed that the heat and mass transfer has stabilizing effect on the stability of the system in the nonlinear analysis for both axisymmetric as well as asymmetric disturbances.
Dynamic analysis of nonlinear rotor-housing systems
NASA Technical Reports Server (NTRS)
Noah, Sherif T.
1988-01-01
Nonlinear analysis methods are developed which will enable the reliable prediction of the dynamic behavior of the space shuttle main engine (SSME) turbopumps in the presence of bearing clearances and other local nonlinearities. A computationally efficient convolution method, based on discretized Duhamel and transition matrix integral formulations, is developed for the transient analysis. In the formulation, the coupling forces due to the nonlinearities are treated as external forces acting on the coupled subsystems. Iteration is utilized to determine their magnitudes at each time increment. The method is applied to a nonlinear generic model of the high pressure oxygen turbopump (HPOTP). As compared to the fourth order Runge-Kutta numerical integration methods, the convolution approach proved to be more accurate and more highly efficient. For determining the nonlinear, steady-state periodic responses, an incremental harmonic balance method was also developed. The method was successfully used to determine dominantly harmonic and subharmonic responses fo the HPOTP generic model with bearing clearances. A reduction method similar to the impedance formulation utilized with linear systems is used to reduce the housing-rotor models to their coordinates at the bearing clearances. Recommendations are included for further development of the method, for extending the analysis to aperiodic and chaotic regimes and for conducting critical parameteric studies of the nonlinear response of the current SSME turbopumps.
Geometrically nonlinear analysis of laminated elastic structures
NASA Technical Reports Server (NTRS)
Reddy, J. N.; Chandrashekhara, K.; Chao, W. C.
1993-01-01
This final technical report contains three parts: Part 1 deals with the 2-D shell theory and its element formulation and applications. Part 2 deals with the 3-D degenerated element. These two parts constitute the two major tasks that were completed under the grant. Another related topic that was initiated during the present investigation is the development of a nonlinear material model. This topic is briefly discussed in Part 3. To make each part self-contained, conclusions and references are included in each part. In the interest of brevity, the discussions presented are relatively brief. The details and additional topics are described in the references cited.
The Nonlinear Response of Cracked Aluminum Shells Subjected to Combined Loads
NASA Technical Reports Server (NTRS)
Rose, Cheryl A.; Young, Richard D.; Starnes, James H., Jr.
2001-01-01
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.
Nonlinear stability analysis, energy exchange and solitons on vortex cores
NASA Astrophysics Data System (ADS)
Eftekhari, Kamran
1999-10-01
The subject of this dissertation is to develop reliable analytical and numerical methods for the study of the nonlinear stability of a class of slender, incompressible axisymmetric swirling flows. We desire to understanding early nonlinear evolution and possibly gain insight into phenomena such as solitary waves observed on vortex filaments and strongly nonlinear phenomena like vortex breakdown. We use an extension of the method used by Leibovich & Ma [1982] for the development of the equations, which differs in some significant aspects from the formulation of the aforementioned authors. We find, in agreement with Leibovich & Ma [1982], that the complex envelope amplitude of weakly nonlinear asymmetric waves is governed by the cubically nonlinear Schrodinger equation (NLS), however our form for coefficients differs from those of Leibovich & Ma [1982]. Most significantly, our formulation includes an axisymmetric disturbance component at second order (a full order lower than Leibovich & Ma) and thus permits energy exchange between asymmetric and axisymmetric disturbance components. The resulting equations also explicitly demonstrate the possibility of singular points where the group (not phase) velocity of linear disturbance equals the local axial flow velocity (group-velocity critical layer in our terminology) and where the NLS coefficients blow up, thus providing a wavenumber selection mechanism for the weakly nonlinear evolution. After implementation of numerical algorithm, our goal is to investigate the effects of weak nonlinearities on the stability of axisymmetric columnar flows. The analysis is applied to several model vortical flows, namely the Q-vortex and the Batchelor [1964] trailing line vortex.
Computational aeroelastic analysis of aircraft wings including geometry nonlinearity
NASA Astrophysics Data System (ADS)
Tian, Binyu
The objective of the present study is to show the ability of solving fluid structural interaction problems more realistically by including the geometric nonlinearity of the structure so that the aeroelastic analysis can be extended into the onset of flutter, or in the post flutter regime. A nonlinear Finite Element Analysis software is developed based on second Piola-Kirchhoff stress and Green-Lagrange strain. The second Piola-Kirchhoff stress and Green-Lagrange strain is a pair of energetically conjugated tensors that can accommodate arbitrary large structural deformations and deflection, to study the flutter phenomenon. Since both of these tensors are objective tensors, i.e., the rigid-body motion has no contribution to their components, the movement of the body, including maneuvers and deformation, can be included. The nonlinear Finite Element Analysis software developed in this study is verified with ANSYS, NASTRAN, ABAQUS, and IDEAS for the linear static, nonlinear static, linear dynamic and nonlinear dynamic structural solutions. To solve the flow problems by Euler/Navier equations, the current nonlinear structural software is then embedded into ENSAERO, which is an aeroelastic analysis software package developed at NASA Ames Research Center. The coupling of the two software, both nonlinear in their own field, is achieved by domain decomposition method first proposed by Guruswamy. A procedure has been set for the aeroelastic analysis process. The aeroelastic analysis results have been obtained for fight wing in the transonic regime for various cases. The influence dynamic pressure on flutter has been checked for a range of Mach number. Even though the current analysis matches the general aeroelastic characteristic, the numerical value not match very well with previous studies and needs farther investigations. The flutter aeroelastic analysis results have also been plotted at several time points. The influences of the deforming wing geometry can be well seen
Plastic folding of buckling structures.
Colin, Jérôme; Coupeau, Christophe; Grilhé, Jean
2007-07-27
Atomic force microscopy observations of the free surface of gold thin films deposited on silicon substrates have evidenced the buckling of the films and the formation of blister patterns undergoing plastic folding. The classical elastic buckling and plastic deformation of the films are analyzed in the framework of the Föppl-Von Kármán theory of thin plates introducing the notion of low-angle tilt boundaries and dislocation distributions to describe this folding effect. It is demonstrated that, in agreement with elementary plasticity of bent crystals, the presence of such tilt-boundaries results in the formation of buckling patterns of lower energy than "classical" elastic blisters. PMID:17678376
Nonlinear analysis of damaged stiffened fuselage shells subjected to combined loads
NASA Technical Reports Server (NTRS)
Starnes, James H., Jr.; Britt, Vicki O.; Young, Richard D.; Rankin, Charles C.; Shore, Charles P.; Bains, Jane C.
1994-01-01
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 that accounts for global and local response phenomena accurately. Results are presented for internal pressure and mechanical bending loads. The effects of crack location and orientation on shell response are described. The effects of mechanical fasteners on the response of a lap joint and the effects of elastic and elastic-plastic material properties on the buckling response of tension-loaded flat panels with cracks are also addressed.
Skin, Stringer, and Fastener Loads in Buckled Fuselage Panels
NASA Technical Reports Server (NTRS)
Young, Richard D.; Rose, Cheryl A.; Starnes, James H., Jr.
2001-01-01
The results of a numerical study to assess the effect of skin buckling on the internal load distribution in a stiffened fuselage panel, with and without longitudinal cracks, are presented. In addition, the impact of changes in the internal loads on the fatigue life and residual strength of a fuselage panel is assessed. A generic narrow-body fuselage panel is considered. The entire panel is modeled using shell elements and considerable detail is included to represent the geometric-nonlinear response of the buckled skin, cross section deformation of the stiffening components, and details of the skin-string attachment with discrete fasteners. Results are presented for a fixed internal pressure and various combinations of axial tension or compression loads. Results illustrating the effect of skin buckling on the stress distribution in the skin and stringer, and fastener loads are presented. Results are presented for the pristine structure, and for cases where damage is introduced in the form of a longitudinal crack adjacent to the stringer, or failed fastener elements. The results indicate that axial compression loads and skin buckling can have a significant effect on the circumferential stress in the skin, and fastener loads, which will influence damage initiation, and a comparable effect on stress intensity factors for cases with cracks. The effects on stress intensity factors will influence damage propagation rates and the residual strength of the panel.
Geometric and material nonlinear analysis of tensegrity structures
NASA Astrophysics Data System (ADS)
Tran, Hoang Chi; Lee, Jaehong
2011-12-01
A numerical method is presented for the large deflection in elastic analysis of tensegrity structures including both geometric and material nonlinearities. The geometric nonlinearity is considered based on both total Lagrangian and updated Lagrangian formulations, while the material nonlinearity is treated through elastoplastic stress-strain relationship. The nonlinear equilibrium equations are solved using an incremental-iterative scheme in conjunction with the modified Newton-Raphson method. A computer program is developed to predict the mechanical responses of tensegrity systems under tensile, compressive and flexural loadings. Numerical results obtained are compared with those reported in the literature to demonstrate the accuracy and efficiency of the proposed program. The flexural behavior of the double layer quadruplex tensegrity grid is sufficiently good for lightweight large-span structural applications. On the other hand, its bending strength capacity is not sensitive to the self-stress level.
Materials constitutive models for nonlinear analysis of thermally cycled structures
NASA Technical Reports Server (NTRS)
Kaufman, A.; Hunt, L. E.
1982-01-01
Effects of inelastic materials models on computed stress-strain solutions for thermally loaded structures were studied by performing nonlinear (elastoplastic creep) and elastic structural analyses on a prismatic, double edge wedge specimen of IN 100 alloy that was subjected to thermal cycling in fluidized beds. Four incremental plasticity creep models (isotropic, kinematic, combined isotropic kinematic, and combined plus transient creep) were exercised for the problem by using the MARC nonlinear, finite element computer program. Maximum total strain ranges computed from the elastic and nonlinear analyses agreed within 5 percent. Mean cyclic stresses, inelastic strain ranges, and inelastic work were significantly affected by the choice of inelastic constitutive model. The computing time per cycle for the nonlinear analyses was more than five times that required for the elastic analysis.
Nonlinear Redundancy Analysis. Research Report 88-1.
ERIC Educational Resources Information Center
van der Burg, Eeke; de Leeuw, Jan
A non-linear version of redundancy analysis is introduced. The technique is called REDUNDALS. It is implemented within the computer program for canonical correlation analysis called CANALS. The REDUNDALS algorithm is of an alternating least square (ALS) type. The technique is defined as minimization of a squared distance between criterion…
A Multilevel Nonlinear Profile Analysis Model for Dichotomous Data
ERIC Educational Resources Information Center
Culpepper, Steven Andrew
2009-01-01
This study linked nonlinear profile analysis (NPA) of dichotomous responses with an existing family of item response theory models and generalized latent variable models (GLVM). The NPA method offers several benefits over previous internal profile analysis methods: (a) NPA is estimated with maximum likelihood in a GLVM framework rather than…
Diagnosis of nonlinear systems using time series analysis
Hunter, N.F. Jr.
1991-01-01
Diagnosis and analysis techniques for linear systems have been developed and refined to a high degree of precision. In contrast, techniques for the analysis of data from nonlinear systems are in the early stages of development. This paper describes a time series technique for the analysis of data from nonlinear systems. The input and response time series resulting from excitation of the nonlinear system are embedded in a state space. The form of the embedding is optimized using local canonical variate analysis and singular value decomposition techniques. From the state space model, future system responses are estimated. The expected degree of predictability of the system is investigated using the state transition matrix. The degree of nonlinearity present is quantified using the geometry of the transfer function poles in the z plane. Examples of application to a linear single-degree-of-freedom system, a single-degree-of-freedom Duffing Oscillator, and linear and nonlinear three degree of freedom oscillators are presented. 11 refs., 9 figs.
Nonlinear Synchronization Analysis of Spatiotemporal Heart Data
NASA Astrophysics Data System (ADS)
Simonotto, Jennifer D.; Furman, Michael D.; Spano, Mark L.; Ditto, William L.; Liu, Gang; Kavanagh, Katherine M.
2003-08-01
A high-speed video camera and voltage-sensitive dyes were used to acquire high resolution (80×80 pixels) and high-speed (500 μs/frame) optical signals of ventricular fibrillation in a Langendorff-perfused porcine heart. The resulting spatiotemporal dynamics were recorded before and after the application of a defibrillation shock in order to study the mechanism of defibrillation failure. We calculate nonlinear synchronization index measures to qualify the evolution of different types of activity on the heart surface (focal, reentry). We observe changes with time in the spatial distribution of the first Fourier mode, showing that two main types of activity compete on the heart surface during a failed defibrillation.
Nonlinear dynamic analysis of flexible multibody systems
NASA Technical Reports Server (NTRS)
Bauchau, Olivier A.; Kang, Nam Kook
1991-01-01
Two approaches are developed to analyze the dynamic behavior of flexible multibody systems. In the first approach each body is modeled with a modal methodology in a local non-inertial frame of reference, whereas in the second approach, each body is modeled with a finite element methodology in the inertial frame. In both cases, the interaction among the various elastic bodies is represented by constraint equations. The two approaches were compared for accuracy and efficiency: the first approach is preferable when the nonlinearities are not too strong but it becomes cumbersome and expensive to use when many modes must be used. The second approach is more general and easier to implement but could result in high computation costs for a large system. The constraints should be enforced in a time derivative fashion for better accuracy and stability.
User's manual for GAMNAS: Geometric and Material Nonlinear Analysis of Structures
NASA Technical Reports Server (NTRS)
Whitcomb, J. D.; Dattaguru, B.
1984-01-01
GAMNAS (Geometric and Material Nonlinear Analysis of Structures) is a two dimensional finite-element stress analysis program. Options include linear, geometric nonlinear, material nonlinear, and combined geometric and material nonlinear analysis. The theory, organization, and use of GAMNAS are described. Required input data and results for several sample problems are included.
Local buckling and crippling of composite stiffener sections
NASA Technical Reports Server (NTRS)
Bonanni, David L.; Johnson, Eric R.; Starnes, James H., Jr.
1988-01-01
Local buckling, postbuckling, and crippling (failure) of channel, zee, and I- and J-section stiffeners made of AS4/3502 graphite-epoxy unidirectional tape are studied by experiment and analysis. Thirty-six stiffener specimens were tested statically to failure in axial compression as intermediate length columns. Web width is 1.25 inches for all specimens, and the flange width-to-thickness ratio ranges from 7 to 28 for the specimens tested. The radius of the stiffener corners is either 0.125 or 0.250 inches. A sixteen-ply orthotropic layup, an eight-ply quasi-isotropic layup, and a sixteen-ply quasi-isotropic layup are examined. Geometrically nonlinear analyses of five specimens were performed with the STAGS finite element code. Analytical results are compared to experimental data. Inplane stresses from STAGS are used to conduct a plane stress failure analysis of these specimens. Also, the development of interlaminar stress equations from equilibrium for classical laminated plate theory is presented. An algorithm to compute high order displacement derivatives required by these equations based on the Discrete Fourier Transform (DFT) is discussed.
THE EFFECT OF COLLAGENASE ON THE CRITICAL BUCKLING PRESSURE OF ARTERIES
Martinez, Ricky; Han, Hai-Chao
2012-01-01
The stability of arteries is essential to normal arterial functions and loss of stability can lead to arterial tortuosity and kinking. Collagen is a main extracellular matrix component that modulates the mechanical properties of arteries and collagen degradation at pathological conditions weakens the mechanical strength of arteries. However, the effect of collagen degradation on the mechanical stability of arteries is unclear. The objective of this study was to investigate the effects of collagen degradation on the critical buckling pressure of arteries. Arterial specimens were subjected to pressurized inflation testing and fitted with nonlinear thick-walled cylindrical model equations to determine their stress strain relationships. The arteries were then tested for the critical buckling pressure at a set of axial stretch ratios. Then, arteries were divided into three groups and treated with Type III collagenase at three different concentrations (64, 128, and 400U/ml). Mechanical properties and buckling pressures of the arteries were determined after collagenase treatment. Additionally, the theoretical buckling pressures were also determined using a buckling equation. Our results demonstrated that the buckling pressure for arteries was lower after collagenase treatment. The difference between pre- and post- treatment was statistically significant for the highest concentration of 400U/ml but not at the lower concentrations. The buckling equation was found to yield a fair estimation to the experimental critical pressure measurements. These results shed light on the role of matrix remodeling on the mechanical stability of arteries and developments of tortuous arteries. PMID:22428361
NASA Astrophysics Data System (ADS)
Świta, P.; Kamiński, M.
2016-05-01
The main purpose is to present the stochastic perturbation-based Finite Element Method analysis of the stability in the issues related to the influence of high temperature resulting from a fire directly connected with the reliability analysis of such structures. The thin-walled beam structures with constant cross-sectional thickness are uploaded with typical constant loads, variable loads and, additionally, a temperature increase and we look for the first critical value equivalent to the global stability loss. Such an analysis is carried out in the probabilistic context to determine as precisely as possible the safety margins according to the civil engineering Eurocode statements. To achieve this goal we employ the additional design-oriented Finite Element Method program and computer algebra system to get the analytical polynomial functions relating the critical pressure (or force) and several random design parameters; all the models are state-dependent as we consider an additional reduction of the strength parameters due to the temperature increase. The first four probabilistic moments of the critical forces are computed assuming that the input random parameters have all Gaussian probability functions truncated to the positive values only. Finally, the reliability index is calculated according to the First Order Reliability Method (FORM) by an application of the limit function as a difference in-between critical pressure and maximum compression stress determined in the given structures to verify their durability according to the demands of EU engineering designing codes related to the fire situation.
Nonlinear analysis of NPP safety against the aircraft attack
NASA Astrophysics Data System (ADS)
Králik, Juraj; Králik, Juraj
2016-06-01
The paper presents the nonlinear probabilistic analysis of the reinforced concrete buildings of nuclear power plant under the aircraft attack. The dynamic load is defined in time on base of the airplane impact simulations considering the real stiffness, masses, direction and velocity of the flight. The dynamic response is calculated in the system ANSYS using the transient nonlinear analysis solution method. The damage of the concrete wall is evaluated in accordance with the standard NDRC considering the spalling, scabbing and perforation effects. The simple and detailed calculations of the wall damage are compared.
Intrinsic buckling strength of graphene: First-principles density functional theory calculations
NASA Astrophysics Data System (ADS)
Kumar, Sandeep; Hembram, K. P. S. S.; Waghmare, Umesh V.
2010-09-01
How graphene, an atomically thin two-dimensional crystal, explores the third spatial dimension by buckling under compression is not yet understood. Knowledge of graphene’s buckling strength, the load at which it transforms from planar to buckled form, is a key to ensure mechanical stability of graphene-based nanoelectronic and nanocomposite devices. Here, we establish using first-principles theoretical analysis that graphene has an intrinsic rigidity against buckling, and it manifests in a weakly linear component in the dispersion of graphene’s flexural acoustic mode, which is believed to be quadratic. Contrary to the expectation from the elastic plate theory, we predict within continuum analysis that a graphene monolayer of macroscopic size buckles at a nonzero critical compressive strain at T=0K , and demonstrate it numerically from first principles. The origin of this rigidity is traced to the coupling between structural and electronic degrees of freedom arising from curvature-induced overlap between π orbitals in graphene.
Artery Buckling: New Phenotypes, Models, and Applications
Han, Hai-Chao; Chesnutt, Jennifer K. W.; Garcia, Justin R.; Liu, Qin; Wen, Qi
2012-01-01
Arteries are under significant mechanical loads from blood pressure, flow, tissue tethering, and body movement. It is critical that arteries remain patent and stable under these loads. This review summarizes the common forms of buckling that occur in blood vessels including cross-sectional collapse, longitudinal twist buckling, and bent buckling. The phenomena, model analyses, experimental measurements, effects on blood flow, and clinical relevance are discussed. It is concluded that mechanical buckling is an important issue for vasculature, in addition to wall stiffness and strength, and requires further studies to address the challenges. Studies of vessel buckling not only enrich vascular biomechanics but also have important clinical applications. PMID:23192265
Buckling modes in pantographic lattices
NASA Astrophysics Data System (ADS)
Giorgio, Ivan; Della Corte, Alessandro; dell'Isola, Francesco; Steigmann, David J.
2016-07-01
We study buckling patterns in pantographic sheets, regarded as two-dimensional continua consisting of lattices of continuously distributed fibers. The fibers are modeled as beams endowed with elastic resistance to stretching, shearing, bending and twist. Included in the theory is a non-standard elasticity due to geodesic bending of the fibers relative to the lattice surface. xml:lang="fr"
Nonlinear Analysis and Modeling of Tires
NASA Technical Reports Server (NTRS)
Noor, Ahmed K.
1996-01-01
The objective of the study was to develop efficient modeling techniques and computational strategies for: (1) predicting the nonlinear response of tires subjected to inflation pressure, mechanical and thermal loads; (2) determining the footprint region, and analyzing the tire pavement contact problem, including the effect of friction; and (3) determining the sensitivity of the tire response (displacements, stresses, strain energy, contact pressures and contact area) to variations in the different material and geometric parameters. Two computational strategies were developed. In the first strategy the tire was modeled by using either a two-dimensional shear flexible mixed shell finite elements or a quasi-three-dimensional solid model. The contact conditions were incorporated into the formulation by using a perturbed Lagrangian approach. A number of model reduction techniques were applied to substantially reduce the number of degrees of freedom used in describing the response outside the contact region. The second strategy exploited the axial symmetry of the undeformed tire, and uses cylindrical coordinates in the development of three-dimensional elements for modeling each of the different parts of the tire cross section. Model reduction techniques are also used with this strategy.
NASA Technical Reports Server (NTRS)
Ko, William L.
1998-01-01
Compressive buckling analysis was performed on metal-matrix composite (MMC) plates with central square holes. The MMC plates have varying aspect ratios and hole sizes and are supported under different boundary conditions. The finite-element structural analysis method was used to study the effects of plate boundary conditions, plate aspect ratio, hole size, and the composite stacking sequence on the compressive buckling strengths of the perforated MMC plates. Studies show that by increasing the hole sizes, compressive buckling strengths of the perforated MMC plates could be considerably increased under certain boundary conditions and aspect ratios ("anomalous" buckling behavior); and that the plate buckling mode could be symmetrical or antisymmetrical, depending on the plate boundary conditions, aspect ratio, and the hole size. For same-sized plates with same-sized holes, the compressive buckling strengths of the perforated MMC plates with [90/0/0/90]2 lamination could be as much as 10 percent higher or lower than those of the [45/- 45/- 45/45]2 laminations, depending on the plate boundary conditions, plate aspect ratios, and the hole size. Clamping the plate edges induces far stronger "anomalous" buckling behavior (enhancing compressive buckling strengths at increasing hole sizes) of the perforated MMC plates than simply supporting the plate edges.
NASTRAN nonlinear vibration analysis of beam and frame structures
NASA Technical Reports Server (NTRS)
Mei, C.; Rogers, J. L., Jr.
1975-01-01
A capability for the nonlinear vibration analysis of beam and frame structures suitable for use with NASTRAN level 15.5 is described. The nonlinearity considered is due to the presence of axial loads induced by longitudinal end restraints and lateral displacements that are large compared to the beam height. A brief discussion is included of the mathematical analysis and the geometrical stiffness matrix for a prismatic beam (BAR) element. Also included are a brief discussion of the equivalent linearization iterative process used to determine the nonlinear frequency, the required modifications to subroutines DBAR and XMPLBD of the NASTRAN code, and the appropriate vibration capability, four example problems are presented. Comparisons with existing experimental and analytical results show that excellent accuracy is achieved with NASTRAN in all cases.
Axisymmetric buckling of laminated thick annular spherical cap
NASA Astrophysics Data System (ADS)
Dumir, P. C.; Dube, G. P.; Mallick, A.
2005-03-01
Axisymmetric buckling analysis is presented for moderately thick laminated shallow annular spherical cap under transverse load. Buckling under central ring load and uniformly distributed transverse load, applied statically or as a step function load is considered. The central circular opening is either free or plugged by a rigid central mass or reinforced by a rigid ring. Annular spherical caps have been analysed for clamped and simple supports with movable and immovable inplane edge conditions. The governing equations of the Marguerre-type, first order shear deformation shallow shell theory (FSDT), formulated in terms of transverse deflection w, the rotation ψ of the normal to the midsurface and the stress function Φ, are solved by the orthogonal point collocation method. Typical numerical results for static and dynamic buckling loads for FSDT are compared with the classical lamination theory and the dependence of the effect of the shear deformation on the thickness parameter for various boundary conditions is investigated.
Thermomechanical buckling of multilayered composite panels with cutouts
NASA Technical Reports Server (NTRS)
Noor, Ahmed K.; Starnes, James H., Jr.; Peters, Jeanne M.
1994-01-01
A study is made of the thermomechanical buckling of flat unstiffened composite panels with central circular cutouts. The panels are subjected to combined temperature changes and applied edge loading (or edge displacements). The analysis is based on a first-order shear deformation plate theory. A mixed formulation is used with the fundamental unknowns consisting of the generalized displacements and the stress resultants of the plate. Both the stability boundary and the sensitivity coefficients are evaluated. The sensitivity coefficients measure the sensitivity of the buckling response to variations in the different lamination and material parameters of the panel. Numerical results are presented showing the effects of the variations in the hole diameter, laminate stacking sequence, fiber orientation, and aspect ratio of the panel on the thermomechanical buckling response and its sensitivity coefficients.
Thermomechanical buckling of multilayered composite panels with cutouts
NASA Technical Reports Server (NTRS)
Noor, Ahmed K.; Starnes, James H., Jr.; Peters, Jeanne M.
1993-01-01
A study is made of the thermomechanical buckling of flat unstiffened composite panels with central circular cutouts. The panels are subjected to combined temperature changes and applied edge loading (or edge displacements). The analysis is based on a first-order shear deformation plate theory. A mixed formulation is used with the fundamental unknowns consisting of the generalized displacements and the stress resultants of the plate. Both the stability boundary and the sensitivity coefficients are evaluated. The sensitivity coefficients measure the sensitivity of the buckling response to variations in the different lamination and material parameters of the panel. Numerical results are presented showing the effects of the variations in the hole diameter, laminate stacking sequence, fiber orientation, and aspect ratio of the panel on the thermomechanical buckling response and its sensitivity coefficients.
Wavelet analysis for non-stationary, nonlinear time series
NASA Astrophysics Data System (ADS)
Schulte, Justin A.
2016-08-01
Methods for detecting and quantifying nonlinearities in nonstationary time series are introduced and developed. In particular, higher-order wavelet analysis was applied to an ideal time series and the quasi-biennial oscillation (QBO) time series. Multiple-testing problems inherent in wavelet analysis were addressed by controlling the false discovery rate. A new local autobicoherence spectrum facilitated the detection of local nonlinearities and the quantification of cycle geometry. The local autobicoherence spectrum of the QBO time series showed that the QBO time series contained a mode with a period of 28 months that was phase coupled to a harmonic with a period of 14 months. An additional nonlinearly interacting triad was found among modes with periods of 10, 16 and 26 months. Local biphase spectra determined that the nonlinear interactions were not quadratic and that the effect of the nonlinearities was to produce non-smoothly varying oscillations. The oscillations were found to be skewed so that negative QBO regimes were preferred, and also asymmetric in the sense that phase transitions between the easterly and westerly phases occurred more rapidly than those from westerly to easterly regimes.
State analysis of nonlinear systems using local canonical variate analysis
Hunter, N.F.
1997-01-01
There are many instances in which time series measurements are used to derive an empirical model of a dynamical system. State space reconstruction from time series measurement has applications in many scientific and engineering disciplines including structural engineering, biology, chemistry, climatology, control theory, and physics. Prediction of future time series values from empirical models was attempted as early as 1927 by Yule, who applied linear prediction methods to the sunspot values. More recently, efforts in this area have centered on two related aspects of time series analysis, namely prediction and modeling. In prediction future time series values are estimated from past values, in modeling, fundamental characteristics of the state model underlying the measurements are estimated, such as dimension and eigenvalues. In either approach a measured time series, [{bold y}(t{sub i})], i= 1,... N is assumed to derive from the action of a smooth dynamical system, s(t+{bold {tau}})=a(s(t)), where the bold notation indicates the (potentially ) multivariate nature of the time series. The time series is assumed to derive from the state evolution via a measurement function c. {bold y}(t)=c(s(t)) In general the states s(t), the state evolution function a and the measurement function c are In unknown, and must be inferred from the time series measurements. We approach this problem from the standpoint of time series analysis. We review the principles of state space reconstruction. The specific model formulation used in the local canonical variate analysis algorithm and a detailed description of the state space reconstruction algorithm are included. The application of the algorithm to a single-degree-of- freedom Duffing-like Oscillator and the difficulties involved in reconstruction of an unmeasured degree of freedom in a four degree of freedom nonlinear oscillator are presented. The advantages and current limitations of state space reconstruction are summarized.
Nonlinear Analysis of Surface EMG Time Series of Back Muscles
NASA Astrophysics Data System (ADS)
Dolton, Donald C.; Zurcher, Ulrich; Kaufman, Miron; Sung, Paul
2004-10-01
A nonlinear analysis of surface electromyography time series of subjects with and without low back pain is presented. The mean-square displacement and entropy shows anomalous diffusive behavior on intermediate time range 10 ms < t < 1 s. This behavior implies the presence of correlations in the signal. We discuss the shape of the power spectrum of the signal.
Applications of Nonlinear Principal Components Analysis to Behavioral Data.
ERIC Educational Resources Information Center
Hicks, Marilyn Maginley
1981-01-01
An empirical investigation of the statistical procedure entitled nonlinear principal components analysis was conducted on a known equation and on measurement data in order to demonstrate the procedure and examine its potential usefulness. This method was suggested by R. Gnanadesikan and based on an early paper of Karl Pearson. (Author/AL)
Painleve analysis for a nonlinear Schroedinger equation in three dimensions
Chowdhury, A.R.; Chanda, P.K.
1987-09-01
A Painleve analysis is performed for the nonlinear Schroedinger equation in (2 + 1) dimensions following the methodology of Weiss et al. simplified in the sense of Kruskal. At least for one branch it is found that the required number of arbitrary functions (as demanded by the Cauchy-Kovalevskaya theorem) exists, signalling complete integrability.
Nonlinear dynamic analysis of hydrodynamically-coupled stainless steel structures
Zhao, Y.
1996-12-01
Spent nuclear fuel is usually stored temporarily on the site of nuclear power plants. The spent fuel storage racks are nuclear-safety-related stainless steel structures required to be analyzed for seismic loads. When the storage pool is subjected to three-dimensional (3-D) floor seismic excitations, rack modules, stored fuel bundles, adjacent racks and pool walls, and surrounding water are hydrodynamically coupled. Hydrodynamic coupling (HC) significantly affects the dynamic responses of the racks that are free-standing and submerged in water within the pool. A nonlinear time-history dynamic analysis is usually needed to describe the motion behavior of the racks that are both geometrically nonlinear and material nonlinear in nature. The nonlinearities include the friction resistance between the rack supporting legs and the pool floor, and various potential impacts of fuel-rack, rack-rack, and rack-pool wall. The HC induced should be included in the nonlinear dynamic analysis using the added-hydrodynamic-mass concept based on potential theory per the US Nuclear Regulatory Commission (USNRC) acceptance criteria. To this end, a finite element analysis constitutes a feasible and effective tool. However, most people perform somewhat simplified 1-D, or 2-D, or 3-D single rack and 2-D multiple rack analyses. These analyses are incomplete because a 3-D single rack model behaves quite differently from a 2-D mode. Furthermore, a 3-D whole pool multi-rack model behaves differently than a 3-D single rack model, especially when the strong HC effects are unsymmetrical. In this paper 3-D nonlinear dynamic time-history analyses were performed in a more quantitative manner using sophisticated finite element models developed for a single rack as well as all twelve racks in the whole-pool. Typical response results due to different HC effects are determined and discussed.
Evans, E A
1983-07-01
Observation of cell membrane buckling and cell folding in micropipette aspiration experiments was used to evaluate the bending rigidity of the red blood cell membrane. The suction pressure required to buckle the membrane surface initially was found to be about one-half to two-thirds of the pressure that caused the cell to fold and move up the pipet. A simple analytical model for buckling of a membrane disk supported at inner and outer radii correlates well with the observed buckling pressures vs. pipet radii. The buckling pressure is predicted to increase in inverse proportion to the cube of the pipet radius; also, the buckling pressure depends inversely on the radial distance to the toroidal rim of the cell, normalized by the pipet radius. As such, the pressure required to buckle the membrane with 1 X 10(-4) cm diam pipet would be about four times greater than with a 2 X 10(-4) cm pipet. This is the behavior observed experimentally. Based on analysis of the observed buckling data, the membrane bending or curvature elastic modulus is calculated to be 1.8 X 10(-12) dyn-cm. PMID:6882860
Application of artificial neural networks in nonlinear analysis of trusses
NASA Technical Reports Server (NTRS)
Alam, J.; Berke, L.
1991-01-01
A method is developed to incorporate neural network model based upon the Backpropagation algorithm for material response into nonlinear elastic truss analysis using the initial stiffness method. Different network configurations are developed to assess the accuracy of neural network modeling of nonlinear material response. In addition to this, a scheme based upon linear interpolation for material data, is also implemented for comparison purposes. It is found that neural network approach can yield very accurate results if used with care. For the type of problems under consideration, it offers a viable alternative to other material modeling methods.
On the solution of creep induced buckling in general structure
NASA Technical Reports Server (NTRS)
Padovan, J.; Tovichakchaikul, S.
1982-01-01
This paper considers the pre and post buckling behavior of general structures exposed to high temperature fields for long durations wherein creep effects become significant. The solution to this problem is made possible through the use of closed upper bounding constraint surfaces which enable the development of a new time stepping algorithm. This permits the stable and efficient solution of structural problems which exhibit indefinite tangent properties. Due to the manner of constraining/bounding successive iterates, the algorithm developed herein is largely self adaptive, inherently stable, sufficiently flexible to handle geometric material and boundary induced nonlinearity, and can be incorporated into either finite element or difference simulations. To illustrate the capability of the procedure, as well as, the physics of creep induced pre and post buckling behavior, the results of several numerical experiments are included.
Simulating Thin Sheets: Buckling, Wrinkling, Folding and Growth
NASA Astrophysics Data System (ADS)
Vetter, Roman; Stoop, Norbert; Wittel, Falk K.; Herrmann, Hans J.
2014-03-01
Numerical simulations of thin sheets undergoing large deformations are computationally challenging. Depending on the scenario, they may spontaneously buckle, wrinkle, fold, or crumple. Nature's thin tissues often experience significant anisotropic growth, which can act as the driving force for such instabilities. We use a recently developed finite element model to simulate the rich variety of nonlinear responses of Kirchhoff-Love sheets. The model uses subdivision surface shape functions in order to guarantee convergence of the method, and to allow a finite element description of anisotropically growing sheets in the classical Rayleigh-Ritz formalism. We illustrate the great potential in this approach by simulating the inflation of airbags, the buckling of a stretched cylinder, as well as the formation and scaling of wrinkles at free boundaries of growing sheets. Finally, we compare the folding of spatially confined sheets subject to growth and shrinking confinement to find that the two processes are equivalent.
Self-adaptive predictor-corrector algorithm for static nonlinear structural analysis
NASA Technical Reports Server (NTRS)
Padovan, J.
1981-01-01
A multiphase selfadaptive predictor corrector type algorithm was developed. This algorithm enables the solution of highly nonlinear structural responses including kinematic, kinetic and material effects as well as pro/post buckling behavior. The strategy involves three main phases: (1) the use of a warpable hyperelliptic constraint surface which serves to upperbound dependent iterate excursions during successive incremental Newton Ramphson (INR) type iterations; (20 uses an energy constraint to scale the generation of successive iterates so as to maintain the appropriate form of local convergence behavior; (3) the use of quality of convergence checks which enable various self adaptive modifications of the algorithmic structure when necessary. The restructuring is achieved by tightening various conditioning parameters as well as switch to different algorithmic levels to improve the convergence process. The capabilities of the procedure to handle various types of static nonlinear structural behavior are illustrated.
Nonlinear analysis of correlations in Alu repeat sequences in DNA
NASA Astrophysics Data System (ADS)
Xiao, Yi; Huang, Yanzhao; Li, Mingfeng; Xu, Ruizhen; Xiao, Saifeng
2003-12-01
We report on a nonlinear analysis of deterministic structures in Alu repeats, one of the richest repetitive DNA sequences in the human genome. Alu repeats contain the recognition sites for the restriction endonuclease AluI, which is what gives them their name. Using the nonlinear prediction method developed in chaos theory, we find that all Alu repeats have novel deterministic structures and show strong nonlinear correlations that are absent from exon and intron sequences. Furthermore, the deterministic structures of Alus of younger subfamilies show panlike shapes. As young Alus can be seen as mutation free copies from the “master genes,” it may be suggested that the deterministic structures of the older subfamilies are results of an evolution from a “panlike” structure to a more diffuse correlation pattern due to mutation.
Asymptotic analysis of a vibrating cantilever with a nonlinear boundary
NASA Astrophysics Data System (ADS)
Chen, Liqun; Lim, C. W.; Hu, Qingquan; Ding, Hu
2009-09-01
Nonlinear vibration of a cantilever in a contact atomic force microscope is analyzed via an asymptotic approach. The asymptotic solution is sought for a beam equation with a nonlinear boundary condition. The steady-state responses are determined in primary resonance and subharmonic resonance. The relations between the response amplitudes and the excitation frequencies and amplitudes are derived from the solvability condition. Multivaluedness occurs in the relations as a consequence of the nonlinearity. The stability of steady-state responses is analyzed by use of the Lyapunov linearized stability theory. The stability analysis predicts the jumping phenomenon for certain parameters. The curves of the response amplitudes changing with the excitation frequencies are numerically compared with those obtained via the method of multiple scales. The calculation results demonstrate that the two methods predict the same varying tendencies while there are small quantitative differences.
Nonlinear Time Series Analysis via Neural Networks
NASA Astrophysics Data System (ADS)
Volná, Eva; Janošek, Michal; Kocian, Václav; Kotyrba, Martin
This article deals with a time series analysis based on neural networks in order to make an effective forex market [Moore and Roche, J. Int. Econ. 58, 387-411 (2002)] pattern recognition. Our goal is to find and recognize important patterns which repeatedly appear in the market history to adapt our trading system behaviour based on them.
Bilinear analysis for kernel selection and nonlinear feature extraction.
Yang, Shu; Yan, Shuicheng; Zhang, Chao; Tang, Xiaoou
2007-09-01
This paper presents a unified criterion, Fisher + kernel criterion (FKC), for feature extraction and recognition. This new criterion is intended to extract the most discriminant features in different nonlinear spaces, and then, fuse these features under a unified measurement. Thus, FKC can simultaneously achieve nonlinear discriminant analysis and kernel selection. In addition, we present an efficient algorithm Fisher + kernel analysis (FKA), which utilizes the bilinear analysis, to optimize the new criterion. This FKA algorithm can alleviate the ill-posed problem existed in traditional kernel discriminant analysis (KDA), and usually, has no singularity problem. The effectiveness of our proposed algorithm is validated by a series of face-recognition experiments on several different databases. PMID:18220192
Fully Nonlinear Modeling and Analysis of Precision Membranes
NASA Technical Reports Server (NTRS)
Pai, P. Frank; Young, Leyland G.
2003-01-01
High precision membranes are used in many current space applications. This paper presents a fully nonlinear membrane theory with forward and inverse analyses of high precision membrane structures. The fully nonlinear membrane theory is derived from Jaumann strains and stresses, exact coordinate transformations, the concept of local relative displacements, and orthogonal virtual rotations. In this theory, energy and Newtonian formulations are fully correlated, and every structural term can be interpreted in terms of vectors. Fully nonlinear ordinary differential equations (ODES) governing the large static deformations of known axisymmetric membranes under known axisymmetric loading (i.e., forward problems) are presented as first-order ODES, and a method for obtaining numerically exact solutions using the multiple shooting procedure is shown. A method for obtaining the undeformed geometry of any axisymmetric membrane with a known inflated geometry and a known internal pressure (i.e., inverse problems) is also derived. Numerical results from forward analysis are verified using results in the literature, and results from inverse analysis are verified using known exact solutions and solutions from the forward analysis. Results show that the membrane theory and the proposed numerical methods for solving nonlinear forward and inverse membrane problems are accurate.
Analysis of nonlinear elastic behavior in miniature pneumatic artificial muscles
NASA Astrophysics Data System (ADS)
Hocking, Erica G.; Wereley, Norman M.
2013-01-01
Pneumatic artificial muscles (PAMs) are well known for their excellent actuator characteristics, including high specific work, specific power, and power density. Recent research has focused on miniaturizing this pneumatic actuator technology in order to develop PAMs for use in small-scale mechanical systems, such as those found in robotic or aerospace applications. The first step in implementing these miniature PAMs was to design and characterize the actuator. To that end, this study presents the manufacturing process, experimental characterization, and analytical modeling of PAMs with millimeter-scale diameters. A fabrication method was developed to consistently produce low-cost, high performance, miniature PAMs using commercially available materials. The quasi-static behavior of these PAMs was determined through experimentation on a single actuator with an active length of 39.16 mm (1.54 in) and a diameter of 4.13 mm (0.1625 in). Testing revealed the PAM’s full evolution of force with displacement for operating pressures ranging from 207 to 552 kPa (30-80 psi in 10 psi increments), as well as the blocked force and free contraction at each pressure. Three key nonlinear phenomena were observed: nonlinear PAM stiffness, hysteresis of the force versus displacement response for a given pressure, and a pressure deadband. To address the analysis of the nonlinear response of these miniature PAMs, a nonlinear stress versus strain model, a hysteresis model, and a pressure bias are introduced into a previously developed force balance analysis. Parameters of these nonlinear model refinements are identified from the measured force versus displacement data. This improved nonlinear force balance model is shown to capture the full actuation behavior of the miniature PAMs at each operating pressure and reconstruct miniature PAM response with much more accuracy than previously possible.
Experimentally Validated Nonlinear Analysis of Bridge Plate Girders with Deformations
NASA Astrophysics Data System (ADS)
Kużawa, Mieszko; Bień, Jan
2015-09-01
Comprehensive methodology of numerical nonlinear analysis of the consecutive phases in the structural behaviour of bridge plate girders with deformations is presented. The analysis concerns all stages of structure loading until failure and especially determination of the ultimate shear load capacity. Verification and validation of the numerical procedures proposed is based on comparison of the calculated results with effects of experimental laboratory shear capacity tests of plate girders carried out at the University of Ljubljana.
Bounded Linear Stability Margin Analysis of Nonlinear Hybrid Adaptive Control
NASA Technical Reports Server (NTRS)
Nguyen, Nhan T.; Boskovic, Jovan D.
2008-01-01
This paper presents a bounded linear stability analysis for a hybrid adaptive control that blends both direct and indirect adaptive control. Stability and convergence of nonlinear adaptive control are analyzed using an approximate linear equivalent system. A stability margin analysis shows that a large adaptive gain can lead to a reduced phase margin. This method can enable metrics-driven adaptive control whereby the adaptive gain is adjusted to meet stability margin requirements.
Computational models for the nonlinear analysis of reinforced concrete plates
NASA Technical Reports Server (NTRS)
Hinton, E.; Rahman, H. H. A.; Huq, M. M.
1980-01-01
A finite element computational model for the nonlinear analysis of reinforced concrete solid, stiffened and cellular plates is briefly outlined. Typically, Mindlin elements are used to model the plates whereas eccentric Timoshenko elements are adopted to represent the beams. The layering technique, common in the analysis of reinforced concrete flexural systems, is incorporated in the model. The proposed model provides an inexpensive and reasonably accurate approach which can be extended for use with voided plates.
Geometrically nonlinear analysis of laminated elastic structures
NASA Technical Reports Server (NTRS)
Reddy, J. N.
1984-01-01
Laminated composite plates and shells that can be used to model automobile bodies, aircraft wings and fuselages, and pressure vessels among many other were analyzed. The finite element method, a numerical technique for engineering analysis of structures, is used to model the geometry and approximate the solution. Various alternative formulations for analyzing laminated plates and shells are developed and their finite element models are tested for accuracy and economy in computation. These include the shear deformation laminate theory and degenerated 3-D elasticity theory for laminates.
Bayesian sensitivity analysis of bifurcating nonlinear models
NASA Astrophysics Data System (ADS)
Becker, W.; Worden, K.; Rowson, J.
2013-01-01
Sensitivity analysis allows one to investigate how changes in input parameters to a system affect the output. When computational expense is a concern, metamodels such as Gaussian processes can offer considerable computational savings over Monte Carlo methods, albeit at the expense of introducing a data modelling problem. In particular, Gaussian processes assume a smooth, non-bifurcating response surface. This work highlights a recent extension to Gaussian processes which uses a decision tree to partition the input space into homogeneous regions, and then fits separate Gaussian processes to each region. In this way, bifurcations can be modelled at region boundaries and different regions can have different covariance properties. To test this method, both the treed and standard methods were applied to the bifurcating response of a Duffing oscillator and a bifurcating FE model of a heart valve. It was found that the treed Gaussian process provides a practical way of performing uncertainty and sensitivity analysis on large, potentially-bifurcating models, which cannot be dealt with by using a single GP, although an open problem remains how to manage bifurcation boundaries that are not parallel to coordinate axes.
Nonlinear Seismic Analysis of Morrow Point Dam
Noble, C R; Nuss, L K
2004-02-20
This research and development project was sponsored by the United States Bureau of Reclamation (USBR), who are best known for the dams, power plants, and canals it constructed in the 17 western states. The mission statement of the USBR's Dam Safety Office, located in Denver, Colorado, is ''to ensure Reclamation dams do not present unacceptable risk to people, property, and the environment.'' The Dam Safety Office does this by quickly identifying the dams which pose an increased threat to the public, and quickly completing the related analyses in order to make decisions that will safeguard the public and associated resources. The research study described in this report constitutes one element of USBR's research and development work to advance their computational and analysis capabilities for studying the response of dams to strong earthquake motions. This project focused on the seismic response of Morrow Point Dam, which is located 263 km southwest of Denver, Colorado.
Finite element study of plate buckling induced by spatial temperature gradients
Thornton, E.A.; Kolenski, J.D.; Marino, R.P.
1993-01-01
Finite element analyses of thermal buckling of thin metallic plates with prescribed spatial temperature distributions are described. Thermally induced compressive membrane stresses and transverse plate displacement imperfections initiate plates buckling. A finite element formulation based on von Karman plate theory is presented. The resulting nonlinear equations are solved for incremental temperature increases by Newton-Raphson iteration. The computational method is used to investigate the buckling response of rectangular plates with steady and unsteady spatially varying temperature distributions. The role of initial plate imperfections and temperature distributions on the nonlinear response of plate displacements and stresses is described. The relatively high levels of stress induced by spatial temperature gradients should be considered carefully in the postbuckling design of panels for aerospace vehicles subjected to combined mechanical and thermal loads. 31 refs.
Finite element study of plate buckling induced by spatial temperature gradients
NASA Technical Reports Server (NTRS)
Thornton, Earl A.; Kolenski, James D.; Marino, Robert P.
1993-01-01
Finite element analyses of thermal buckling of thin metallic plates with prescribed spatial temperature distributions are described. Thermally induced compressive membrane stresses and transverse plate displacement imperfections initiate plates buckling. A finite element formulation based on von Karman plate theory is presented. The resulting nonlinear equations are solved for incremental temperature increases by Newton-Raphson iteration. The computational method is used to investigate the buckling response of rectangular plates with steady and unsteady spatially varying temperature distributions. The role of initial plate imperfections and temperature distributions on the nonlinear response of plate displacements and stresses is described. The relatively high levels of stress induced by spatial temperature gradients should be considered carefully in the postbuckling design of panels for aerospace vehicles subjected to combined mechanical and thermal loads.
Effects of geometric nonlinearities on the response of optimized box beam structures
NASA Technical Reports Server (NTRS)
Ragon, S.; Gurdal, Z.
1993-01-01
The present minimum-mass designs for a two-spar rectangular box beam were derived on the basis of linear-buckling FEM analysis constraints. In order to ascertain the effects of any geometric nonlinearities on these designs, each was subjected to a geometrically nonlinear FEM analysis. In all cases, the structure collapses below the design load, and does so in a mode which differs from that of linear theory. This discrepancy is attributable to such nonlinear panel-interaction mechanisms as rib-crusing loads. The optimized design is highly sensitive to crushing loads, relative to the nonoptimal design.
NASA Technical Reports Server (NTRS)
Stroud, W. J.; Agranoff, N.
1976-01-01
An analytical procedure is presented for designing hat stiffened and corrugated panels made of composite material and subjected to longitudinal (in the direction of the stiffeners) compression and shear loadings. The procedure is based on nonlinear mathematical programming techniques and a simplified set of buckling equations. Design requirements considered are buckling, strength, and extensional and shear stiffness. The effects of specified thickness, variation of cross-section dimensions, stiffness requirements, local buckling boundary conditions, and the effect of combined compression and shear loadings are shown.
And the Variscan Orogen Buckled
NASA Astrophysics Data System (ADS)
Pastor-Galán, D.; Groenewegen, T.; Gutiérrez-Alonso, G.; Langereis, C. G.
2013-12-01
Oroclines are the largest scale folds in nature, and as folds can be produced by bending or by buckling. The most commonly invoked bending mechanisms are indentation (the Himalayan syntaxes) and slab roll-back (The Calabria Arc) whereas buckling usually are commonly related with collision of the apex of ribbon continents along strike (Alaskan oroclines). In Western Europe the tectonostratigraphic zonation of Variscan orogen shows a complex 'S' shape pattern recently interpreted as a double orocline consisting of a northern and southern arc. The northern arc, known as Cantabria-Asturias Arc or Cantabrian Orocline, was developed after closure of the Rheic Ocean and the building and collapse of the Variscan orogenic edifice and, therefore, is considered post-Variscan in age. On the other hand, neither the geometry nor the kinematics of the so-called Central Iberian orocline, situated at the south of the Iberian peninsula are properly known. However, it seems reasonable to think that both oroclines developed at the same time as other coupled oroclines, such as the New England oroclines or the Carpathian oroclines. The particular paleogeography of the Variscan belt in Pangea and the kinematics of the oroclinal formation make impossible the mechanisms of indentation or buckling of a ribbon continent. The occurrence of an intense syn- and slightly post-Cantabrian orocline magmatic event (310-290 Ma) has been linked to the development of the orocline(s) due to the particular spatial-temporal distribution of these post-tectonic granitoids and its isotopic signature which would imply that the oroclines (if synchronous) are thick-skinned. This magmatic pulse has also been interpreted as due to slab roll-back. We present widespread evidences of buckling around the whole orocline at different lithospheric levels and new insights of the particular geometry of the southern orocline which is difficult to reconcile with a roll-back related origin. Therefore, a major change in the
Nonlinear constitutive theory for turbine engine structural analysis
NASA Technical Reports Server (NTRS)
Thompson, R. L.
1982-01-01
A number of viscoplastic constitutive theories and a conventional constitutive theory are evaluated and compared in their ability to predict nonlinear stress-strain behavior in gas turbine engine components at elevated temperatures. Specific application of these theories is directed towards the structural analysis of combustor liners undergoing transient, cyclic, thermomechanical load histories. The combustor liner material considered in this study is Hastelloy X. The material constants for each of the theories (as a function of temperature) are obtained from existing, published experimental data. The viscoplastic theories and a conventional theory are incorporated into a general purpose, nonlinear, finite element computer program. Several numerical examples of combustor liner structural analysis using these theories are given to demonstrate their capabilities. Based on the numerical stress-strain results, the theories are evaluated and compared.
Geometrically nonlinear analysis of layered composite plates and shells
NASA Technical Reports Server (NTRS)
Chao, W. C.; Reddy, J. N.
1983-01-01
A degenerated three dimensional finite element, based on the incremental total Lagrangian formulation of a three dimensional layered anisotropic medium was developed. Its use in the geometrically nonlinear, static and dynamic, analysis of layered composite plates and shells is demonstrated. A two dimenisonal finite element based on the Sanders shell theory with the von Karman (nonlinear) strains was developed. It is shown that the deflections obtained by the 2D shell element deviate from those obtained by the more accurate 3D element for deep shells. The 3D degenerated element can be used to model general shells that are not necessarily doubly curved. The 3D degenerated element is computationally more demanding than the 2D shell theory element for a given problem. It is found that the 3D element is an efficient element for the analysis of layered composite plates and shells undergoing large displacements and transient motion.
Nonlinear analysis of laminated fibrous composites. Ph.D. Thesis
NASA Technical Reports Server (NTRS)
Renieri, G. D.; Herakovich, C. T.
1976-01-01
A computerized analysis of the nonlinear behavior of fibrous composite laminates including axial loading, thermal loading, temperature dependent properties, and edge effects is presented. Ramberg-Osgood approximations are used to represent lamina stress-strain behavior and percent retention curves are employed to model the variation of properties with temperature. Balanced, symmetric laminates comprised of either boron/epoxy, graphite/epoxy, or borsic-aluminum are analyzed using a quasi-three-dimensional finite element analysis. Results are presented for the interlaminar stress distributions in cross-ply, angle-ply, and more complex laminates. Nonlinear stress-strain curves for a variety of composite laminates in tension and compression are obtained and compared to other existing theories and experimental results.
An integrated approach to the synthesis of geometrically non-linear structures
NASA Technical Reports Server (NTRS)
Smaoui, H.; Schmit, L. A.
1988-01-01
An integrated approach to the minimum weight design of geometrically nonlinear three-dimensional truss structures with geometric imperfections, subject to inequality constraints on static displacements, stresses, local buckling and cross sectional areas, is investigated. The integrated structural synthesis problem involves design and response quantities as independent variables and equilibrium equations, describing the finite element model, as equality constraints. The nonlinear structural analysis and the optimization are thus merged together into a single process. A computer program developed to compute the constraint values and analytical gradients is coupled with a generalized reduced gradient algorithm to solve the integrated problem. Numerical results for a geometrically nonlinear shallow dome example problem are presented for various types of imperfections. Furthermore, it is found that the algorithm is capable of detecting and guarding against system as well as element elastic instability using equilibrium information only, that is, without imposing system and local buckling inequality constraints.
Nonlinear analysis of a prestressed concrete pole section
Healy, G.S.
1982-08-01
This paper attacks the analysis of prestressed concrete structures. The attack is made assuming that the steel prestress members behave linearly and that the concrete is a nonlinear material obeying a second order stress-strain relationship. The entire analysis depends only on one empirical assumption and is developed from fundamental concepts of statics. The theoretical ground work is presented; and, then, a familiar example is solved. Additional theoretical development is presented as the solution of the example problem develops. This particular method of analysis presents an alternative to the empirically based ACI method.
Geometrically Nonlinear Finite Element Analysis of a Composite Space Reflector
NASA Technical Reports Server (NTRS)
Lee, Kee-Joo; Leet, Sung W.; Clark, Greg; Broduer, Steve (Technical Monitor)
2001-01-01
Lightweight aerospace structures, such as low areal density composite space reflectors, are highly flexible and may undergo large deflection under applied loading, especially during the launch phase. Accordingly, geometrically nonlinear analysis that takes into account the effect of finite rotation may be needed to determine the deformed shape for a clearance check and the stress and strain state to ensure structural integrity. In this study, deformation of the space reflector is determined under static conditions using a geometrically nonlinear solid shell finite element model. For the solid shell element formulation, the kinematics of deformation is described by six variables that are purely vector components. Because rotational angles are not used, this approach is free of the limitations of small angle increments. This also allows easy connections between substructures and large load increments with respect to the conventional shell formulation using rotational parameters. Geometrically nonlinear analyses were carried out for three cases of static point loads applied at selected points. A chart shows results for a case when the load is applied at the center point of the reflector dish. The computed results capture the nonlinear behavior of the composite reflector as the applied load increases. Also, they are in good agreement with the data obtained by experiments.
Accurate feature detection and estimation using nonlinear and multiresolution analysis
NASA Astrophysics Data System (ADS)
Rudin, Leonid; Osher, Stanley
1994-11-01
A program for feature detection and estimation using nonlinear and multiscale analysis was completed. The state-of-the-art edge detection was combined with multiscale restoration (as suggested by the first author) and robust results in the presence of noise were obtained. Successful applications to numerous images of interest to DOD were made. Also, a new market in the criminal justice field was developed, based in part, on this work.
Linear Algebraic Method for Non-Linear Map Analysis
Yu,L.; Nash, B.
2009-05-04
We present a newly developed method to analyze some non-linear dynamics problems such as the Henon map using a matrix analysis method from linear algebra. Choosing the Henon map as an example, we analyze the spectral structure, the tune-amplitude dependence, the variation of tune and amplitude during the particle motion, etc., using the method of Jordan decomposition which is widely used in conventional linear algebra.
Global-local methodologies and their application to nonlinear analysis
NASA Technical Reports Server (NTRS)
Noor, Ahmed K.
1989-01-01
An assessment is made of the potential of different global-local analysis strategies for predicting the nonlinear and postbuckling responses of structures. Two postbuckling problems of composite panels are used as benchmarks and the application of different global-local methodologies to these benchmarks is outlined. The key elements of each of the global-local strategies are discussed and future research areas needed to realize the full potential of global-local methodologies are identified.
Nonlinear analysis of blood flux in human vessels.
Bräuer, K; Hahn, M
1999-07-01
Laser Doppler fluxmetry (LDF) is frequently used in research on microcirculation of blood. Usually LDF time series are analysed by conventional linear methods, mainly Fourier analysis. These methods may not be optimal for the investigation of nonlinear effects of vasomotion, heartbeat or vessels. Nonlinear methods are based on a reconstruction of the system trajectory in an embedding space describing not only the measured time series but the behaviour of the whole system. The fill factor is a tool for displaying the main properties of this attractor in two dimensions and for determining diverse parameters for further analysis. A quantitative characterization of the system is possible by the distribution of correlation dimensions in the embedding space. The singular value decomposition (SVD) can be used to display and characterize individual degrees of freedom. These methods were applied to LDF time series from nine healthy controls and nine patients with Raynaud's phenomenon due to connective tissue disease. The fill factor and the SVD indicate qualitatively that in the controls vasomotion and heartbeat are the main influences on blood flow and act fairly independently of each other. In the patients there was a mixture of strong but irregular degrees of freedom. The mean and the maximal local correlation dimensions were significantly higher in the patient group. Nonlinear analysis of LDF time series provides additional information which cannot be detected using conventional approaches. PMID:10442708
Pulsatile instability in rapid directional solidification - Strongly-nonlinear analysis
NASA Technical Reports Server (NTRS)
Merchant, G. J.; Braun, R. J.; Brattkus, K.; Davis, S. H.
1992-01-01
In the rapid directional solidification of a dilute binary alloy, analysis reveals that, in addition to the cellular mode of Mullins and Sekerka (1964), there is an oscillatory instability. For the model analyzed by Merchant and Davis (1990), the preferred wavenumber is zero; the mode is one of pulsation. Two strongly nonlinear analyses are performed that describe this pulsatile mode. In the first case, nonequilibrium effects that alter solute rejection at the interface are taken asymptotically small. A nonlinear oscillator equation governs the position of the solid-liquid interface at leading order, and amplitude and phase evolution equations are derived for the uniformly pulsating interface. The analysis provides a uniform description of both subcritical and supercritical bifurcation and the transition between the two. In the second case, nonequilibrium effects that alter solute rejection are taken asymptotically large, and a different nonlinear oscillator equation governs the location of the interface to leading order. A similar analysis allows for the derivation of an amplitude evolution equation for the uniformly pulsating interface. In this case, the bifurcation is always supercritical. The results are used to make predictions about the characteristics of solute bands that would be frozen into the solid.
Weakly nonlinear analysis and localised structures in nonlinear cavities with metamaterials
NASA Astrophysics Data System (ADS)
Slimani, N.; Makhoute, A.; Tlidi, M.
2016-04-01
We consider an optical ring cavity filled with a metamaterial and with a Kerr medium. The cavity is driven by a coherent radiation beam. The modelling of this device leads to the well known Lugiato-Lefever equation with high order diffraction term. We assume that both left-handed and right-handed materials possess a Kerr focusing type of nonlinearity. We show that close to the zero-diffraction regime, high-order diffraction effect allows us to stabilise dark localised structures in this device. These structures consist of dips or holes in the transverse profile of the intracavity field and do not exist without high-order diffraction effects. We show that high order diffraction effects alter in depth the space-time dynamics of this device. A weakly nonlinear analysis in the vicinity of the first threshold associated with the Turing instability is performed. This analysis allows us to determine the parameter regime where the transition from super- to sub-critical bifurcation occurs. When the modulational instability appears subcritically, we show that bright localised structures of light may be generated in two-dimensional setting. Close to the second threshold associated with the Turing instability, dark localised structures are generated.
Buckling behavior of long anisotropic plates subjected to combined loads
NASA Technical Reports Server (NTRS)
Nemeth, Michael P.
1995-01-01
A parametric study is presented of the buckling behavior of infinitely long symmetrically laminated anisotropic plates subjected to combined loads. The study focuses on the interaction of a subcritical (stable) secondary loading state of constant magnitude and a primary destabilizing load that is increased in magnitude until buckling occurs. The loads, considered in this report are uniform axial compression, pure in-plane bending, transverse tension and compression, and shear. Results are presented that were obtained by using a special purpose nondimensional analysis that is well suited for parametric studies of clamped and simply supported plates. In particular, results are presented for a +/- 45(sub S) graphite-epoxy laminate that is highly anisotropic and representative of a laminate used for spacecraft applications. In addition, generic buckling-design charts are presented for a wide range of nondimensional parameters that are applicable to a broad class of laminate constructions. These results show the general behavioral trends of specially orthotropic plates and the effects of flexural anisotropy on plates subjected to various combined loading conditions. An important finding of the present study is that the effects of flexural anisotropy on the buckling resistance of a plate can be significantly more important for plates subjected to combined loads than for plates subjected to single-component loads.
Buckling Behavior of Long Anisotropic Plates Subjected to Combined Loads
NASA Technical Reports Server (NTRS)
Nemeth, Michael P.
1995-01-01
A parametric study of the buckling behavior of infinitely long symmetrically laminated anisotropic plates subjected to combined loads is presented. The study focuses on the interaction of a stable subcritical secondary loading state of constant magnitude and a primary destabilizing load that is increased in magnitude until buckling occurs. The loads considered are uniform axial compression, pure inplane bending, transverse tension and compression, and shear. Results obtained using a special purpose plates with a significant potential for reducing structural nondimensional analysis that is well suited for parametric studies are presented for clamped and simply supported plates. In particular, results are presented for a (+/- 45)(sub s) graphite-epoxy laminate, and generic buckling design charts are presented for a wide range of non-dimensional parameters that are applicable to a broad class of laminate constructions. These results show the effects of flexural orthotropy and flexural anisotropy on plates subjected to various combined loading conditions. An important finding of the present study is that the effect of flexural anisotropy herein as flexural anisotropy on the buckling resistance of a plate can be increased significantly for certain types of combined loads.
A triangular thin shell finite element: Nonlinear analysis. [structural analysis
NASA Technical Reports Server (NTRS)
Thomas, G. R.; Gallagher, R. H.
1975-01-01
Aspects of the formulation of a triangular thin shell finite element which pertain to geometrically nonlinear (small strain, finite displacement) behavior are described. The procedure for solution of the resulting nonlinear algebraic equations combines a one-step incremental (tangent stiffness) approach with one iteration in the Newton-Raphson mode. A method is presented which permits a rational estimation of step size in this procedure. Limit points are calculated by means of a superposition scheme coupled to the incremental side of the solution procedure while bifurcation points are calculated through a process of interpolation of the determinants of the tangent-stiffness matrix. Numerical results are obtained for a flat plate and two curved shell problems and are compared with alternative solutions.
Conditions for Symmetries in the Buckle Patterns of Laminated-Composite Plates
NASA Technical Reports Server (NTRS)
Nemeth, Michael P.
2012-01-01
Conditions for the existence of certain symmetries to exist in the buckle patterns of symmetrically laminated composite plates are presented. The plates considered have a general planform with cutouts, variable thickness and stiffnesses, and general support and loading conditions. The symmetry analysis is based on enforcing invariance of the corresponding eigenvalue problem for a group of coordinate transformations associated with buckle patterns commonly exhibited by symmetrically laminated plates. The buckle-pattern symmetries examined include a central point of inversion symmetry, one plane of reflective symmetry, and two planes of reflective symmetry.
NASA Astrophysics Data System (ADS)
Muc, A.
The paper deals with the static buckling and postbuckling behavior of clamped elastic imperfect laminated shallow spherical shells subjected to uniform external pressure. Three types of initial geometrical imperfections are analyzed: two local described by a convex or a concave curve, and one global in the form of the Legendre polynomial. Applying the Rayleigh-Ritz procedure to Marguerre's equations combined with the precise prebuckling numerical analysis, reasonably accurate solutions are obtained for upper and lower buckling pressures. The effects of fiber orientations on pre- and postbuckling behavior, imperfection sensitivity, buckling loads, and modes are considered. The results for composite shells are compared with those calculated for quasi-isotropic ones.
Nonlinear analysis of epileptic activity in rabbit neocortex.
Sarnthein, J; Abarbanel, H D; Pockberger, H
1998-01-01
We report on the nonlinear analysis of electroencephalogram (EEG) recordings in the rabbit visual cortex. Epileptic seizures were induced by local penicillin application and triggered by visual stimulation. The analysis procedures for nonlinear signals have been developed over the past few years and applied primarily to physical systems. This is an early application to biological systems and the first to EEG data. We find that during epileptic activity, both global and local embedding dimensions are reduced with respect to nonepileptic activity. Interestingly, these values are very low (dE approximately equal to 3) and do not change between preictal and tonic stages of epileptic activity, also the Lyapunov dimension remains constant. However, between these two stages the manifestations of the local dynamics change quite drastically, as can be seen, e.g., from the shape of the attractors. Furthermore, the largest Lyapunov exponent is reduced by a factor of about two in the second stage and characterizes the difference in dynamics. Thus, the occurrence of clinical symptoms associated with the tonic seizure activity seems to be mainly related to the local dynamics of the nonlinear system. These results thus seem to give a strong indication that the dynamics remains much the same in these stages of behavior, and changes are due to alterations in model parameters and consequent bifurcations of the observed orbits. PMID:9485585
Selecting Earthquake Records for Nonlinear Dynamic Analysis of Structures
Rodriguez, Mario E.
2008-07-08
An area in earthquake risk reduction that needs an urgent examination is the selection of earthquake records for nonlinear dynamic analysis of structures. An often-mentioned shortcoming from results of nonlinear dynamic analyses of structures is that these results are limited to the type of records that these analyses use as input data. This paper proposes a procedure for selecting earthquake records for nonlinear dynamic analysis of structures. This procedure uses a seismic damage index evaluated using the hysteretic energy dissipated by a Single Degree of Freedom System (SDOF) representing a multi-degree-of freedom structure responding to an earthquake record, and the plastic work capacity of the system at collapse. The type of structural system is considered using simple parameters. The proposed method is based on the evaluation of the damage index for a suite of earthquake records and a selected type of structural system. A set of 10 strong ground motion records is analyzed to show an application of the proposed procedure for selecting earthquake records for structural design.
Nonlinear dynamic analysis of quasi-symmetric anisotropic structures
NASA Technical Reports Server (NTRS)
Noor, Ahmed K.; Peters, Jeanne M.
1987-01-01
An efficient computational method for the nonlinear dynamic analysis of quasi-symmetric anisotropic structures is proposed. The application of mixed models simplifies the analytical development and improves the accuracy of the response predictions, and operator splitting allows the reduction of the analysis model of the quasi-symmetric structure to that of the corresponding symmetric structure. The preconditoned conjugate gradient provides a stable and effective technique for generating the unsymmetric response of the structure as the sum of a symmetrized response plus correction modes. The effectiveness of the strategy is demonstrated with the example of a laminated anisotropic shallow shell of quadrilateral planform subjected to uniform normal loading.
Nonlinear bulk viscosity in FRW cosmology: a phase space analysis.
NASA Astrophysics Data System (ADS)
Acquaviva, G.; Beesham, A.
2015-11-01
We consider a Friedmann-Robertson-Walker spacetime filled with both viscous radiation and nonviscous dust. The former has a bulk viscosity that is proportional to an arbitrary power of the energy density, i.e. \\zeta \\propto {ρ }{{v}}ν , and viscous pressure satisfying a nonlinear evolution equation. The analysis is carried out in the context of dynamical systems and the properties of solutions corresponding to the fixed points are discussed. For some ranges of the relevant parameter ν we find that the trajectories in the phase space evolve from a FRW singularity towards an asymptotic de Sitter attractor, confirming and extending previous analysis in the literature.
A comparison of experimental and calculated thin-shell leading-edge buckling due to thermal stresses
NASA Technical Reports Server (NTRS)
Jenkins, Jerald M.
1988-01-01
High-temperature thin-shell leading-edge buckling test data are analyzed using NASA structural analysis (NASTRAN) as a finite element tool for predicting thermal buckling characteristics. Buckling points are predicted for several combinations of edge boundary conditions. The problem of relating the appropriate plate area to the edge stress distribution and the stress gradient is addressed in terms of analysis assumptions. Local plasticity was found to occur on the specimen analyzed, and this tended to simplify the basic problem since it effectively equalized the stress gradient from loaded edge to loaded edge. The initial loading was found to be difficult to select for the buckling analysis because of the transient nature of thermal stress. Multiple initial model loadings are likely required for complicated thermal stress time histories before a pertinent finite element buckling analysis can be achieved. The basic mode shapes determined from experimentation were correctly identified from computation.
Energy harvesting from controlled buckling of piezoelectric beams
NASA Astrophysics Data System (ADS)
Ansari, M. H.; Karami, M. Amin
2015-11-01
A piezoelectric vibration energy harvester is presented that can generate electricity from the weight of passing cars or crowds. The energy harvester consists of a piezoelectric beam, which buckles when the device is stepped on. The energy harvester can have a horizontal or vertical configuration. In the vertical (direct) configuration, the piezoelectric beam is vertical and directly sustains the weight of the vehicles or people. In the horizontal (indirect) configuration, the vertical weight is transferred to a horizontal axial force through a scissor-like mechanism. Buckling of the beam results in significant stresses and, thus, large power production. However, if the beam’s buckling is not controlled, the beam will fracture. To prevent this, the axial deformation is constrained to limit the deformations of the beam. In this paper, the energy harvester is analytically modeled. The considered piezoelectric beam is a general non-uniform beam. The natural frequencies, mode shapes, and the critical buckling force corresponding to each mode shape are calculated. The electro-mechanical coupling and the geometric nonlinearities are included in the model. The design criteria for the device are discussed. It is demonstrated that a device, realized with commonly used piezoelectric patches, can generate tens of milliwatts of power from passing car traffic. The proposed device could also be implemented in the sidewalks or integrated in shoe soles for energy generation. One of the key features of the device is its frequency up-conversion characteristics. The piezoelectric beam undergoes free vibrations each time the weight is applied to or removed from the energy harvester. The frequency of the free vibrations is orders of magnitude larger than the frequency of the load. The device is, thus, both efficient and insensitive to the frequency of the force excitations.
Nonlinear analysis of magnetization dynamics excited by spin Hall effect
NASA Astrophysics Data System (ADS)
Taniguchi, Tomohiro
2015-03-01
We investigate the possibility of exciting self-oscillation in a perpendicular ferromagnet by the spin Hall effect on the basis of a nonlinear analysis of the Landau-Lifshitz-Gilbert (LLG) equation. In the self-oscillation state, the energy supplied by the spin torque during a precession on a constant energy curve should equal the dissipation due to damping. Also, the current to balance the spin torque and the damping torque in the self-oscillation state should be larger than the critical current to destabilize the initial state. We find that these conditions in the spin Hall system are not satisfied by deriving analytical solutions of the energy supplied by the spin transfer effect and the dissipation due to the damping from the nonlinear LLG equation. This indicates that the self-oscillation of a perpendicular ferromagnet cannot be excited solely by the spin Hall torque.
NASA Astrophysics Data System (ADS)
Asaka, Koji; Kato, Ryoei; Miyazawa, Kun'ichi; Kizuka, Tokushi
2006-08-01
The authors demonstrated the mechanics of materials for crystalline whiskers composed of C60 molecules; compressive deformation of the whiskers was observed by in situ transmission electron microscopy with simultaneous force measurement by means of an optical cantilever method, as used in atomic force microscopy. In response to compression along the long axis, the whiskers bent first elastically, then buckled. A whisker with 160nm diameter fractured brittlely at a strain of 0.08. According to Euler's formula, Young's modulus of the whisker was estimated to be 32-54GPa, which is 160%-650% of that of C60 bulk crystals.
State-variable analysis of non-linear circuits with a desk computer
NASA Technical Reports Server (NTRS)
Cohen, E.
1981-01-01
State variable analysis was used to analyze the transient performance of non-linear circuits on a desk top computer. The non-linearities considered were not restricted to any circuit element. All that is required for analysis is the relationship defining each non-linearity be known in terms of points on a curve.
Nonlinear mathematical modeling and sensitivity analysis of hydraulic drive unit
NASA Astrophysics Data System (ADS)
Kong, Xiangdong; Yu, Bin; Quan, Lingxiao; Ba, Kaixian; Wu, Liujie
2015-09-01
The previous sensitivity analysis researches are not accurate enough and also have the limited reference value, because those mathematical models are relatively simple and the change of the load and the initial displacement changes of the piston are ignored, even experiment verification is not conducted. Therefore, in view of deficiencies above, a nonlinear mathematical model is established in this paper, including dynamic characteristics of servo valve, nonlinear characteristics of pressure-flow, initial displacement of servo cylinder piston and friction nonlinearity. The transfer function block diagram is built for the hydraulic drive unit closed loop position control, as well as the state equations. Through deriving the time-varying coefficient items matrix and time-varying free items matrix of sensitivity equations respectively, the expression of sensitivity equations based on the nonlinear mathematical model are obtained. According to structure parameters of hydraulic drive unit, working parameters, fluid transmission characteristics and measured friction-velocity curves, the simulation analysis of hydraulic drive unit is completed on the MATLAB/Simulink simulation platform with the displacement step 2 mm, 5 mm and 10 mm, respectively. The simulation results indicate that the developed nonlinear mathematical model is sufficient by comparing the characteristic curves of experimental step response and simulation step response under different constant load. Then, the sensitivity function time-history curves of seventeen parameters are obtained, basing on each state vector time-history curve of step response characteristic. The maximum value of displacement variation percentage and the sum of displacement variation absolute values in the sampling time are both taken as sensitivity indexes. The sensitivity indexes values above are calculated and shown visually in histograms under different working conditions, and change rules are analyzed. Then the sensitivity
Develop advanced nonlinear signal analysis topographical mapping system
NASA Technical Reports Server (NTRS)
1994-01-01
The Space Shuttle Main Engine (SSME) has been undergoing extensive flight certification and developmental testing, which involves some 250 health monitoring measurements. Under the severe temperature, pressure, and dynamic environments sustained during operation, numerous major component failures have occurred, resulting in extensive engine hardware damage and scheduling losses. To enhance SSME safety and reliability, detailed analysis and evaluation of the measurements signal are mandatory to assess its dynamic characteristics and operational condition. Efficient and reliable signal detection techniques will reduce catastrophic system failure risks and expedite the evaluation of both flight and ground test data, and thereby reduce launch turn-around time. The basic objective of this contract are threefold: (1) develop and validate a hierarchy of innovative signal analysis techniques for nonlinear and nonstationary time-frequency analysis. Performance evaluation will be carried out through detailed analysis of extensive SSME static firing and flight data. These techniques will be incorporated into a fully automated system; (2) develop an advanced nonlinear signal analysis topographical mapping system (ATMS) to generate a Compressed SSME TOPO Data Base (CSTDB). This ATMS system will convert tremendous amount of complex vibration signals from the entire SSME test history into a bank of succinct image-like patterns while retaining all respective phase information. High compression ratio can be achieved to allow minimal storage requirement, while providing fast signature retrieval, pattern comparison, and identification capabilities; and (3) integrate the nonlinear correlation techniques into the CSTDB data base with compatible TOPO input data format. Such integrated ATMS system will provide the large test archives necessary for quick signature comparison. This study will provide timely assessment of SSME component operational status, identify probable causes of
Develop advanced nonlinear signal analysis topographical mapping system
NASA Technical Reports Server (NTRS)
Jong, Jen-Yi
1993-01-01
The SSME has been undergoing extensive flight certification and developmental testing, which involves some 250 health monitoring measurements. Under the severe temperature pressure, and dynamic environments sustained during operation, numerous major component failures have occurred, resulting in extensive engine hardware damage and scheduling losses. To enhance SSME safety and reliability, detailed analysis and evaluation of the measurements signal are mandatory to assess its dynamic characteristics and operational condition. Efficient and reliable signal detection techniques will reduce catastrophic system failure risks and expedite the evaluation of both flight and ground test data, and thereby reduce launch turn-around time. The basic objective of this contract are threefold: (1) Develop and validate a hierarchy of innovative signal analysis techniques for nonlinear and nonstationary time-frequency analysis. Performance evaluation will be carried out through detailed analysis of extensive SSME static firing and flight data. These techniques will be incorporated into a fully automated system. (2) Develop an advanced nonlinear signal analysis topographical mapping system (ATMS) to generate a Compressed SSME TOPO Data Base (CSTDB). This ATMS system will convert tremendous amounts of complex vibration signals from the entire SSME test history into a bank of succinct image-like patterns while retaining all respective phase information. A high compression ratio can be achieved to allow the minimal storage requirement, while providing fast signature retrieval, pattern comparison, and identification capabilities. (3) Integrate the nonlinear correlation techniques into the CSTDB data base with compatible TOPO input data format. Such integrated ATMS system will provide the large test archives necessary for a quick signature comparison. This study will provide timely assessment of SSME component operational status, identify probable causes of malfunction, and indicate
Nonlinear Analysis of Bonded Composite Single-LAP Joints
NASA Technical Reports Server (NTRS)
Oterkus, E.; Barut, A.; Madenci, E.; Smeltzer, S. S.; Ambur, D. R.
2004-01-01
This study presents a semi-analytical solution method to analyze the geometrically nonlinear response of bonded composite single-lap joints with tapered adherend edges under uniaxial tension. The solution method provides the transverse shear and normal stresses in the adhesive and in-plane stress resultants and bending moments in the adherends. The method utilizes the principle of virtual work in conjunction with von Karman s nonlinear plate theory to model the adherends and the shear lag model to represent the kinematics of the thin adhesive layer between the adherends. Furthermore, the method accounts for the bilinear elastic material behavior of the adhesive while maintaining a linear stress-strain relationship in the adherends. In order to account for the stiffness changes due to thickness variation of the adherends along the tapered edges, their in-plane and bending stiffness matrices are varied as a function of thickness along the tapered region. The combination of these complexities results in a system of nonlinear governing equilibrium equations. This approach represents a computationally efficient alternative to finite element method. Comparisons are made with corresponding results obtained from finite-element analysis. The results confirm the validity of the solution method. The numerical results present the effects of taper angle, adherend overlap length, and the bilinear adhesive material on the stress fields in the adherends, as well as the adhesive, of a single-lap joint
Analysis and correction of gradient nonlinearity bias in ADC measurements
Malyarenko, Dariya I.; Ross, Brian D.; Chenevert, Thomas L.
2013-01-01
Purpose Gradient nonlinearity of MRI systems leads to spatially-dependent b-values and consequently high non-uniformity errors (10–20%) in ADC measurements over clinically relevant field-of-views. This work seeks practical correction procedure that effectively reduces observed ADC bias for media of arbitrary anisotropy in the fewest measurements. Methods All-inclusive bias analysis considers spatial and time-domain cross-terms for diffusion and imaging gradients. The proposed correction is based on rotation of the gradient nonlinearity tensor into the diffusion gradient frame where spatial bias of b-matrix can be approximated by its Euclidean norm. Correction efficiency of the proposed procedure is numerically evaluated for a range of model diffusion tensor anisotropies and orientations. Results Spatial dependence of nonlinearity correction terms accounts for the bulk (75–95%) of ADC bias for FA = 0.3–0.9. Residual ADC non-uniformity errors are amplified for anisotropic diffusion. This approximation obviates need for full diffusion tensor measurement and diagonalization to derive a corrected ADC. Practical scenarios are outlined for implementation of the correction on clinical MRI systems. Conclusions The proposed simplified correction algorithm appears sufficient to control ADC non-uniformity errors in clinical studies using three orthogonal diffusion measurements. The most efficient reduction of ADC bias for anisotropic medium is achieved with non-lab-based diffusion gradients. PMID:23794533
Nonlinear rotordynamics analysis. [Space Shuttle Main Engine turbopumps
NASA Technical Reports Server (NTRS)
Noah, Sherif T.
1991-01-01
Effective analysis tools were developed for predicting the nonlinear rotordynamic behavior of the Space Shuttle Main Engine (SSME) turbopumps under steady and transient operating conditions. Using these methods, preliminary parametric studies were conducted on both generic and actual HPOTP (high pressure oxygen turbopump) models. In particular, a novel modified harmonic balance/alternating Fourier transform (HB/AFT) method was developed and used to conduct a preliminary study of the effects of fluid, bearing and seal forces on the unbalanced response of a multi-disk rotor in the presence of bearing clearances. The method makes it possible to determine periodic, sub-, super-synchronous and chaotic responses of a rotor system. The method also yields information about the stability of the obtained response, thus allowing bifurcation analyses. This provides a more effective capability for predicting the response under transient conditions by searching in proximity of resonance peaks. Preliminary results were also obtained for the nonlinear transient response of an actual HPOTP model using an efficient, newly developed numerical method based on convolution integration. Currently, the HB/AFT is being extended for determining the aperiodic response of nonlinear systems. Initial results show the method to be promising.
Classification of Asthma Based on Nonlinear Analysis of Breathing Pattern.
Raoufy, Mohammad Reza; Ghafari, Tara; Darooei, Reza; Nazari, Milad; Mahdaviani, Seyed Alireza; Eslaminejad, Ali Reza; Almasnia, Mehdi; Gharibzadeh, Shahriar; Mani, Ali R; Hajizadeh, Sohrab
2016-01-01
Normal human breathing exhibits complex variability in both respiratory rhythm and volume. Analyzing such nonlinear fluctuations may provide clinically relevant information in patients with complex illnesses such as asthma. We compared the cycle-by-cycle fluctuations of inter-breath interval (IBI) and lung volume (LV) among healthy volunteers and patients with various types of asthma. Continuous respiratory datasets were collected from forty age-matched men including 10 healthy volunteers, 10 patients with controlled atopic asthma, 10 patients with uncontrolled atopic asthma, and 10 patients with uncontrolled non-atopic asthma during 60 min spontaneous breathing. Complexity of breathing pattern was quantified by calculating detrended fluctuation analysis, largest Lyapunov exponents, sample entropy, and cross-sample entropy. The IBI as well as LV fluctuations showed decreased long-range correlation, increased regularity and reduced sensitivity to initial conditions in patients with asthma, particularly in uncontrolled state. Our results also showed a strong synchronization between the IBI and LV in patients with uncontrolled asthma. Receiver operating characteristic (ROC) curve analysis showed that nonlinear analysis of breathing pattern has a diagnostic value in asthma and can be used in differentiating uncontrolled from controlled and non-atopic from atopic asthma. We suggest that complexity analysis of breathing dynamics may represent a novel physiologic marker to facilitate diagnosis and management of patients with asthma. However, future studies are needed to increase the validity of the study and to improve these novel methods for better patient management. PMID:26824900
Classification of Asthma Based on Nonlinear Analysis of Breathing Pattern
Raoufy, Mohammad Reza; Ghafari, Tara; Darooei, Reza; Nazari, Milad; Mahdaviani, Seyed Alireza; Eslaminejad, Ali Reza; Almasnia, Mehdi; Gharibzadeh, Shahriar; Mani, Ali R.; Hajizadeh, Sohrab
2016-01-01
Normal human breathing exhibits complex variability in both respiratory rhythm and volume. Analyzing such nonlinear fluctuations may provide clinically relevant information in patients with complex illnesses such as asthma. We compared the cycle-by-cycle fluctuations of inter-breath interval (IBI) and lung volume (LV) among healthy volunteers and patients with various types of asthma. Continuous respiratory datasets were collected from forty age-matched men including 10 healthy volunteers, 10 patients with controlled atopic asthma, 10 patients with uncontrolled atopic asthma, and 10 patients with uncontrolled non-atopic asthma during 60 min spontaneous breathing. Complexity of breathing pattern was quantified by calculating detrended fluctuation analysis, largest Lyapunov exponents, sample entropy, and cross-sample entropy. The IBI as well as LV fluctuations showed decreased long-range correlation, increased regularity and reduced sensitivity to initial conditions in patients with asthma, particularly in uncontrolled state. Our results also showed a strong synchronization between the IBI and LV in patients with uncontrolled asthma. Receiver operating characteristic (ROC) curve analysis showed that nonlinear analysis of breathing pattern has a diagnostic value in asthma and can be used in differentiating uncontrolled from controlled and non-atopic from atopic asthma. We suggest that complexity analysis of breathing dynamics may represent a novel physiologic marker to facilitate diagnosis and management of patients with asthma. However, future studies are needed to increase the validity of the study and to improve these novel methods for better patient management. PMID:26824900
Locking and its treatment for nonlinear isogeometric analysis
NASA Astrophysics Data System (ADS)
Cardoso, Rui P. R.; Cesar de Sa, Jose M. A.
2013-12-01
Isogeometric Analysis (IGA) has become very popular for the analysis of structures, fluids and fluid-structure interaction problems. IGA suffers from the same problems depicted by other numerical methods when dealing with constrained problems as those associated with handling of incompressibility or transverse shear effects on thin structures, giving rise to the well-known locking problems. In this work, some methodologies to alleviate locking problems in IGA will be presented. They include an analysis of the subspace of the constrained fields underlying the numerical solution and include projection techniques to extrapolate those field representations at points associated with reduced Gaussian integration rules. The basis functions used are grounded on Non-Uniform Rational B-Splines (NURBS), which are very popular on the solid modeling (CAD) community. The extension of the proposed locking remedies to nonlinear isogeometric analysis is also considered.
Effects of Shell-Buckling Knockdown Factors in Large Cylindrical Shells
NASA Technical Reports Server (NTRS)
Hrinda, Glenn A.
2012-01-01
Shell-buckling knockdown factors (SBKF) have been used in large cylindrical shell structures to account for uncertainty in buckling loads. As the diameter of the cylinder increases, achieving the manufacturing tolerances becomes increasingly more difficult. Knockdown factors account for manufacturing imperfections in the shell geometry by decreasing the allowable buckling load of the cylinder. In this paper, large-diameter (33 ft) cylinders are investigated by using various SBKF's. An investigation that is based on finite-element analysis (FEA) is used to develop design sensitivity relationships. Different manufacturing imperfections are modeled into a perfect cylinder to investigate the effects of these imperfections on buckling. The analysis results may be applicable to large- diameter rockets, cylindrical tower structures, bulk storage tanks, and silos.
NASA Technical Reports Server (NTRS)
Nemeth, Michael P.
2004-01-01
An approach for synthesizing buckling results for thin balanced and unbalanced symmetric laminates that are subjected to uniform heating or cooling and elastically restrained against thermal expansion or contraction is presented. This approach uses a nondimensional analysis for infinitely long, flexural anisotropic plates that are subjected to combined mechanical loads. In addition, stiffness-weighted laminate thermal-expansion parameters and compliance coefficients are derived that are used to determine critical temperatures in terms of physically intuitive mechanical-buckling coefficients. Many results are presented for some common laminates that are intended to facilitate a structural designer s transition to the use of the generic buckling design curves. Several curves that illustrate the fundamental parameters used in the analysis are presented, for nine contemporary material systems, that provide physical insight into the buckling response in addition to providing useful design data. Examples are presented that demonstrate the use of the generic design curves.
NASA Technical Reports Server (NTRS)
Zoladz, T.; Earhart, E.; Fiorucci, T.
1995-01-01
Utilizing high-frequency data from a highly instrumented rotor assembly, seeded bearing defect signatures are characterized using both conventional linear approaches, such as power spectral density analysis, and recently developed nonlinear techniques such as bicoherence analysis. Traditional low-frequency (less than 20 kHz) analysis and high-frequency envelope analysis of both accelerometer and acoustic emission data are used to recover characteristic bearing distress information buried deeply in acquired data. The successful coupling of newly developed nonlinear signal analysis with recovered wideband envelope data from accelerometers and acoustic emission sensors is the innovative focus of this research.
Vector algorithms for geometrically nonlinear 3D finite element analysis
NASA Technical Reports Server (NTRS)
Whitcomb, John D.
1989-01-01
Algorithms for geometrically nonlinear finite element analysis are presented which exploit the vector processing capability of the VPS-32, which is closely related to the CYBER 205. By manipulating vectors (which are long lists of numbers) rather than individual numbers, very high processing speeds are obtained. Long vector lengths are obtained without extensive replication or reordering by storage of intermediate results in strategic patterns at all stages of the computations. Comparisons of execution times with those from programs using either scalar or other vector programming techniques indicate that the algorithms presented are quite efficient.
Improved Design Formulae for Buckling of Orthotropic Plates under Combined Loading
NASA Technical Reports Server (NTRS)
Weaver, Paul M.; Nemeth, Michael P.
2008-01-01
Simple, accurate buckling interaction formulae are presented for long orthotropic plates with either simply supported or clamped longitudinal edges and under combined loading that are suitable for design studies. The loads include 1) combined uniaxial compression (or tension) and shear, 2) combined pure inplane bending and 3) shear and combined uniaxial compression (or tension) and pure inplane bending. The interaction formulae are the results of detailed regression analysis of buckling data obtained from a very accurate Rayleigh-Ritz method.
Buckling of regular, chiral and hierarchical honeycombs under a general macroscopic stress state
Haghpanah, Babak; Papadopoulos, Jim; Mousanezhad, Davood; Nayeb-Hashemi, Hamid; Vaziri, Ashkan
2014-01-01
An approach to obtain analytical closed-form expressions for the macroscopic ‘buckling strength’ of various two-dimensional cellular structures is presented. The method is based on classical beam-column end-moment behaviour expressed in a matrix form. It is applied to sample honeycombs with square, triangular and hexagonal unit cells to determine their buckling strength under a general macroscopic in-plane stress state. The results were verified using finite-element Eigenvalue analysis. PMID:25002823
Weakly nonlinear analysis of the Saffman-Taylor problem
NASA Astrophysics Data System (ADS)
Miranda, Jose A.
The Saffman-Taylor viscous fingering instability occurs when a less viscous fluid displaces a more viscous one between narrowly spaced parallel plates in a Hele-Shaw cell. Experiments in radial and rectangular flow geometries form finger-like patterns, in which fingers of different lengths compete, spread and split. Our weakly nonlinear analysis of the instability predicts these phenomena, which are beyond the scope of linear stability theory. Finger competition arises through enhanced growth of sub-harmonic perturbations, while spreading and splitting occur through the growth of harmonic modes. Nonlinear mode-coupling enhances the growth of these specific perturbations with appropriate relative phases, as we demonstrate through a symmetry analysis of the mode coupling equations. We extend our mode coupling theory to include the situation in which one of the fluids is a ferrofluid and a magnetic field is applied normal to the Hele-Shaw cell. Our analysis indicates that the onset of interface symmetry breaking observed in experiments involving ferrofluids depends on viscosity contrast, not on the applied magnetic field. We also show how magnetic fields lead to finger tip-splitting.
The Smooth Decomposition as a nonlinear modal analysis tool
NASA Astrophysics Data System (ADS)
Bellizzi, Sergio; Sampaio, Rubens
2015-12-01
The Smooth Decomposition (SD) is a statistical analysis technique for finding structures in an ensemble of spatially distributed data such that the vector directions not only keep the maximum possible variance but also the motions, along the vector directions, are as smooth in time as possible. In this paper, the notion of the dual smooth modes is introduced and used in the framework of oblique projection to expand a random response of a system. The dual modes define a tool that transforms the SD in an efficient modal analysis tool. The main properties of the SD are discussed and some new optimality properties of the expansion are deduced. The parameters of the SD give access to modal parameters of a linear system (mode shapes, resonance frequencies and modal energy participations). In case of nonlinear systems, a richer picture of the evolution of the modes versus energy can be obtained analyzing the responses under several excitation levels. This novel analysis of a nonlinear system is illustrated by an example.
NASA Technical Reports Server (NTRS)
Knight, Norman F., Jr. (Principal Investigator)
1996-01-01
The goal of this research project is to develop assumed-stress hybrid elements with rotational degrees of freedom for analyzing composite structures. During the first year of the three-year activity, the effort was directed to further assess the AQ4 shell element and its extensions to buckling and free vibration problems. In addition, the development of a compatible 2-node beam element was to be accomplished. The extensions and new developments were implemented in the Computational Structural Mechanics Testbed COMET. An assessment was performed to verify the implementation and to assess the performance of these elements in terms of accuracy. During the second and third years, extensions to geometrically nonlinear problems were developed and tested. This effort involved working with the nonlinear solution strategy as well as the nonlinear formulation for the elements. This research has resulted in the development and implementation of two additional element processors (ES22 for the beam element and ES24 for the shell elements) in COMET. The software was developed using a SUN workstation and has been ported to the NASA Langley Convex named blackbird. Both element processors are now part of the baseline version of COMET.
Wang, S.S.; Srinivasan, S.; Su, K.B.; Dunham, M.G.
1994-12-31
Recent advances in fiber-composites manufacturing and structural efficiency requirements have led to the consideration of large isogrid-stiffened fiber-composite laminate shells for various aeronautical and space structural applications. Very little information, if any, on buckling and postbuckling of these grid-stiffened shells is currently available in the literature. In this paper, a combined analytical and experimental study is reported on the buckling and postbuckling behavior of these filament-wound fiber-composite laminate shells constructed with continuous-filament isogrid stiffeners made of the same composite material system. Solutions from linear bifurcation and geometric nonlinear postbuckling analyses have been obtained for stiffened composite shells, monocoque shells and isogrid stiffeners. Experiments have been conducted in parallel to the analyses, and buckling loads and postbuckling deformation characteristics have been studied for these structures.
Perturbation and nonlinear dynamic analysis of different singing styles.
Butte, Caitlin J; Zhang, Yu; Song, Huangqiang; Jiang, Jack J
2009-11-01
Previous research has used perturbation analysis methods to study the singing voice. Using perturbation and nonlinear dynamic analysis (NDA) methods in conjunction may provide more accurate information on the singing voice and may distinguish vocal usage in different styles. Acoustic samples from different styles of singing were compared using nonlinear dynamic and perturbation measures. Twenty-six songs from different musical styles were obtained from an online music database (Rhapsody, RealNetworks, Inc., Seattle, WA). One-second samples were selected from each song for analysis. Perturbation analyses of jitter, shimmer, and signal-to-noise ratio and NDA of correlation dimension (D(2)) were performed on samples from each singing style. Percent jitter and shimmer median values were low normal for country (0.32% and 3.82%), musical theater (MT) (0.280% and 2.80%), jazz (0.440% and 2.34%), and soul (0.430% and 6.42%). The popular style had slightly higher median jitter and shimmer values (1.13% and 6.78%) than other singing styles, although this was not statistically significant. The opera singing style had median jitter of 0.520%, and yielded significantly high shimmer (P=0.001) of 7.72%. All six singing styles were measured reliably using NDA, indicating that operatic singing is notably more chaotic than other singing styles. Median correlation dimension values were low to normal, compared to healthy voices, in country (median D(2)=2.14), jazz (median D(2)=2.24), pop (median D(2)=2.60), MT (median D(2)=2.73), and soul (mean D(2)=3.26). Correlation dimension was significantly higher in opera (P<0.001) with median D(2)=6.19. In this study, acoustic analysis in opera singing gave significantly high values for shimmer and D(2), suggesting that it is more irregular than other singing styles; a previously unknown quality of opera singing. Perturbation analysis also suggested significant differences in vocal output in different singing styles. This preliminary study
Buckling of Aluminum Honeycomb Core and Its Effect on Ultrasonic Velocity
NASA Astrophysics Data System (ADS)
Hsu, David K.; Dayal, Vinay; Harris, Aaron L.; Peters, John J.
2004-02-01
This paper reports an investigation on the interior buckling morphology of impact-damaged honeycomb core and its effects on the amplitude and velocity of transmitted ultrasound. In a systematic experiment, honeycomb core specimens were compressed to various degrees of buckling and the transmitted ultrasonic amplitude and time-of-flight were measured as a function of percent deformation. The measured time-of-flight showed a dramatic increase with increasing degree of buckling. As a comparison, the time of flight was modeled in a transient finite element analysis of a buckled honeycomb cell wall. A single cycle load was applied to the top end of the simplified model and the response was recorded at the bottom end of the wall. The finite element simulation results for time-of-flight showed qualitative agreement with the experimental data.
NASA Astrophysics Data System (ADS)
Sasaoka, Ryu; Azegami, Hideyuki; Murachi, Shunji; Kitoh, Junzoh; Ishida, Yoshito; Kawakami, Noriaki; Makino, Mitsunori; Matsuyama, Yukihiro
A hypothesis that idiopathic scoliosis is a buckling phenomenon of the fourth or sixth mode, which is the second or third lateral bending mode, induced by the growth of vertebral bodies was presented in a previous paper by the authors using numerical simulations with a finite-element model of the spine. This paper presents experimental proof of the buckling phenomenon using mechanical spine models constructed with the geometrical data of the finite-element model used in a previous work. Using three spine mechanical models with different materials at intervertebral joints, the change in the natural vibration eigenvalue of the second lateral bending mode with the growth of vertebral bodies was measured by experimental modal analysis. From the result, it was observed that natural vibration eigenvalue decreased with the growth of vertebral bodies. Since the increase in primary factor inducing the buckling phenomenon decreases natural vibration eigenvalue, the obtained result confirms the buckling hypothesis.
A hybrid neurocomputing/numerical strategy for nonlinear structural analysis
NASA Technical Reports Server (NTRS)
Szewczyk, Z. Peter; Noor, Ahmed K.
1995-01-01
A hybrid neurocomputing/numerical strategy is presented for geometrically nonlinear analysis of structures. The strategy combines model-free data processing capabilities of computational neural networks with a Pade approximants-based perturbation technique to predict partial information about the nonlinear response of structures. In the hybrid strategy, multilayer feedforward neural networks are used to extend the validity of solutions by using training samples produced by Pade approximations to the Taylor series expansion of the response function. The range of validity of the training samples is taken to be the radius of convergence of Pade approximants and is estimated by setting a tolerance on the diverging approximants. The norm of residual vector of unbalanced forces in a given element is used as a measure to assess the quality of network predictions. To further increase the accuracy and the range of network predictions, additional training data are generated by either applying linear regression to weight matrices or expanding the training data by using predicted coefficients in a Taylor series. The effectiveness of the hybrid strategy is assessed by performing large-deflection analysis of a doubly-curved composite panel with a circular cutout, and postbuckling analyses of stiffened composite panels subjected to an in-plane edge shear load. In all the problems considered, the hybrid strategy is used to predict selective information about the structural response, namely the total strain energy and the maximum displacement components only.
Nonlinear thermoelastic stress analysis of spherically curved solar panels
Vallabhan, C.V.G.; Vungutur, K.; Selvam, R.P.
1984-10-01
Spherically curved glass panels are used to concentrate solar energy onto a line focus in fixed mirror distributed focus type solar collectors. These solar panels consists of thin flat glass plates bent to form a spherical surface, glued onto a paper honeycomb backing, and covered with steel plate at the back and with plastic strips on the sides. Stresses are produced in the glass plates as they are formed into spherical surfaces. In addition, when the solar receiver is not in focus relative to the bowl and the sun, a mirror hot spot condition is developed, resulting in large thermally induced stresses within glass plates. The curved glass panel is modeled as a plate on elastic foundation in order to represent the behavior of the plate in relation to other panel components. Since lateral deflections of these plates are large compared to their thickness, nonlinear von Karman plate equations are used in the analysis. A computer model has been prepared to assist in the nonlinear analysis of stresses using finite difference method. The model has flexibility to analyze a variety of rectangular plate geometries subjected to thermal and other applied loads.
Active control of buckling of flexible beams
NASA Technical Reports Server (NTRS)
Baz, A.; Tampe, L.
1989-01-01
Mathematical models are presented that simulate the dynamic characteristics of shape memory alloy actuators made of nickel-titanium alloy (Nitinol) controlling the buckling of compressive structural members. A closed-loop computer-controlled system has been designed, based on the proposed mathematical models, and has been implemented to control the buckling of simple beams. The performance of the computer-controlled system is evaluated experimentally and compared with the theoretical predictions to validate the developed models. The results emphasized the importance of buckling control and suggest the potential of shape memory alloy actuators as attractive means for controlling structural deformation in a simple and reliable way.
Dual Solutions for Nonlinear Flow Using Lie Group Analysis
Awais, Muhammad; Hayat, Tasawar; Irum, Sania; Saleem, Salman
2015-01-01
`The aim of this analysis is to investigate the existence of the dual solutions for magnetohydrodynamic (MHD) flow of an upper-convected Maxwell (UCM) fluid over a porous shrinking wall. We have employed the Lie group analysis for the simplification of the nonlinear differential system and computed the absolute invariants explicitly. An efficient numerical technique namely the shooting method has been employed for the constructions of solutions. Dual solutions are computed for velocity profile of an upper-convected Maxwell (UCM) fluid flow. Plots reflecting the impact of dual solutions for the variations of Deborah number, Hartman number, wall mass transfer are presented and analyzed. Streamlines are also plotted for the wall mass transfer effects when suction and blowing situations are considered. PMID:26575996
Analysis of the human electroencephalogram with methods from nonlinear dynamics
Mayer-Kress, G.; Holzfuss, J.
1986-09-08
We apply several different methods from nonlinear dynamical systems to the analysis of the degree of temporal disorder in data from human EEG. Among these are methods of geometrical reconstruction, dimensional complexity, mutual information content, and two different approaches for estimating Lyapunov characteristic exponents. We show how the naive interpretation of numerical results can lead to a considerable underestimation of the dimensional complexity. This is true even when the errors from least squares fits are small. We present more realistic error estimates and show that they seem to contain additional, important information. By applying independent methods of analysis to the same data sets for a given lead, we find that the degree of temporal disorder is minimal in a ''resting awake'' state and increases in sleep as well as in fluroxene induced general anesthesia. At the same time the statistical errors appear to decrease, which can be interpretated as a transition to a more uniform dynamical state. 29 refs., 10 figs.
Nonlinear Aeroelastic Analysis of Joined-Wing Configurations
NASA Astrophysics Data System (ADS)
Cavallaro, Rauno
Aeroelastic design of joined-wing configurations is yet a relatively unexplored topic which poses several difficulties. Due to the overconstrained nature of the system combined with structural geometric nonlinearities, the behavior of Joined Wings is often counterintuitive and presents challenges not seen in standard layouts. In particular, instability observed on detailed aircraft models but never thoroughly investigated, is here studied with the aid of a theoretical/computational framework. Snap-type of instabilities are shown for both pure structural and aeroelastic cases. The concept of snap-divergence is introduced to clearly identify the true aeroelastic instability, as opposed to the usual aeroelastic divergence evaluated through eigenvalue approach. Multi-stable regions and isola-type of bifurcations are possible characterizations of the nonlinear response of Joined Wings, and may lead to branch-jumping phenomena well below nominal critical load condition. Within this picture, sensitivity to (unavoidable) manufacturing defects could have potential catastrophic effects. The phenomena studied in this work suggest that the design process for Joined Wings needs to be revisited and should focus, when instability is concerned, on nonlinear post-critical analysis since linear methods may provide wrong trend indications and also hide potentially catastrophical situations. Dynamic aeroelastic analyses are also performed. Flutter occurrence is critically analyzed with frequency and time-domain capabilities. Sensitivity to different-fidelity aeroelastic modeling (fluid-structure interface algorithm, aerodynamic solvers) is assessed showing that, for some configurations, wake modeling (rigid versus free) has a strong impact on the results. Post-flutter regimes are also explored. Limit cycle oscillations are observed, followed, in some cases, by flip bifurcations (period doubling) and loss of periodicity of the solution. Aeroelastic analyses are then carried out on a
Applications of Automation Methods for Nonlinear Fracture Test Analysis
NASA Technical Reports Server (NTRS)
Allen, Phillip A.; Wells, Douglas N.
2013-01-01
Using automated and standardized computer tools to calculate the pertinent test result values has several advantages such as: 1. allowing high-fidelity solutions to complex nonlinear phenomena that would be impractical to express in written equation form, 2. eliminating errors associated with the interpretation and programing of analysis procedures from the text of test standards, 3. lessening the need for expertise in the areas of solid mechanics, fracture mechanics, numerical methods, and/or finite element modeling, to achieve sound results, 4. and providing one computer tool and/or one set of solutions for all users for a more "standardized" answer. In summary, this approach allows a non-expert with rudimentary training to get the best practical solution based on the latest understanding with minimum difficulty.Other existing ASTM standards that cover complicated phenomena use standard computer programs: 1. ASTM C1340/C1340M-10- Standard Practice for Estimation of Heat Gain or Loss Through Ceilings Under Attics Containing Radiant Barriers by Use of a Computer Program 2. ASTM F 2815 - Standard Practice for Chemical Permeation through Protective Clothing Materials: Testing Data Analysis by Use of a Computer Program 3. ASTM E2807 - Standard Specification for 3D Imaging Data Exchange, Version 1.0 The verification, validation, and round-robin processes required of a computer tool closely parallel the methods that are used to ensure the solution validity for equations included in test standard. The use of automated analysis tools allows the creation and practical implementation of advanced fracture mechanics test standards that capture the physics of a nonlinear fracture mechanics problem without adding undue burden or expense to the user. The presented approach forms a bridge between the equation-based fracture testing standards of today and the next generation of standards solving complex problems through analysis automation.
Nonlinear analysis of bonded joints with thermal effects
NASA Technical Reports Server (NTRS)
Humphreys, E. A.; Herakovich, C. T.
1977-01-01
Nonlinear results are presented for adhesive bonded joints. It is shown that adhesive nonlinearities are only significant in the predicted adhesive shear stresses. Adherend nonlinearities and temperature dependent properties are shown to have little effect upon the adhesive stress predictions under mechanical and thermal loadings.
Isotopomer Spectral Analysis: Utilizing Nonlinear Models in Isotopic Flux Studies.
Kelleher, Joanne K; Nickol, Gary B
2015-01-01
We present the principles underlying the isotopomer spectral analysis (ISA) method for evaluating biosynthesis using stable isotopes. ISA addresses a classic conundrum encountered in the use of radioisotopes to estimate biosynthesis rates whereby the information available is insufficient to estimate biosynthesis. ISA overcomes this difficulty capitalizing on the additional information available from the mass isotopomer labeling profile of a polymer. ISA utilizes nonlinear regression to estimate the two unknown parameters of the model. A key parameter estimated by ISA represents the fractional contribution of the tracer to the precursor pool for the biosynthesis, D. By estimating D in cells synthesizing lipids, ISA quantifies the relative importance of two distinct pathways for flux of glutamine to lipid, reductive carboxylation, and glutaminolysis. ISA can also evaluate the competition between different metabolites, such as glucose and acetoacetate, as precursors for lipogenesis and thereby reveal regulatory properties of the biosynthesis pathway. The model is flexible and may be expanded to quantify sterol biosynthesis allowing tracer to enter the pathway at three different positions, acetyl CoA, acetoacetyl CoA, and mevalonate. The nonlinear properties of ISA provide a method of testing for the presence of gradients of precursor enrichment illustrated by in vivo sterol synthesis. A second ISA parameter provides the fraction of the polymer that is newly synthesized over the time course of the experiment. In summary, ISA is a flexible framework for developing models of polymerization biosynthesis providing insight into pools and pathway that are not easily quantified by other techniques. PMID:26358909
An analysis of characteristics in nonlinear massive gravity
NASA Astrophysics Data System (ADS)
Izumi, Keisuke; Ong, Yen Chin
2013-09-01
We study the Cauchy problem in a special case of nonlinear massive gravity. Despite being ghost free, it has recently been argued that the theory is inherently problematic due to the existence of superluminal shock waves. Furthermore, it is claimed that an acausal characteristic can arise for any choice of background. In order to further understand the causal structure of the theory, we carefully perform a detailed analysis of the characteristic equations and show that the theory does admit a well-posed Cauchy problem, i.e., there exists hypersurfaces that are not a characteristic hypersurface. Puzzles remain regarding the existence of a superluminal propagating mode in both the minimal ghost-free theory that we analyzed, as well as in the full nonlinear massive gravity. That is, our result should not be taken as any indication of the healthiness of the theory. We also give a detailed review of Cauchy-Kovalevskaya theorem and its application in the appendix, which should be useful for investigating causal structures of other theories of gravity.
Nonlinear microscopy, infrared, and Raman microspectroscopy for brain tumor analysis
NASA Astrophysics Data System (ADS)
Meyer, Tobias; Bergner, Norbert; Bielecki, Christiane; Krafft, Christoph; Akimov, Denis; Romeike, Bernd F. M.; Reichart, Rupert; Kalff, Rolf; Dietzek, Benjamin; Popp, Jürgen
2011-02-01
Contemporary brain tumor research focuses on two challenges: First, tumor typing and grading by analyzing excised tissue is of utmost importance for choosing a therapy. Second, for prognostication the tumor has to be removed as completely as possible. Nowadays, histopathology of excised tissue using haematoxylin-eosine staining is the gold standard for the definitive diagnosis of surgical pathology specimens. However, it is neither applicable in vivo, nor does it allow for precise tumor typing in those cases when only nonrepresentative specimens are procured. Infrared and Raman spectroscopy allow for very precise cancer analysis due to their molecular specificity, while nonlinear microscopy is a suitable tool for rapid imaging of large tissue sections. Here, unstained samples from the brain of a domestic pig have been investigated by a multimodal nonlinear imaging approach combining coherent anti-Stokes Raman scattering, second harmonic generation, and two photon excited fluorescence microscopy. Furthermore, a brain tumor specimen was additionally analyzed by linear Raman and Fourier transform infrared imaging for a detailed assessment of the tissue types that is required for classification and to validate the multimodal imaging approach. Hence label-free vibrational microspectroscopic imaging is a promising tool for fast and precise in vivo diagnostics of brain tumors.
Nonlinear global stability analysis of compressor stall phenomena
NASA Technical Reports Server (NTRS)
Razavi, H.
1985-01-01
Compressor stall phenomena are analyzed from the point of view of nonlinear control theory, based on bifurcation-catastrophe techniques. This new approach appears promising and offers insight into such well-known compressor instability problems as surge and rotating stall and suggests strategies for recovery. Three interlocking dynamic nonlinear state space models are developed. It is shown that the problem of rotating stall can be viewed as an induced bifurcation of solution of the unstalled model. Hysteresis effects are shown to exist in the stall/recovery process. Surge cycles are observed for some critical parameter values. The oscillatory behavior is seen to be due to development of limit cycles, generated by Hopf bifurcation of solutions. More specifically, it is observed that at certain critical values of parameters, a family of stable limit cycles with growning and then diminishing amplitudes is generated, then giving rise to an unstable family of limit cycles. This unstable family in turn bifurcates into other unstable families. To further illustrate the utility of the methodology, some partial computation of domains is carried out, and parameter sensitivity analysis is performed.
Finite element buckling and postbuckling solutions for multilayered composite panels
NASA Technical Reports Server (NTRS)
Noor, Ahmed K.; Peters, Jeanne M.
1995-01-01
A study is made of the buckling and postbuckling responses of flat, unstiffened composite panels subjected to various combinations of mechanical and thermal loads. The analysis is based on a first-order shear deformation von Karman-type plate theory. A mixed formulation is used with the fundamental unknowns consisting of the strain components, stress resultants and the generalized displacements of the plate. The stability boundary, postbuckling response and the sensitivity coefficients are evaluated. The sensitivity coefficients measure the sensitivity of the buckling and postbuckling responses to variations in the different lamination and material parameters of the panel. Numerical results are presented for both solid panels and panels with central circular cutouts. The results show the effects of the variations in the fiber orientation angels, aspect ratio of the panel, and the hole diameter (for panels with cutouts) on the stability boundary, postbuckling response and sensitivity coefficients.
Nonlinear Finite Element Analysis of FRP Strengthened Reinforced Concrete Beams
NASA Astrophysics Data System (ADS)
Sasmal, S.; Kalidoss, S.; Srinivas, V.
2012-12-01
This paper focuses on nonlinear analysis of parent and fiber reinforced polymer (FRP) strengthened reinforced concrete (RC) beam using general purpose finite element software, ANSYS. Further, it is aimed to investigate the suitability of different elements available in ANSYS library to represent FRP, epoxy and interface. 3-D structural RC solid element has been used to model concrete and truss element is employed for modeling the reinforcements. FRP has been modelled using 3-D membrane element and layered element with number of layers, epoxy is modelled using eight node brick element, and eight node layered solid shell is used to mathematically represent the concrete-FRP interface behavior. Initially, the validation of the numerical model for the efficacy of different elements (SOLID65 for concrete and LINK8 for reinforcement) and material models is carried out on the experimental beam reported in literature. The validated model, elements and material properties is used to evaluate the load-displacement and load-strain response behavior and crack patterns of the FRP strengthened RC beams. The numerical results indicated that significant improvement in the displacement in the strengthened RC beams with the advancement of cracks. The study shows that FRP with shell elements is recommended when single layer of FRP is used. When multi layered FRP is used, solid layered element can be a reasonably good choice whereas the epoxy matrix with linear solid element does not need further complicated model. Interfacial element makes the analysis minimally improved at the cost of complicated modeling issues and considerable computation time. Hence, for nonlinear analysis of usual strengthened structures, unless it is specifically required for, interface element may not be required and a full contact can be assumed at interface.
Weakly nonlinear analysis of impulsively-forced Faraday waves.
Catllá, Anne; Porter, Jeff; Silber, Mary
2005-11-01
Parametrically-excited surface waves, forced by a repeating sequence of delta-function impulses, are considered within the framework of the Zhang-Viñals model [W. Zhang and J. Viñals, J. Fluid Mech. 336, 301 (1997)]. With impulsive forcing, the linear stability analysis can be carried out exactly and leads to an implicit equation for the neutral stability curves. As noted previously [J. Bechhoefer and B. Johnson, Am. J. Phys. 64, 1482 (1996)], in the simplest case of N=2 equally-spaced impulses per period (which alternate up and down) there are only subharmonic modes of instability. The familiar situation of alternating subharmonic and harmonic resonance tongues emerges only if an asymmetry in the spacing between the impulses is introduced. We extend the linear analysis for N=2 impulses per period to the weakly nonlinear regime, where we determine the leading order nonlinear saturation of one-dimensional standing waves as a function of forcing strength. Specifically, an analytic expression for the cubic Landau coefficient in the bifurcation equation is derived as a function of the dimensionless spacing between the two impulses and the fluid parameters that appear in the Zhang-Viñals model. As the capillary parameter is varied, one finds a parameter regime of wave amplitude suppression, which is due to a familiar 1:2 spatiotemporal resonance between the subharmonic mode of instability and a damped harmonic mode. This resonance occurs for impulsive forcing even when harmonic resonance tongues are absent from the neutral stability curves. The strength of this resonance feature can be tuned by varying the spacing between the impulses. This finding is interpreted in terms of a recent symmetry-based analysis of multifrequency forced Faraday waves [J. Porter, C. M. Topaz, and M. Silber, Phys. Lett. 93, 034502 (2004); C. M. Topaz, J. Porter, and M. Silber, Phys. Rev. E 70, 066206 (2004)]. PMID:16383732
Buckling optimisation of sandwich cylindrical panels
NASA Astrophysics Data System (ADS)
Abouhamzeh, M.; Sadighi, M.
2016-06-01
In this paper, the buckling load optimisation is performed on sandwich cylindrical panels. A finite element program is developed in MATLAB to solve the governing differential equations of the global buckling of the structure. In order to find the optimal solution, the genetic algorithm Toolbox in MATLAB is implemented. Verifications are made for both the buckling finite element code and also the results from the genetic algorithm by comparisons to the results available in literature. Sandwich cylindrical panels are optimised for the buckling strength with isotropic or orthotropic cores with different boundary conditions. Results are presented in terms of stacking sequence of fibers in the face sheets and core to face sheet thickness ratio.
A three-layer model for buckling of a human aortic segment under specific flow-pressure conditions.
Amabili, M; Karazis, K; Mongrain, R; Païdoussis, M P; Cartier, R
2012-05-01
Human aortas are subjected to large mechanical stresses because of blood flow pressurization and through contact with the surrounding tissue. It is essential that the aorta does not lose stability by buckling with deformation of the cross-section (shell-like buckling) (i) for its proper functioning to ensure blood flow and (ii) to avoid high stresses in the aortic wall. A numerical bifurcation analysis employs a refined reduced-order model to investigate the stability of a straight aorta segment conveying blood flow. The structural model assumes a nonlinear cylindrical orthotropic laminated composite shell composed of three layers representing the tunica intima, media and adventitia. Residual stresses because of pressurization are evaluated and included in the model. The fluid is formulated using a hybrid model that contains the unsteady effects obtained from linear potential flow theory and the steady viscous effects obtained from the time-averaged Navier-Stokes equations. The aortic segment loses stability by divergence with deformation of the cross-section at a critical flow velocity for a given static pressure, exhibiting a strong subcritical behaviour with partial or total collapse of the inner wall. Preliminary results suggest directions for further study in relation to the appearance and growth of dissection in the aorta. PMID:25099454
Bayesian sensitivity analysis of a nonlinear finite element model
NASA Astrophysics Data System (ADS)
Becker, W.; Oakley, J. E.; Surace, C.; Gili, P.; Rowson, J.; Worden, K.
2012-10-01
A major problem in uncertainty and sensitivity analysis is that the computational cost of propagating probabilistic uncertainty through large nonlinear models can be prohibitive when using conventional methods (such as Monte Carlo methods). A powerful solution to this problem is to use an emulator, which is a mathematical representation of the model built from a small set of model runs at specified points in input space. Such emulators are massively cheaper to run and can be used to mimic the "true" model, with the result that uncertainty analysis and sensitivity analysis can be performed for a greatly reduced computational cost. The work here investigates the use of an emulator known as a Gaussian process (GP), which is an advanced probabilistic form of regression. The GP is particularly suited to uncertainty analysis since it is able to emulate a wide class of models, and accounts for its own emulation uncertainty. Additionally, uncertainty and sensitivity measures can be estimated analytically, given certain assumptions. The GP approach is explained in detail here, and a case study of a finite element model of an airship is used to demonstrate the method. It is concluded that the GP is a very attractive way of performing uncertainty and sensitivity analysis on large models, provided that the dimensionality is not too high.
Develop Advanced Nonlinear Signal Analysis Topographical Mapping System
NASA Technical Reports Server (NTRS)
Jong, Jen-Yi
1997-01-01
During the development of the SSME, a hierarchy of advanced signal analysis techniques for mechanical signature analysis has been developed by NASA and AI Signal Research Inc. (ASRI) to improve the safety and reliability for Space Shuttle operations. These techniques can process and identify intelligent information hidden in a measured signal which is often unidentifiable using conventional signal analysis methods. Currently, due to the highly interactive processing requirements and the volume of dynamic data involved, detailed diagnostic analysis is being performed manually which requires immense man-hours with extensive human interface. To overcome this manual process, NASA implemented this program to develop an Advanced nonlinear signal Analysis Topographical Mapping System (ATMS) to provide automatic/unsupervised engine diagnostic capabilities. The ATMS will utilize a rule-based Clips expert system to supervise a hierarchy of diagnostic signature analysis techniques in the Advanced Signal Analysis Library (ASAL). ASAL will perform automatic signal processing, archiving, and anomaly detection/identification tasks in order to provide an intelligent and fully automated engine diagnostic capability. The ATMS has been successfully developed under this contract. In summary, the program objectives to design, develop, test and conduct performance evaluation for an automated engine diagnostic system have been successfully achieved. Software implementation of the entire ATMS system on MSFC's OISPS computer has been completed. The significance of the ATMS developed under this program is attributed to the fully automated coherence analysis capability for anomaly detection and identification which can greatly enhance the power and reliability of engine diagnostic evaluation. The results have demonstrated that ATMS can significantly save time and man-hours in performing engine test/flight data analysis and performance evaluation of large volumes of dynamic test data.
Calculating Buckling And Vibrations Of Lattice Structures
NASA Technical Reports Server (NTRS)
Anderson, M. S.; Durling, B. J.; Herstrom, C. L.; Williams, F. W.; Banerjee, J. R.; Kennedy, D.; Warnaar, D. B.
1989-01-01
BUNVIS-RG computer program designed to calculate vibration frequencies or buckling loads of prestressed lattice structures used in outer space. For buckling and vibration problems, BUNVIS-RG calculates deadload axial forces caused in members by any combination of externally-applied static point forces and moments at nodes, axial preload or prestrain in members, and such acceleration loads as those due to gravity. BUNVIS-RG is FORTRAN 77 computer program implemented on CDC CYBER and VAX computer.
NASA Astrophysics Data System (ADS)
Lloyd, Lewis John
This work focused on developing a novel method for solving the nonlinear partial differential equations associated with thermal-hydraulic safety analysis software. Traditional methods involve solving large systems of nonlinear equations. One class of methods linearizes the nonlinear equations and attempts to minimize the nonlinear truncation error with timestep size selection. These linearized methods are characterized by low computational cost but reduced accuracy. Another class resolves those nonlinearities by using an iterative nonlinear refinement technique. However, these iterative methods are computationally expensive when multiple iterates are required to resolve the nonlinearities. These two paradigms stand at the opposite ends of a spectrum, and the middle ground had yet to be investigated. This research sought to find that middle ground, a balance between the competing incentives of computational cost and accuracy, by creating a hybrid method: a spatially-selective, nonlinear refinement (SNR) algorithm. As part of this work, the two-phase, three-field software COBRA was converted from a linearized semi-implicit solver to a nonlinearly convergent solver; an operator-based scaling that provides a physically meaningful convergence measure was developed and implemented; and the SNR algorithm was developed to enable a subdomain of the simulation to be subjected to multiple nonlinear iterates while maintaining global consistency. By selecting those areas of the computational domain where nonlinearities are expected to be high and subjecting only them to multiple nonlinear iterations, the accuracy of the nonlinear solver may be obtained without its associated computational cost.
NASA Technical Reports Server (NTRS)
Schmit, L. A., Jr.; Ramanathan, R. K.
1977-01-01
A rational multilevel approach for minimum weight structural design of truss and wing structures including local and system buckling constraints is presented. Overall proportioning of the structure is achieved at the system level subject to strength, displacement and system buckling constraints, while the detailed component designs are carried out separately at the component level satisfying local buckling constraints. Total structural weight is taken to be the objective function at the system level while employing the change in the equivalent system stiffness of the component as the component level objective function. Finite element analysis is used to predict static response while system buckling behavior is handled by incorporating a geometric stiffness matrix capability. Buckling load factors and the corresponding mode shapes are obtained by solving the eigenvalue problem associated with the assembled elastic stiffness and geometric stiffness matrices for the structural system. At the component level various local buckling failure modes are guarded against using semi-empirical formulas. Mathematical programming techniques are employed at both the system and component level.
Buckling transition in long α-helices
Palenčár, Peter; Bleha, Tomáš
2014-11-07
The treatment of bending and buckling of stiff biopolymer filaments by the popular worm-like chain model does not provide adequate understanding of these processes at the microscopic level. Thus, we have used the atomistic molecular-dynamic simulations and the Amber03 force field to examine the compression buckling of α-helix (AH) filaments at room temperature. It was found that the buckling instability occurs in AHs at the critical force f{sub c} in the range of tens of pN depending on the AH length. The decrease of the force f{sub c} with the contour length follows the prediction of the classic thin rod theory. At the force f{sub c} the helical filament undergoes the swift and irreversible transition from the smoothly bent structure to the buckled one. A sharp kink in the AH contour arises at the transition, accompanied by the disruption of the hydrogen bonds in its vicinity. The kink defect brings in an effective softening of the AH molecule at buckling. Nonbonded interactions between helical branches drive the rearrangement of a kinked AH into the ultimate buckled structure of a compact helical hairpin described earlier in the literature.
Scleral Buckle Infection with Aspergillus Flavus
Bouhaimed, Manal; Al-Dhibi, Hassan; Al-Assiri, Abdullah
2008-01-01
Purpose: To present a case of scleral buckle infection with Aspergillus flavus in a tertiary eye center in Saudi Arabia. Methods: A retrospective case report of a 28-year-old Saudi male who presented with a six-month history of conjunctival injection and discharge from the left eye which had undergone uncomplicated conventional retinal detachment surgery, at the King Khaled Eye Specialist Hospital in Riyadh, Saudi Arabia, in the form of cryopexy, subretinal fluid drainage and scleral buckle (grooved segmental sponge and circumferential band with sleeve) for a macula on retinal detachment four years earlier. A diagnosis of infected extruded scleral buckle was made and the buckle was removed. Results: The infected scleral buckle was removed under local anesthesia with administration of sub-conjunctival irrigation of 50 mg solution of Vancomycin, and sub-conjunctival injection of 25mg of Vancomycin. Post operative microbiological studies revealed infection with silver staining of moderate Aspergillus flavus hyphae. Visual acuity of the left eye improved from 20/200 before surgery to 20/60 in the two years follow-up visit. Conclusion: This case report indicates the importance of considering infection with multiple organisms – including fungal ones – in cases of scleral buckle infections in our population. PMID:20379425
Adaptive methods for nonlinear structural dynamics and crashworthiness analysis
NASA Technical Reports Server (NTRS)
Belytschko, Ted
1993-01-01
The objective is to describe three research thrusts in crashworthiness analysis: adaptivity; mixed time integration, or subcycling, in which different timesteps are used for different parts of the mesh in explicit methods; and methods for contact-impact which are highly vectorizable. The techniques are being developed to improve the accuracy of calculations, ease-of-use of crashworthiness programs, and the speed of calculations. The latter is still of importance because crashworthiness calculations are often made with models of 20,000 to 50,000 elements using explicit time integration and require on the order of 20 to 100 hours on current supercomputers. The methodologies are briefly reviewed and then some example calculations employing these methods are described. The methods are also of value to other nonlinear transient computations.
Nonlinear analysis of ubitron, orbitron, and gyroharmonitron mechanisms. Final report
Not Available
1987-11-01
The research program during the contract period consisted of the analysis of the Ubitron/FEL amplifier in three-dimensions. The principal configuration of interest consisted of the propagation of an energetic electron beam through a loss-free rectangular waveguide in the presence of a linearly polarized wiggler field with parabolically tapered pole pieces. The purpose of the tapered pole faces is to provide a mechanism for focussing the electron beam in the plane of the bulk wiggler induced oscillation. A nonlinear theory and simulation code has been developed to study this configuration which can treat a multiple mode interaction, harmonic growth, efficiency enhancement by means of a tapered wiggler, the effect of beam thermal spread on the interaction, the injection of the beam into the wiggler, and detailed facets of the particle dynamics such as Betatron oscillations and velocity shear. Comparisons of the experiment at the Lawrence Livermore National Laboratory are excellent.
Analysis of nonlinear internal waves in the New York Bight
NASA Technical Reports Server (NTRS)
Liu, Antony K.
1988-01-01
An analysis of the nonlinear-internal-wave evolution in the New York Bight was performed on the basis of current meter mooring data obtained in the New York Bight during the SAR Internal Wave Signature Experiment (SARSEX). The solitary wave theory was extended to include dissipation and shoaling effects, and a series of numerical experiments were performed by solving the wave evolution equation, with waveforms observed in the SARSEX area as initial conditions. The results of calculations demonstrate that the relative balance of dissipation and shoaling effects is crucial to the detailed evolution of internal wave packets. From an observed initial wave packet at the upstream mooring, the numerical evolution simulation agreed reasonably well with the measurements at the distant mooring for the leading two large solitons.
Nonlinear Laplacian spectral analysis of Rayleigh-Bénard convection
NASA Astrophysics Data System (ADS)
Brenowitz, N. D.; Giannakis, D.; Majda, A. J.
2016-06-01
The analysis of physical datasets using modern methods developed in machine learning presents unique challenges and opportunities. These datasets typically feature many degrees of freedom, which tends to increase the computational cost of statistical methods and complicate interpretation. In addition, physical systems frequently exhibit a high degree of symmetry that should be exploited by any data analysis technique. The classic problem of Rayleigh Benárd convection in a periodic domain is an example of such a physical system with trivial symmetries. This article presents a technique for analyzing the time variability of numerical simulations of two-dimensional Rayleigh-Bénard convection at large aspect ratio and intermediate Rayleigh number. The simulated dynamics are highly unsteady and consist of several convective rolls that are distributed across the domain and oscillate with a preferred frequency. Intermittent extreme events in the net heat transfer, as quantified by the time-weighted probability distribution function of the Nusselt number, are a hallmark of these simulations. Nonlinear Laplacian Spectral Analysis (NLSA) is a data-driven method which is ideally suited for the study of such highly nonlinear and intermittent dynamics, but the trivial symmetries of the Rayleigh-Bénard problem such as horizontal shift-invariance can mask the interesting dynamics. To overcome this issue, the vertical velocity is averaged over parcels of similar temperature and height, which substantially compresses the size of the dataset and removes trivial horizontal symmetries. This isothermally averaged dataset, which is shown to preserve the net convective heat-flux across horizontal surfaces, is then used as an input to NLSA. The analysis generates a small number of orthogonal modes which describe the spatiotemporal variability of the heat transfer. A regression analysis shows that the extreme events of the net heat transfer are primarily associated with a family of
NASA Technical Reports Server (NTRS)
Hopkins, D. A.
1984-01-01
A unique upward-integrated top-down-structured approach is presented for nonlinear analysis of high-temperature multilayered fiber composite structures. Based on this approach, a special purpose computer code was developed (nonlinear COBSTRAN) which is specifically tailored for the nonlinear analysis of tungsten-fiber-reinforced superalloy (TFRS) composite turbine blade/vane components of gas turbine engines. Special features of this computational capability include accounting of; micro- and macro-heterogeneity, nonlinear (stess-temperature-time dependent) and anisotropic material behavior, and fiber degradation. A demonstration problem is presented to mainfest the utility of the upward-integrated top-down-structured approach, in general, and to illustrate the present capability represented by the nonlinear COBSTRAN code. Preliminary results indicate that nonlinear COBSTRAN provides the means for relating the local nonlinear and anisotropic material behavior of the composite constituents to the global response of the turbine blade/vane structure.
Buckling condensation in constrained growth
NASA Astrophysics Data System (ADS)
Dervaux, Julien; Ben Amar, Martine
2011-03-01
The multiple complexities inherent to living objects have motivated the search for abiotic substitutes, able to mimic some of their relevant physical properties. Hydrogels provide a highly monitorable counterpart and have thus found many applications in medicine and bioengineering. Recently, it has been recognized that their ability to swell could be used to unravel some of the universal physical processes at work during biological growth. However, it is yet unknown how the microscopic distinctions between swelling and biological growth affect macroscopic changes (shape, stresses) induced by volume variations. To answer this question, we focus on a clinically motivated example of growth. Some solid tumors such as melanoma or glioblastoma undergo a shape transition during their evolution. This bifurcation appears when growth is confined at the periphery of the tumor and is concomitant with the transition from the avascular to the vascular stage of the tumor evolution. To model this phenomenon, we consider in this paper the deformation of an elastic ring enclosing a core of different stiffness. When the volume of the outer ring increases, the system develops a periodic instability. We consider two possible descriptions of the volume variation process: either by imposing a homogeneous volumetric strain (biological growth) or through migration of solvent molecules inside a solid network (swelling). For thin rings, both theories are in qualitative agreement. When the interior is soft, we predict the emergence of a large wavelength buckling. Upon increasing the stiffness of the inner disc, the wavelength of the instability decreases until a condensation of the buckles occurs at the free boundary. This short wavelength pattern is independent of the stiffness of the disc and is only limited by the presence of surface tension. For thicker rings, two scenarios emerge. When a volumetric strain is prescribed, compressive stresses accumulate in the vicinity of the core and the
Distortion Analysis Toolkit—A Software Tool for Easy Analysis of Nonlinear Audio Systems
NASA Astrophysics Data System (ADS)
Pakarinen, Jyri
2010-12-01
Several audio effects devices deliberately add nonlinear distortion to the processed signal in order to create a desired sound. When creating virtual analog models of nonlinearly distorting devices, it would be very useful to carefully analyze the type of distortion, so that the model could be made as realistic as possible. While traditional system analysis tools such as the frequency response give detailed information on the operation of linear and time-invariant systems, they are less useful for analyzing nonlinear devices. Furthermore, although there do exist separate algorithms for nonlinear distortion analysis, there is currently no unified, easy-to-use tool for rapid analysis of distorting audio systems. This paper offers a remedy by introducing a new software tool for easy analysis of distorting effects. A comparison between a well-known guitar tube amplifier and two commercial software simulations is presented as a case study. This freely available software is written in Matlab language, but the analysis tool can also run as a standalone program, so the user does not need to have Matlab installed in order to perform the analysis.
NASA Technical Reports Server (NTRS)
Bednarcyk, Brett A.; Arnold, Steven M.
2011-01-01
A framework for the multiscale design and analysis of composite materials and structures is presented. The ImMAC software suite, developed at NASA Glenn Research Center, embeds efficient, nonlinear micromechanics capabilities within higher scale structural analysis methods such as finite element analysis. The result is an integrated, multiscale tool that relates global loading to the constituent scale, captures nonlinearities at this scale, and homogenizes local nonlinearities to predict their effects at the structural scale. Example applications of the multiscale framework are presented for the stochastic progressive failure of a SiC/Ti composite tensile specimen and the effects of microstructural variations on the nonlinear response of woven polymer matrix composites.
NASA Technical Reports Server (NTRS)
Bednarcyk, Brett A.; Arnold, Steven M.
2012-01-01
A framework for the multiscale design and analysis of composite materials and structures is presented. The ImMAC software suite, developed at NASA Glenn Research Center, embeds efficient, nonlinear micromechanics capabilities within higher scale structural analysis methods such as finite element analysis. The result is an integrated, multiscale tool that relates global loading to the constituent scale, captures nonlinearities at this scale, and homogenizes local nonlinearities to predict their effects at the structural scale. Example applications of the multiscale framework are presented for the stochastic progressive failure of a SiC/Ti composite tensile specimen and the effects of microstructural variations on the nonlinear response of woven polymer matrix composites.
A variational approach to magneto-elastic buckling problems
NASA Astrophysics Data System (ADS)
Vanlieshout, Peter Henricus
A variational principle that can serve as the basis for a magnetoelastic stability (or buckling) problem is constructed, starting from a specific choice for a magnetoelastic Lagrangian. For evaluation of the principle the first and second variations of the Lagrangian are calculated both inside and outside the solid magnetoelastic body. Thus a general buckling criterion, consisting of an expression for the critical field value together with a set of constraints for the field variables, is constructed. Detailed formulations are given for soft ferromagnetic and superconducting structures. Applications of the principle to one single Ferromagnetic or Superconducting Beam (FSB), a system of two parallel FSBs, and a system of two concentric and coaxial superconducting tori, are solved analytically using Green's identities, integral equations, fundamental solutions and complex analysis. Application to a system of an arbitrary number of parallel superconducting beams is solved using a numerical method involving standard procedures for the eigenvalue problem solution. The advantage of the variational method is that at the moment a reasonable eigenfunctions approximation leads to a very good buckling value approximation.
Buckling of a beam extruded into highly viscous fluid.
Gosselin, F P; Neetzow, P; Paak, M
2014-11-01
Inspired by microscopic Paramecia which use trichocyst extrusion to propel themselves away from thermal aggression, we propose a macroscopic experiment to study the stability of a slender beam extruded in a highly viscous fluid. Piano wires were extruded axially at constant speed in a tank filled with corn syrup. The force necessary to extrude the wire was measured to increase linearly at first until the compressive viscous force causes the wire to buckle. A numerical model, coupling a lengthening elastica formulation with resistive-force theory, predicts a similar behavior. The model is used to study the dynamics at large time when the beam is highly deformed. It is found that at large time, a large deformation regime exists in which the force necessary to extrude the beam at constant speed becomes constant and length independent. With a proper dimensional analysis, the beam can be shown to buckle at a critical length based on the extrusion speed, the bending rigidity, and the dynamic viscosity of the fluid. Hypothesizing that the trichocysts of Paramecia must be sized to maximize their thrust per unit volume as well as avoid buckling instabilities, we predict that their bending rigidity must be about 3×10^{-9}Nμm^{2}. The verification of this prediction is left for future work. PMID:25493827
Buckling of a beam extruded into highly viscous fluid
NASA Astrophysics Data System (ADS)
Gosselin, F. P.; Neetzow, P.; Paak, M.
2014-11-01
Inspired by microscopic Paramecia which use trichocyst extrusion to propel themselves away from thermal aggression, we propose a macroscopic experiment to study the stability of a slender beam extruded in a highly viscous fluid. Piano wires were extruded axially at constant speed in a tank filled with corn syrup. The force necessary to extrude the wire was measured to increase linearly at first until the compressive viscous force causes the wire to buckle. A numerical model, coupling a lengthening elastica formulation with resistive-force theory, predicts a similar behavior. The model is used to study the dynamics at large time when the beam is highly deformed. It is found that at large time, a large deformation regime exists in which the force necessary to extrude the beam at constant speed becomes constant and length independent. With a proper dimensional analysis, the beam can be shown to buckle at a critical length based on the extrusion speed, the bending rigidity, and the dynamic viscosity of the fluid. Hypothesizing that the trichocysts of Paramecia must be sized to maximize their thrust per unit volume as well as avoid buckling instabilities, we predict that their bending rigidity must be about 3 ×10-9N μ m2 . The verification of this prediction is left for future work.
Developing the Next Generation Shell Buckling Design Factors and Technologies
NASA Technical Reports Server (NTRS)
Hilburger, Mark W.
2012-01-01
NASA s Shell Buckling Knockdown Factor (SBKF) Project was established in the spring of 2007 by the NASA Engineering and Safety Center (NESC) in collaboration with the Constellation Program and Exploration Systems Mission Directorate. The SBKF project has the current goal of developing less-conservative, robust shell buckling design factors (a.k.a. knockdown factors) and design and analysis technologies for light-weight stiffened metallic launch vehicle (LV) structures. Preliminary design studies indicate that implementation of these new knockdown factors can enable significant reductions in mass and mass-growth in these vehicles and can help mitigate some of NASA s LV development and performance risks. In particular, it is expected that the results from this project will help reduce the reliance on testing, provide high-fidelity estimates of structural performance, reliability, robustness, and enable increased payload capability. The SBKF project objectives and approach used to develop and validate new design technologies are presented, and provide a glimpse into the future of design of the next generation of buckling-critical launch vehicle structures.
Ab initio study of the buckling on silicene and germanene
NASA Astrophysics Data System (ADS)
Martinez-Guerra, Edgar; Hernández, Karla; Cifuentes-Quintal, Eduardo; de Coss, Romeo
2013-03-01
Recently, a new graphene-like silicon structure was discovered: silicene. Since its discovery, silicene has been more exciting than graphene because this is a semiconductor and it should be compatible with silicon-based electronic. Silicon and germanium atoms have similar electronic configurations as those of carbon and this the reason that the bandstructure of silicene and germacene exhibits the Dirac cones at K point, with a very similar linear dispersion around it, like in graphene. The disvintage is that sp2 bonded Si is much less stable than for carbon resulting that to be stable in the planar layer their atoms must buckle. In this work, we calculated the sp character on silicene and germacene to correlate its hibridization with the velocity of electrons and holes at Dirac cones. The calculations were performed using the pseudopotential LCAO method with GGA for the exchange-correlation energy functional. The buckling of silicene and germacene layer was 0.50 and 0.69 Å, respectively. In addition, the sp- character of silicene and germacene buckled was 2.33 and 2.64, respectively. Thus, a detailed analysis on the electronic band structure of these system show that as sp character goes from sp2 to sp3 it is correlated with a decrease of velocity of electrons and holes at Dirac cones. This study is primarly important and it could address a new future to modulate carrier velocities on bidimensional systems. This research was supported by Conacyt under Grant No. 133022.
Buckling of a Flexible Strip Sliding on a Frictional Base
NASA Astrophysics Data System (ADS)
Huynen, Alexandre; Marck, Julien; Denoel, Vincent; Detournay, Emmanuel
2013-03-01
The main motivation for this contribution is the buckling of a drillstring sliding on the bottom of the horizontal section of borehole. The open questions that remain today are related to the determination of the onset of instability, and to the conditions under which different modes of constrained buckling occur. In this presentation, we are concerned by a two-dimensional version of this problem; namely, the sliding of a flexible strip being fed inside a conduit. The ribbon, which has a flexural rigidity EI and a weight per unit length w, is treated as an inextensible elastica of negligible thickness. The contact between the ribbon and the wall of the conduit is characterized by a friction coefficient μ. First, we report the result of a stability analysis that aims at determining the critical inserted length of the ribbon l* (μ) (scaled by the characteristic length λ =(EI / w) 1 / 3) at which there is separation between the strip and the conduit bottom, as well as the buckling mode. Next, the relationship between the feeding force F and the inserted length l after bifurcation is computed. Finally, the results of a ``kitchen table'' experiment involving a strip of silicon rubber being pushed on a plank are reported and compared with predictions.
Assessing Spontaneous Combustion Instability with Nonlinear Time Series Analysis
NASA Technical Reports Server (NTRS)
Eberhart, C. J.; Casiano, M. J.
2015-01-01
Considerable interest lies in the ability to characterize the onset of spontaneous instabilities within liquid propellant rocket engine (LPRE) combustion devices. Linear techniques, such as fast Fourier transforms, various correlation parameters, and critical damping parameters, have been used at great length for over fifty years. Recently, nonlinear time series methods have been applied to deduce information pertaining to instability incipiency hidden in seemingly stochastic combustion noise. A technique commonly used in biological sciences known as the Multifractal Detrended Fluctuation Analysis has been extended to the combustion dynamics field, and is introduced here as a data analysis approach complementary to linear ones. Advancing, a modified technique is leveraged to extract artifacts of impending combustion instability that present themselves a priori growth to limit cycle amplitudes. Analysis is demonstrated on data from J-2X gas generator testing during which a distinct spontaneous instability was observed. Comparisons are made to previous work wherein the data were characterized using linear approaches. Verification of the technique is performed by examining idealized signals and comparing two separate, independently developed tools.
Nonlinear Transient Thermal Analysis by the Force-Derivative Method
NASA Technical Reports Server (NTRS)
Balakrishnan, Narayani V.; Hou, Gene
1997-01-01
High-speed vehicles such as the Space Shuttle Orbiter must withstand severe aerodynamic heating during reentry through the atmosphere. The Shuttle skin and substructure are constructed primarily of aluminum, which must be protected during reentry with a thermal protection system (TPS) from being overheated beyond the allowable temperature limit, so that the structural integrity is maintained for subsequent flights. High-temperature reusable surface insulation (HRSI), a popular choice of passive insulation system, typically absorbs the incoming radiative or convective heat at its surface and then re-radiates most of it to the atmosphere while conducting the smallest amount possible to the structure by virtue of its low diffusivity. In order to ensure a successful thermal performance of the Shuttle under a prescribed reentry flight profile, a preflight reentry heating thermal analysis of the Shuttle must be done. The surface temperature profile, the transient response of the HRSI interior, and the structural temperatures are all required to evaluate the functioning of the HRSI. Transient temperature distributions which identify the regions of high temperature gradients, are also required to compute the thermal loads for a structural thermal stress analysis. Furthermore, a nonlinear analysis is necessary to account for the temperature-dependent thermal properties of the HRSI as well as to model radiation losses.
Applications of Automation Methods for Nonlinear Fracture Test Analysis
NASA Technical Reports Server (NTRS)
Allen, Phillip A.; Wells, Douglas N.
2013-01-01
As fracture mechanics material testing evolves, the governing test standards continue to be refined to better reflect the latest understanding of the physics of the fracture processes involved. The traditional format of ASTM fracture testing standards, utilizing equations expressed directly in the text of the standard to assess the experimental result, is self-limiting in the complexity that can be reasonably captured. The use of automated analysis techniques to draw upon a rich, detailed solution database for assessing fracture mechanics tests provides a foundation for a new approach to testing standards that enables routine users to obtain highly reliable assessments of tests involving complex, non-linear fracture behavior. Herein, the case for automating the analysis of tests of surface cracks in tension in the elastic-plastic regime is utilized as an example of how such a database can be generated and implemented for use in the ASTM standards framework. The presented approach forms a bridge between the equation-based fracture testing standards of today and the next generation of standards solving complex problems through analysis automation.
Probabilistic nonlinear finite element analysis of composite structures
NASA Technical Reports Server (NTRS)
Engelstad, S. P.; Reddy, J. N.
1993-01-01
A probabilistic finite element analysis procedure for laminated composite shells is developed. A total Lagrangian finite element formulation, employing a degenerated three-dimensional laminated composite shell element with the full Green-Lagrange strains and first-order shear deformable kinematics, is used. The first-order second-moment technique for probabilistic finite element analysis of random fields is employed, and results are presented in the form of mean and variance of the structural response. Reliability calculations are made by using the first-order reliability method combined with sensitivity derivatives from the finite element analysis. Both ply-level and micromechanics-level random variables are incorporated, the latter by means of the Aboudi micromechanics model. Two sample problems are solved to verify the accuracy of the procedures developed and to quantify the variability of certain material type/structure combinations. In general, the procedure is quite effective in determining the response statistics and reliability for linear and geometric nonlinear behavior of laminated composite shells.
NASA Astrophysics Data System (ADS)
Tang, You-Fu; Liu, Shu-Lin; Jiang, Rui-Hong; Liu, Ying-Hui
2013-03-01
We study the correlation between detrended fluctuation analysis (DFA) and the Lempel-Ziv complexity (LZC) in nonlinear time series analysis in this paper. Typical dynamic systems including a logistic map and a Duffing model are investigated. Moreover, the influence of Gaussian random noise on both the DFA and LZC are analyzed. The results show a high correlation between the DFA and LZC, which can quantify the non-stationarity and the nonlinearity of the time series, respectively. With the enhancement of the random component, the exponent a and the normalized complexity index C show increasing trends. In addition, C is found to be more sensitive to the fluctuation in the nonlinear time series than α. Finally, the correlation between the DFA and LZC is applied to the extraction of vibration signals for a reciprocating compressor gas valve, and an effective fault diagnosis result is obtained.
Nonlinear instability and reliability analysis of composite laminated beams
NASA Astrophysics Data System (ADS)
Fereidooni, Alireza
the beam subjected to substantial excitation loading parameters increases in a typical nonlinear manner and leads to the beats phenomena. The principal regions of dynamic instability are determined for various loading and boundary conditions using the Floquet's theory. The beam response in the regions of instability is investigated. Axially loaded beam may be unstable not just in load equal to critical load and/or loading frequency equal to beam natural frequency. In fact there are infinite points in region of instability in plane load vs. frequency that the beam can be unstable. The region of instability of the shear deformable beams is wider compare to the non-shear deformable beams. The lower bound of the instability region of the shear deformable beams changes faster than upper bound. Probabilistic stability analysis of the uncertain laminated beams subject to both conservative and nonconservative loads is studied. The effects of material and geometry uncertainties on dynamics instability of the beam, is investigated through a probabilistic finite element analysis and Monte Carlo Simulation methods. For non-conservative systems variations of uncertain material properties has a smaller influence than variations of geometric properties over the instability of the beam.
Frequency domain stability analysis of nonlinear active disturbance rejection control system.
Li, Jie; Qi, Xiaohui; Xia, Yuanqing; Pu, Fan; Chang, Kai
2015-05-01
This paper applies three methods (i.e., root locus analysis, describing function method and extended circle criterion) to approach the frequency domain stability analysis of the fast tool servo system using nonlinear active disturbance rejection control (ADRC) algorithm. Root locus qualitative analysis shows that limit cycle is generated because the gain of the nonlinear function used in ADRC varies with its input. The parameters in the nonlinear function are adjustable to suppress limit cycle. In the process of root locus analysis, the nonlinear function is transformed based on the concept of equivalent gain. Then, frequency domain description of the nonlinear function via describing function is presented and limit cycle quantitative analysis including estimating prediction error is presented, which virtually and theoretically demonstrates that the describing function method cannot guarantee enough precision in this case. Furthermore, absolute stability analysis based on extended circle criterion is investigated as a complement. PMID:25532936
Thermodynamic analysis of black hole solutions in gravitating nonlinear electrodynamics
NASA Astrophysics Data System (ADS)
Diaz-Alonso, J.; Rubiera-Garcia, D.
2013-10-01
We perform a general study of the thermodynamic properties of static electrically charged black hole solutions of nonlinear electrodynamics minimally coupled to gravitation in three space dimensions. The Lagrangian densities governing the dynamics of these models in flat space are defined as arbitrary functions of the gauge field invariants, constrained by some requirements for physical admissibility. The exhaustive classification of these theories in flat space, in terms of the behaviour of the Lagrangian densities in vacuum and on the boundary of their domain of definition, defines twelve families of admissible models. When these models are coupled to gravity, the flat space classification leads to a complete characterization of the associated sets of gravitating electrostatic spherically symmetric solutions by their central and asymptotic behaviours. We focus on nine of these families, which support asymptotically Schwarzschild-like black hole configurations, for which the thermodynamic analysis is possible and pertinent. In this way, the thermodynamic laws are extended to the sets of black hole solutions of these families, for which the generic behaviours of the relevant state variables are classified and thoroughly analyzed in terms of the aforementioned boundary properties of the Lagrangians. Moreover, we find universal scaling laws (which hold and are the same for all the black hole solutions of models belonging to any of the nine families) running the thermodynamic variables with the electric charge and the horizon radius. These scale transformations form a one-parameter multiplicative group, leading to universal "renormalization group"-like first-order differential equations. The beams of characteristics of these equations generate the full set of black hole states associated to any of these gravitating nonlinear electrodynamics. Moreover the application of the scaling laws allows to find a universal finite relation between the thermodynamic variables
Nonlinear times series analysis of epileptic human electroencephalogram (EEG)
NASA Astrophysics Data System (ADS)
Li, Dingzhou
The problem of seizure anticipation in patients with epilepsy has attracted significant attention in the past few years. In this paper we discuss two approaches, using methods of nonlinear time series analysis applied to scalp electrode recordings, which is able to distinguish between epochs temporally distant from and just prior to, the onset of a seizure in patients with temporal lobe epilepsy. First we describe a method involving a comparison of recordings taken from electrodes adjacent to and remote from the site of the seizure focus. In particular, we define a nonlinear quantity which we call marginal predictability. This quantity is computed using data from remote and from adjacent electrodes. We find that the difference between the marginal predictabilities computed for the remote and adjacent electrodes decreases several tens of minutes prior to seizure onset, compared to its value interictally. We also show that these difl'crcnc es of marginal predictability intervals are independent of the behavior state of the patient. Next we examine the please coherence between different electrodes both in the long-range and the short-range. When time is distant from seizure onsets ("interictally"), epileptic patients have lower long-range phase coherence in the delta (1-4Hz) and beta (18-30Hz) frequency band compared to nonepileptic subjects. When seizures approach (''preictally"), we observe an increase in phase coherence in the beta band. However, interictally there is no difference in short-range phase coherence between this cohort of patients and non-epileptic subjects. Preictally short-range phase coherence also increases in the alpha (10-13Hz) and the beta band. Next we apply the quantity marginal predictability on the phase difference time series. Such marginal predictabilities are lower in the patients than in the non-epileptic subjects. However, when seizure approaches, the former moves asymptotically towards the latter.
Linear and Nonlinear Analysis of Brain Dynamics in Children with Cerebral Palsy
ERIC Educational Resources Information Center
Sajedi, Firoozeh; Ahmadlou, Mehran; Vameghi, Roshanak; Gharib, Masoud; Hemmati, Sahel
2013-01-01
This study was carried out to determine linear and nonlinear changes of brain dynamics and their relationships with the motor dysfunctions in CP children. For this purpose power of EEG frequency bands (as a linear analysis) and EEG fractality (as a nonlinear analysis) were computed in eyes-closed resting state and statistically compared between 26…
Torsional Buckling and Writhing Dynamics of Elastic Cables and DNA
Goyal, S; Perkins, N C; Lee, C L
2003-02-14
Marine cables under low tension and torsion on the sea floor can undergo a dynamic buckling process during which torsional strain energy is converted to bending strain energy. The resulting three-dimensional cable geometries can be highly contorted and include loops and tangles. Similar geometries are known to exist for supercoiled DNA and these also arise from the conversion of torsional strain energy to bending strain energy or, kinematically, a conversion of twist to writhe. A dynamic form of Kirchhoff rod theory is presented herein that captures these nonlinear dynamic processes. The resulting theory is discretized using the generalized-method for finite differencing in both space and time. The important kinematics of cross-section rotation are described using an incremental rotation ''vector'' as opposed to traditional Euler angles or Euler parameters. Numerical solutions are presented for an example system of a cable subjected to increasing twist at one end. The solutions show the dynamic evolution of the cable from an initially straight element, through a buckled element in the approximate form of a helix, and through the dynamic collapse of this helix through a looped form.
NASA Astrophysics Data System (ADS)
Shrivastava, Sachin; Mohite, P. M.
2015-01-01
A redesign of canard control-surface of an advanced all-metallic fighter aircraft was carried out by using carbon fibre composite (CFC) for ribs and panels. In this study ply-orientations of CFC structure are optimized using a Genetic-Algorithm (GA) with an objective function to have minimum failure index (FI) according to Tsai-Wu failure criterion. The redesigned CFC structure was sufficiently strong to withstand aerodynamic loads from stress and deflection points of view. Now, in the present work CFC canard structure has been studied for its buckling strength in comparison to existing metallic design. In this study, the existing metallic design was found to be weak in buckling. Upon a detailed investigation, it was revealed that there are reported failures in the vicinity of zones where initial buckling modes are excited as predicted by the finite element based buckling analysis. In view of buckling failures, the redesigned CFC structure is sufficiently reinforced with stringers at specific locations. After providing reinforcements against buckling, the twist and the camber variations of the airfoil are checked and compared with existing structure data. Finally, the modal analysis has been carried out to compare the variation in excitation frequency due to material change. The CFC structure thus redesigned is safe from buckling and aerodynamic aspects as well.
Nonlinear analysis of the ground-based magnetometer network
NASA Astrophysics Data System (ADS)
DiTommaso, Joseph Henry
When the first magnetometer was created by Frederick Gauss in 1833, scientists gained a powerful tool for studying the structure, dynamics, and strength of the Earth's magnetic field: the magnetosphere. Since Gauss' time, the world's scientific community has established ground-based magnetometer stations around the globe in an effort to study local and global perturbations and patterns of the Earth's magnetic field. The main focus of this network has been monitoring the magnetic flux and impact from the Sun's constant outflow of radiation and particles known as the solar wind, as well as its more violent eruptive events. There has been little work, by comparison, into the signals and correlations within the network itself. Since the Earth's field can roughly be mapped to a dipole and disturbances often have a large scale structure, one can surmise there should be some correlation between stations based on their relative positions to one another. What that correlation is or represents is not clear. To investigate this possible correlation and its nature, a set of nonlinear analytic methods were conducted on magnetic data collected from stations scattered across North America over an 18 year period. The analysis was focused on searching for spatial and temporal correlations of nonperiodic signals in the magnetometer network. The findings from that analysis suggest there exist nonlocal correlations between stations that are dependent on position, which could be useful in the development of a space weather risk assessment.
Nonlinear explicit transient finite element analysis on the Intel Delta
Plaskacz, E.J.; Ramirez, M.R.; Gupta, S.
1993-03-01
Many large scale finite element problems are intractable on current generation production supercomputers. High-performance computer architectures offer effective avenues to bridge the gap between computational needs and the power of computational hardware. The biggest challenge lies in the substitution of the key algorithms in an application program with redesigned algorithms which exploit the new architectures and use better or more appropriate numerical techniques. A methodology for implementing nonlinear finite element analysis on a homogeneous distributed processing network is discussed. The method can also be extended to heterogeneous networks comprised of different machine architectures provided that they have a mutual communication interface. This unique feature has greatly facilitated the port of the code to the 8-node Intel Touchstone Gamma and then the 512-node Intel Touchstone Delta. The domain is decomposed serially in a preprocessor. Separate input files are written for each subdomain. These files are read in by local copies of the program executable operating in parallel. Communication between processors is addressed utilizing asynchronous and synchronous message passing. The basic kernel of message passing is the internal force exchange which is analogous to the computed interactions between sections of physical bodies in static stress analysis. Benchmarks for the Intel Delta are presented. Performance exceeding 1 gigaflop was attained. Results for two large-scale finite element meshes are presented.
Nonlinear explicit transient finite element analysis on the Intel Delta
Plaskacz, E.J. ); Ramirez, M.R.; Gupta, S. . Dept. of Civil Engineering)
1993-01-01
Many large scale finite element problems are intractable on current generation production supercomputers. High-performance computer architectures offer effective avenues to bridge the gap between computational needs and the power of computational hardware. The biggest challenge lies in the substitution of the key algorithms in an application program with redesigned algorithms which exploit the new architectures and use better or more appropriate numerical techniques. A methodology for implementing nonlinear finite element analysis on a homogeneous distributed processing network is discussed. The method can also be extended to heterogeneous networks comprised of different machine architectures provided that they have a mutual communication interface. This unique feature has greatly facilitated the port of the code to the 8-node Intel Touchstone Gamma and then the 512-node Intel Touchstone Delta. The domain is decomposed serially in a preprocessor. Separate input files are written for each subdomain. These files are read in by local copies of the program executable operating in parallel. Communication between processors is addressed utilizing asynchronous and synchronous message passing. The basic kernel of message passing is the internal force exchange which is analogous to the computed interactions between sections of physical bodies in static stress analysis. Benchmarks for the Intel Delta are presented. Performance exceeding 1 gigaflop was attained. Results for two large-scale finite element meshes are presented.
Unified nonlinear analysis for nonhomogeneous anisotropic beams with closed cross sections
NASA Technical Reports Server (NTRS)
Atilgan, Ali R.; Hodges, Dewey H.
1991-01-01
A unified methodology for geometrically nonlinear analysis of nonhomogeneous, anisotropic beams is presented. A 2D cross-sectional analysis and a nonlinear 1D global deformation analysis are derived from the common framework of a 3D, geometrically nonlinear theory of elasticity. The only restrictions are that the strain and local rotation are small compared to unity and that warping displacements are small relative to the cross-sectional dimensions. It is concluded that the warping solutions can be affected by large deformation and that this could alter the incremental stiffnes of the section. It is shown that sectional constants derived from the published, linear analysis can be used in the present nonlinear, 1D analysis governing the global deformation of the beam, which is based on intrinsic equations for nonlinear beam behavior. Excellent correlation is obtained with published experimental results for both isotropic and anisotropic beams undergoing large deflections.
Nonlinear analysis on vertical distribution of suspended load
NASA Astrophysics Data System (ADS)
Wang, Fuquan; Li, Houqiang; Ding, Jing
1998-06-01
In turbulent two-phase flows, the vertical distribution of suspended load has complex features under the actions of turbulence and gravity. The nonlinear dynamics and fractal features are investigated, and the nonlinear distribution is calculated. Some shortcomings of classical theories have been overcome.
Nonlinear analysis of axisymmetric layered pressure vessels; Part 2: steady-state applications
Leigh, D.C.; Taucherty, T.R.; Blandford, G.E. )
1989-05-01
Steady-state applications of the theory in Part 1 of the paper are made to a particular layered pressure vessel design subjected to a typical set of pressure and thernal loadings. Results are compared for several analyses: elastic analysis, linear thermoelastic analysis for a solid-wall vessel, nonlinear analysis for solid-wall, and nonlinear analysis for a layered vessel. Due to the thermal resistance between layers, the maximum circumferential stress is, for the nonlinear analysis, about 35 percent greater for the layered vessel than it is for the solid-wall vessel.
Comparative analysis of nonlinear optofluidic processes in microdroplets
NASA Astrophysics Data System (ADS)
Zhang, Peng; Jung, Sunghwan; Lee, Aram; Xu, Yong
2016-06-01
Our prior work has shown that high quality (Q ) factor whispering gallery modes (WGMs) in liquid microdroplets can potentially induce single-photon-level nonlinear effects through radiation pressure on the interface. However, little is known about the nonlinear effects of other processes involving scattering force and thermocapillarity. In this study, we establish a numerical framework that can calculate the fluid motion and the resultant nonlinearity induced by the optical scattering force and thermocapillarity. Then, we compare the magnitude of various nonlinear optofluidic processes induced by the radiation pressure, the thermocapillary effect, the scattering-induced optical force, and the Kerr effect. Using realistic fluid parameters, we show that the radiation pressure due to the WGM produces the strongest nonlinear optofluidic effect.
Comparative analysis of nonlinear optofluidic processes in microdroplets.
Zhang, Peng; Jung, Sunghwan; Lee, Aram; Xu, Yong
2016-06-01
Our prior work has shown that high quality (Q) factor whispering gallery modes (WGMs) in liquid microdroplets can potentially induce single-photon-level nonlinear effects through radiation pressure on the interface. However, little is known about the nonlinear effects of other processes involving scattering force and thermocapillarity. In this study, we establish a numerical framework that can calculate the fluid motion and the resultant nonlinearity induced by the optical scattering force and thermocapillarity. Then, we compare the magnitude of various nonlinear optofluidic processes induced by the radiation pressure, the thermocapillary effect, the scattering-induced optical force, and the Kerr effect. Using realistic fluid parameters, we show that the radiation pressure due to the WGM produces the strongest nonlinear optofluidic effect. PMID:27415370
Nonlinear large-deflection analysis of orthodontic wires.
Hayashi, Kazuo; Araki, Yoshima; Mizoguchi, Itaru
2004-02-01
The purposes of this study were (1) to measure the nonlinear force-deflection behavior of selected orthodontic wires using a conventional tensile test, (2) to extend a mathematical model for simulating the force system produced by orthodontic wires based on the small-deflection linear theory to the large-deflection nonlinear theory, and (3) to examine the effects of the cross-section and mechanical properties of orthodontic wires on nonlinear characteristics. A method for extending a mathematical model for simulating the force system produced by orthodontic wires based on the small-deflection linear theory to the large-deflection nonlinear theory was established, and this can provide a clear view of the true nature of orthodontic wires. Furthermore, our results demonstrated that the nonlinear properties of orthodontic wires were affected more by the cross-sectional shape than by mechanical properties. PMID:15038499
Active control of buckling of flexible beams
NASA Technical Reports Server (NTRS)
Baz, A.; Tampe, L.
1989-01-01
The feasibility of using the rapidly growing technology of the shape memory alloys actuators in actively controlling the buckling of large flexible structures is investigated. The need for such buckling control systems is becoming inevitable as the design trends of large space structures have resulted in the use of structural members that are long, slender, and very flexible. In addition, as these truss members are subjected mainly to longitudinal loading they become susceptible to structural instabilities due to buckling. Proper control of such instabilities is essential to the effective performance of the structures as stable platforms for communication and observation. Mathematical models are presented that simulate the dynamic characteristics of the shape memory actuator, the compressive structural members, and the associated active control system. A closed-loop computer-controlled system is designed, based on the developed mathematical models, and implemented to control the buckling of simple beams. The performance of the computer-controlled system is evaluated experimentally and compared with the theoretical predictions to validate the developed models. The obtained results emphasize the importance of buckling control and suggest the potential of the shape memory actuators as attractive means for controlling structural deformation in a simple and reliable way.
Mechanical buckling of veins under internal pressure.
Martinez, Ricky; Fierro, Cesar A; Shireman, Paula K; Han, Hai-Chao
2010-04-01
Venous tortuosity is associated with multiple disease states and is often thought to be a consequence of venous hypertension and chronic venous disease. However, the underlying mechanisms of vein tortuosity are unclear. We hypothesized that increased pressure causes vein buckling that leads to a tortuous appearance. The specific aim of this study was to determine the critical buckling pressure of veins. We determined the buckling pressure of porcine jugular veins and measured the mechanical properties of these veins. Our results showed that the veins buckle when the transmural pressure exceeds a critical pressure that is strongly related to the axial stretch ratio in the veins. The critical pressures of the eight veins tested were 14.2 +/- 5.4 and 26.4 +/- 9.0 mmHg at axial stretch ratio 1.5 and 1.7, respectively. In conclusion, veins buckle into a tortuous shape at high lumen pressures or reduced axial stretch ratios. Our results are useful in understanding the development of venous tortuosity associated with varicose veins, venous valvular insufficiency, diabetic retinopathy, and vein grafts. PMID:20094913
Mechanical Buckling of Veins under Internal Pressure
Martinez, Ricky; Fierro, Cesar A.; Shireman, Paula K.; Han, Hai-Chao
2010-01-01
Venous tortuosity is associated with multiple disease states and is often thought to be a consequence of venous hypertension and chronic venous disease. However, the underlying mechanisms of vein tortuosity are unclear. We hypothesized that increased pressure causes vein buckling that leads to a tortuous appearance. The specific aim of this study was to determine the critical buckling pressure of veins. We determined the buckling pressure of porcine jugular veins and measured the mechanical properties of these veins. Our results showed that veins buckle when the transmural pressure exceeds a critical pressure that is strongly related to the axial stretch ratio in the veins. The critical pressures of the eight veins tested were 14.2 ± 5.4 mmHg and 26.4 ± 9.0 mmHg at axial stretch ratio 1.5 and 1.7, respectively. In conclusion, veins buckle into a tortuous shape at high lumen pressures or reduced axial stretch ratios. Our results are useful in understanding the development of venous tortuosity associated with varicose veins, venous valvular insufficiency, diabetic retinopathy and vein grafts. PMID:20094913
NASA Technical Reports Server (NTRS)
Gates, Thomas S.; Odegard, Gregory M.; Nemeth, Michael P.; Frankland, Sarah-Jane V.
2004-01-01
A multi-scale analysis of the structural stability of a carbon nanotube-polymer composite material is developed. The influence of intrinsic molecular structure, such as nanotube length, volume fraction, orientation and chemical functionalization, is investigated by assessing the relative change in critical, in-plane buckling loads. The analysis method relies on elastic properties predicted using the hierarchical, constitutive equations developed from the equivalent-continuum modeling technique applied to the buckling analysis of an orthotropic plate. The results indicate that for the specific composite materials considered in this study, a composite with randomly orientated carbon nanotubes consistently provides the highest values of critical buckling load and that for low volume fraction composites, the non-functionalized nanotube material provides an increase in critical buckling stability with respect to the functionalized system.
NASA Astrophysics Data System (ADS)
Stam, Samantha; Gardel, Margaret
Viscoelastic networks of biopolymers coordinate the motion of intracellular objects during transport. These networks have nonlinear mechanical properties due to events such as filament buckling or breaking of cross-links. The influence of such nonlinear properties on the time and length scales of transport is not understood. Here, we use in vitro networks of actin and the motor protein myosin II to clarify how intracellular forces regulate active diffusion. We observe two transitions in the mean-squared displacement of cross-linked actin with increasing motor concentration. The first is a sharp transition from initially subdiffusive to diffusive-like motion that requires filament buckling but does not cause net contraction of the network. Further increase of the motor density produces a second transition to network rupture and ballistic actin transport. This corresponds with an increase in the correlation of motion and thus may be caused when forces propagate far enough for global motion. We conclude that filament buckling and overall network contraction require different amounts of force and produce distinct transport properties. These nonlinear transitions may act as mechanical switches that can be turned on to produce observed motion within cells.
NASA Technical Reports Server (NTRS)
Arbocz, Johann; deVries, J.; Hol, J. M. A. M.
1998-01-01
A rigorous solution is presented for the case of stiffened anisotropic cylindrical shells with general imperfections under combined loading, where the edge supports are provided by symmetrical or unsymmetrical elastic rings. The circumferential dependence is eliminated by a truncated Fourier series. The resulting nonlinear 2-point boundary value problem is solved numerically via the "Parallel Shooting Method". The changing deformation patterns resulting from the different degrees of interaction between the given initial imperfections and the specified end rings are displayed. Recommendations are made as to the minimum ring stiffnesses required for optimal load carrying configurations.
Nonlinear analysis of an electrodynamic broadband energy harvester
NASA Astrophysics Data System (ADS)
Bradai, S.; Naifar, S.; Viehweger, C.; Kanoun, O.; Litak, G.
2015-11-01
In order to maximize energy from ambient vibration sources, wide band harvesters working at a range of frequencies are important. This paper presents an electrodynamic energy harvester model working for a frequency band from 25 Hz to 45 Hz. The developed converter consists of a magnetic spring formed by one moving magnet placed between two fixed magnets. A ring magnet is placed around the moving magnet leading to additional nonlinear stiffness to increase the power output. A comparison to a basic configuration electrodynamic converter was carried out by finite element analysis to show that a significant increase in power output was realized. Simulation results have been confirmed by experimental investigations under harmonic excitations. Based on the experimental time series, we have examined the frequency spectrum and phase portraits to identify the dynamic response of the system. In conclusion, the generator is able to harvest 1.5 times more energy than the simple generator for the bandwidth of 20 Hz with the resonant frequency of 35 Hz and the excitation amplitude of 2 mm.
Nonlinear analysis of EEG in major depression with fractal dimensions.
Akar, Saime A; Kara, Sadik; Agambayev, Sumeyra; Bilgic, Vedat
2015-08-01
Major depressive disorder (MDD) is a psychiatric mood disorder characterized by cognitive and functional impairments in attention, concentration, learning and memory. In order to investigate and understand its underlying neural activities and pathophysiology, EEG methodologies can be used. In this study, we estimated the nonlinearity features of EEG in MDD patients to assess the dynamical properties underlying the frontal and parietal brain activity. EEG data were obtained from 16 patients and 15 matched healthy controls. A wavelet-chaos methodology was used for data analysis. First, EEGs of subjects were decomposed into 5 EEG sub-bands by discrete wavelet transform. Then, both the Katz's and Higuchi's fractal dimensions (KFD and HFD) were calculated as complexity measures for full-band and sub-bands EEGs. Last, two-way analyses of variances were used to test EEG complexity differences on each fractality measures. As a result, a significantly increased complexity was found in both parietal and frontal regions of MDD patients. This significantly increased complexity was observed not only in full-band activity but also in beta and gamma sub-bands of EEG. The findings of the present study indicate the possibility of using the wavelet-chaos methodology to discriminate the EEGs of MDD patients from healthy controls. PMID:26738004
Nonlinear dynamical analysis for displaced orbits above a planet
NASA Astrophysics Data System (ADS)
Xu, Ming; Xu, Shijie
2008-12-01
Nonlinear dynamical analysis and the control problem for a displaced orbit above a planet are discussed. It is indicated that there are two equilibria for the system, one hyperbolic (saddle) and one elliptic (center), except for the degenerate h {/z max}, a saddle-node bifurcation point. Motions near the equilibria for the nonresonance case are investigated by means of the Birkhoff normal form and dynamical system techniques. The Kolmogorov Arnold Moser (KAM) torus filled with quasiperiodic trajectories is measured in the τ 1 and τ 2 directions, and a rough algorithm for calculating τ 1 and τ 2 is proposed. A general iterative algorithm to generate periodic Lyapunov orbits is also presented. Transitions in the neck region are demonstrated, respectively, in the nonresonance, resonance, and degradation cases. One of the important contributions of the paper is to derive necessary and sufficiency conditions for stability of the motion near the equilibria. Another contribution is to demonstrate numerically that the critical KAM torus of nontransition is filled with the (1,1)-homoclinic orbits of the Lyapunov orbit.
Analysis of nonlinear optical properties in donor–acceptor materials
Day, Paul N.; Pachter, Ruth; Nguyen, Kiet A.
2014-05-14
Time-dependent density functional theory has been used to calculate nonlinear optical (NLO) properties, including the first and second hyperpolarizabilities as well as the two-photon absorption cross-section, for the donor-acceptor molecules p-nitroaniline and dimethylamino nitrostilbene, and for respective materials attached to a gold dimer. The CAMB3LYP, B3LYP, PBE0, and PBE exchange-correlation functionals all had fair but variable performance when compared to higher-level theory and to experiment. The CAMB3LYP functional had the best performance on these compounds of the functionals tested. However, our comprehensive analysis has shown that quantitative prediction of hyperpolarizabilities is still a challenge, hampered by inadequate functionals, basis sets, and solvation models, requiring further experimental characterization. Attachment of the Au{sub 2}S group to molecules already known for their relatively large NLO properties was found to further enhance the response. While our calculations show a modest enhancement for the first hyperpolarizability, the enhancement of the second hyperpolarizability is predicted to be more than an order of magnitude.
BUCKLE: A Model of Unobserved Cause Learning
Luhmann, Christian C.; Ahn, Woo-kyoung
2009-01-01
Dealing with alternative causes is necessary to avoid making inaccurate causal inferences from covariation data. However, information about alternative causes is frequently unavailable, rendering them unobserved. The current article reviews the way in which current learning models deal, or could deal, with unobserved causes. A new model of causal learning, BUCKLE (bidirectional unobserved cause learning) extends existing models of causal learning by dynamically inferring information about unobserved, alternative causes. During the course of causal learning, BUCKLE continually computes the probability that an unobserved cause is present during a given observation and then uses the results of these inferences to learn the causal strengths of the unobserved as well as observed causes. The current results demonstrate that BUCKLE provides a better explanation of people's causal learning than the existing models. PMID:17638500
On numerical nonlinear analysis of highly flexible spinning cantilevers
NASA Technical Reports Server (NTRS)
Utku, S.; El-Essawi, M.; Salama, M.
1981-01-01
The general nonlinear discretized equations of motion of spinning elastic solids and structures are derived as a set of nonlinear ordinary differential equations for the case when the strain-displacement and velocity-displacement relations are nonlinear up to the second order. It is shown that the cost of generation of such equations is proportional to the fourth power of the number of degrees of freedom. A computer program is written to automatically generate the equations for the case of spinning cantilevers with initial imperfections. The types and the number of the coordinate functions used in the trial solution are parameters of the program.
Analysis of non-linearity in differential wavefront sensing technique.
Duan, Hui-Zong; Liang, Yu-Rong; Yeh, Hsien-Chi
2016-03-01
An analytical model of a differential wavefront sensing (DWS) technique based on Gaussian Beam propagation has been derived. Compared with the result of the interference signals detected by quadrant photodiode, which is calculated by using the numerical method, the analytical model has been verified. Both the analytical model and numerical simulation show milli-radians level non-linearity effect of DWS detection. In addition, the beam clipping has strong influence on the non-linearity of DWS. The larger the beam clipping is, the smaller the non-linearity is. However, the beam walking effect hardly has influence on DWS. Thus, it can be ignored in laser interferometer. PMID:26974079
Nonlinear analysis of axisymmetrix layered pressure vessels; Part 1: theory
Blandford, G.E.; Tauchert, T.R.; Leigh, D.C. )
1989-05-01
A finite element formulation for the nonlinear heat conduction and thermoelastic analyses of orthotropic, axisymmetric layered pressure vessels is presented. Nonlinearities include temperature-dependent material properties and stress-dependent layer interface conditions. Solution of the nonlinear heat conduction equations is iteratively obtained using a modified Newton-Raphson scheme. Direct iteration between heat conduction and stress analyses is employed when stress-dependent interface thermal resistance is considered. A modified time integration scheme to reduce oscillatory noise is introduced, and the stability and accuracy of the time integration scheme are discussed.
The Buckling of Curved Tension-field Girders
NASA Technical Reports Server (NTRS)
Limpert, G
1938-01-01
The present paper reports on experiments made to determine the buckling load under shear of circular curved tension-field webs. The buckling load of the webs may be expressed with reference to the buckling load of the stiffeners. It is found that within the explored range the buckling load is approximately twice as great as that of the identically stiffened flat wall of equal web depth.
NASA Technical Reports Server (NTRS)
1976-01-01
The development of two new shell finite elements for applications to large deflection problems is considered. The elements in question are doubly curved and of triangular and quadrilateral planform. They are restricted to small strains of elastic materials, and can accommodate large rotations. The elements described, which are based on relatively simple linear elements, make use of a new displacement function approach specifically designed for strongly nonlinear problems. The displacement function development for nonlinear applications is based on certain beam element formulations, and the strain-displacement equations are of a shallow shell type. Additional terms were included in these equations in an attempt to avoid the large errors characteristic of shallow shell elements in certain types of problems. An incremental nonlinear solution procedure specifically adopted to the element formulation was developed. The solution procedure is of combined incremental and total Lagrangian type, and uses a new updating scheme. A computer program was written to evaluate the developed formulations. This program can accommodate small element groups in arbitrary arrangements. Two simple programs were successfully solved. The results indicate that this new type of element has definite promise and should be a fruitful area for further research.
Buckling Behavior of Long Anisotropic Plates Subjected to Fully Restrained Thermal Expansion
NASA Technical Reports Server (NTRS)
Nemeth, Michael P.
2003-01-01
An approach for synthesizing buckling results and behavior for thin, balanced and unbalanced symmetric laminates that are subjected to uniform heating or cooling and which are fully-restrained against thermal expansion or contraction is presented. This approach uses a nondimensional analysis for infinitely long, flexurally anisotropic plates that are subjected to combined mechanical loads and is based on useful nondimensional parameters. In addition, stiffness-weighted laminate thermal-expansion parameters are derived and used to determine critical temperature changes in terms of physically intuitive mechanical buckling coefficients. The effects of membrane orthotropy and anisotropy are included. Many results are presented for some common laminates that are intended to facilitate a structural designer's transition to the use of the generic buckling design curves that are presented in the paper. Several generic buckling design curves are presented that provide physical insight into buckling response and provide useful design data. Examples are presented that demonstrate the use of generic design curves. The analysis approach and generic results indicate the effects and characteristics of laminate thermal expansion, membrane orthotropy and anisotropy, and flexural orthotropy and anisotropy in a very general, unifying manner.
Buckling Behavior of Long Anisotropic Plates Subjected to Fully Restrained Thermal Expansion
NASA Technical Reports Server (NTRS)
Nemeth, Michael P.
2001-01-01
An approach for synthesizing buckling results and behavior for thin balanced and unbalanced symmetric laminates that are subjected to uniform heating or cooling and fully restrained against thermal expansion or contraction is presented. This approach uses a nondimensional analysis for infinitely long, flexurally anisotropic plates that are subjected to combined mechanical loads and is based on useful nondimensional parameters. In addition, stiffness-weighted laminate thermal-expansion parameters are derived that are used to determine critical temperatures in terms of physically intuitive mechanical buckling coefficients, and the effects of membrane orthotropy and membrane anisotropy are included. Many results are presented for some common laminates that are intended to facilitate a structural designer's transition to the use of the generic buckling design curves that are presented in the paper. Several generic buckling design curves are presented that provide physical insight into the buckling response in addition to providing useful design data. Examples are presented that demonstrate the use of the generic design curves. The analysis approach and generic results indicate the effects and characteristics of laminate thermal expansion, membrane orthotropy and anisotropy, and flexural orthotropy and anisotropy in a very general and unifying manner.
Buckling Behavior of Individual and Bundled Microtubules
Soheilypour, Mohammad; Peyro, Mohaddeseh; Peter, Stephen J.; Mofrad, Mohammad R.K.
2015-01-01
As the major structural constituent of the cytoskeleton, microtubules (MTs) serve a variety of biological functions that range from facilitating organelle transport to maintaining the mechanical integrity of the cell. Neuronal MTs exhibit a distinct configuration, hexagonally packed bundles of MT filaments, interconnected by MT-associated protein (MAP) tau. Building on our previous work on mechanical response of axonal MT bundles under uniaxial tension, this study is focused on exploring the compression scenarios. Intracellular MTs carry a large fraction of the compressive loads sensed by the cell and therefore, like any other column-like structure, are prone to substantial bending and buckling. Various biological activities, e.g., actomyosin contractility and many pathological conditions are driven or followed by bending, looping, and buckling of MT filaments. The coarse-grained model previously developed in our lab has been used to study the mechanical behavior of individual and bundled in vivo MT filaments under uniaxial compression. Both configurations show tip-localized, decaying, and short-wavelength buckling. This behavior highlights the role of the surrounding cytoplasm and MAP tau on MT buckling behavior, which allows MT filaments to bear much larger compressive forces. It is observed that MAP tau interconnections improve this effect by a factor of two. The enhanced ability of MT bundles to damp buckling waves relative to individual MT filaments, may be interpreted as a self-defense mechanism because it helps axonal MTs to endure harsher environments while maintaining their function. The results indicate that MT filaments in a bundle do not buckle simultaneously implying that the applied stress is not equally shared among the MT filaments, that is a consequence of the nonuniform distribution of MAP tau proteins along the bundle length. Furthermore, from a pathological perspective, it is observed that axonal MT bundles are more vulnerable to failure in
Selective buckling via states of self-stress in topological metamaterials
Paulose, Jayson; Meeussen, Anne S.; Vitelli, Vincenzo
2015-01-01
States of self-stress—tensions and compressions of structural elements that result in zero net forces—play an important role in determining the load-bearing ability of structures ranging from bridges to metamaterials with tunable mechanical properties. We exploit a class of recently introduced states of self-stress analogous to topological quantum states to sculpt localized buckling regions in the interior of periodic cellular metamaterials. Although the topological states of self-stress arise in the linear response of an idealized mechanical frame of harmonic springs connected by freely hinged joints, they leave a distinct signature in the nonlinear buckling behavior of a cellular material built out of elastic beams with rigid joints. The salient feature of these localized buckling regions is that they are indistinguishable from their surroundings as far as material parameters or connectivity of their constituent elements are concerned. Furthermore, they are robust against a wide range of structural perturbations. We demonstrate the effectiveness of this topological design through analytical and numerical calculations as well as buckling experiments performed on two- and three-dimensional metamaterials built out of stacked kagome lattices. PMID:26056303
A parametric study on inelastic buckling in steel cylindrical shells with circular cutouts
NASA Astrophysics Data System (ADS)
Miladi, S.; Razzaghi, M. S.
2014-03-01
Thin-walled cylindrical shells are important components of many industrial complexes. Most of these components have circular cutouts in manholes and pipe-to-shell junctions. Performance of cylindrical shells due to the extreme loading conditions shows that buckling is the major failure mode in such components. This study aims to indicate the effect of circular cutouts on buckling capacity of cylindrical shells due to pure axial compression. To this end, cylindrical shells of different geometric specifications and various arrangements and sizes of cutouts were considered. Numerical nonlinear analyses were conducted using ANSYS software. Result of this study revealed that cutouts can play a noticeable role in creating stress concentration and affect destructively the stability of structures. It is shown that there is a noticeable difference between the effects on cutouts in buckling of thinner shells and thicker ones. Cutouts reduce the local buckling capacity of shell about 10-15 % in the cylindrical shells, with the diameter to thickness ratio of less than 1,000. Meanwhile in shells with diameter to thickness, more than 1,000 such cutouts reduce the shell capacity about 30-35 %.
Spectral theory and nonlinear analysis with applications to spatial ecology
NASA Astrophysics Data System (ADS)
Cano-Casanova, S.; López-Gómez, Juliá.; Mora-Corral, C.
On the positive solutions of the logistic weighted elliptic BVP with sublinear mixed boundary conditions --Logarithmic interpolation spaces -- Remarks on large solutions -- Well posedness and asymptotic behaviour of a closed loop thermosyphon -- Uniqueness of large solutions for a class of radially symmetric elliptic equations -- Cooperation and competition, strategic alliances, and the cambrian explosion -- Local smith form and equivalence for one-parameter families of F'redholm operators of index zero -- Multilump solutions of the non-linear Schrodinger equation - a scaling approach -- Some elliptic problems with nonlinear boundary conditions -- Dynamical systems method (DSM) and nonlinear problems -- Some recent results on periodic, jumping nonlinearity problems -- Some remarks about the cubic Schrodinger equation on the line -- Some remarks on the invariance of level sets in dynamical systems.
Repeated buckling of composite shear panels
NASA Technical Reports Server (NTRS)
Singer, Josef; Weller, Tanchum
1990-01-01
Failures in service of aerospace structures and research at the Technion Aircraft Structures Laboratory have revealed that repeatedly buckled stiffened shear panels might be susceptible to premature fatigue failures. Extensive experimental and analytical studies have been performed at Technion on repeated buckling, far in excess of initial buckling, for both metal and composite shear panels with focus on the influence of the surrounding structure. The core of the experimental investigation consisted of repeated buckling and postbuckling tests on Wagner beams in a three-point loading system under realistic test conditions. The effects of varying sizes of stiffeners, of the magnitude of initial buckling loads, of the panel aspect ratio and of the cyclic shearing force, V sub cyc, were studied. The cyclic to critical shear buckling ratios, (V sub cyc/V sub cr) were on the high side, as needed for efficient panel design, yet all within possible flight envelopes. The experiments were supplemented by analytical and numerical analyses. For the metal shear panels the test and numerical results were synthesized into prediction formulas, which relate the life of the metal shear panels to two cyclic load parameters. The composite shear panels studied were hybrid beams with graphite/epoxy webs bonded to aluminum alloy frames. The test results demonstrated that composite panels were less fatigue sensitive than comparable metal ones, and that repeated buckling, even when causing extensive damage, did not reduce the residual strength by more than 20 percent. All the composite panels sustained the specified fatigue life of 250,000 cycles. The effect of local unstiffened holes on the durability of repeatedly buckled shear panels was studied for one series of the metal panels. Tests on 2024 T3 aluminum panels with relatively small unstiffened holes in the center of the panels demonstrated premature fatigue failure, compared to panels without holes. Preliminary tests on two graphite
Buckled diamond-like carbon nanomechanical resonators.
Tomi, Matti; Isacsson, Andreas; Oksanen, Mika; Lyashenko, Dmitry; Kaikkonen, Jukka-Pekka; Tervakangas, Sanna; Kolehmainen, Jukka; Hakonen, Pertti J
2015-09-21
We have developed capacitively-transduced nanomechanical resonators using sp(2)-rich diamond-like carbon (DLC) thin films as conducting membranes. The electrically conducting DLC films were grown by physical vapor deposition at a temperature of 500 °C. Characterizing the resonant response, we find a larger than expected frequency tuning that we attribute to the membrane being buckled upwards, away from the bottom electrode. The possibility of using buckled resonators to increase frequency tuning can be of advantage in rf applications such as tunable GHz filters and voltage-controlled oscillators. PMID:26284626
21 CFR 886.3300 - Absorbable implant (scleral buckling method).
Code of Federal Regulations, 2010 CFR
2010-04-01
... 21 Food and Drugs 8 2010-04-01 2010-04-01 false Absorbable implant (scleral buckling method). 886... SERVICES (CONTINUED) MEDICAL DEVICES OPHTHALMIC DEVICES Prosthetic Devices § 886.3300 Absorbable implant (scleral buckling method). (a) Identification. An absorbable implant (scleral buckling method) is a...
Buckling of angle-ply laminated circular cylindrical shells
NASA Technical Reports Server (NTRS)
Hirano, Y.
1979-01-01
This note presents closed-form solutions for axisymmetrical and axially unsymmetrical buckling of angle-ply laminated circular cylindrical shells under axial compression. The axisymmetrical and axially unsymmetrical buckling stress are found to be different from each other, and the best lamination angles which give the highest buckling stress are obtained.
21 CFR 886.3300 - Absorbable implant (scleral buckling method).
Code of Federal Regulations, 2014 CFR
2014-04-01
... 21 Food and Drugs 8 2014-04-01 2014-04-01 false Absorbable implant (scleral buckling method). 886... SERVICES (CONTINUED) MEDICAL DEVICES OPHTHALMIC DEVICES Prosthetic Devices § 886.3300 Absorbable implant (scleral buckling method). (a) Identification. An absorbable implant (scleral buckling method) is a...
21 CFR 886.3300 - Absorbable implant (scleral buckling method).
Code of Federal Regulations, 2013 CFR
2013-04-01
... 21 Food and Drugs 8 2013-04-01 2013-04-01 false Absorbable implant (scleral buckling method). 886... SERVICES (CONTINUED) MEDICAL DEVICES OPHTHALMIC DEVICES Prosthetic Devices § 886.3300 Absorbable implant (scleral buckling method). (a) Identification. An absorbable implant (scleral buckling method) is a...
21 CFR 886.3300 - Absorbable implant (scleral buckling method).
Code of Federal Regulations, 2012 CFR
2012-04-01
... 21 Food and Drugs 8 2012-04-01 2012-04-01 false Absorbable implant (scleral buckling method). 886... SERVICES (CONTINUED) MEDICAL DEVICES OPHTHALMIC DEVICES Prosthetic Devices § 886.3300 Absorbable implant (scleral buckling method). (a) Identification. An absorbable implant (scleral buckling method) is a...
21 CFR 886.3300 - Absorbable implant (scleral buckling method).
Code of Federal Regulations, 2011 CFR
2011-04-01
... 21 Food and Drugs 8 2011-04-01 2011-04-01 false Absorbable implant (scleral buckling method). 886... SERVICES (CONTINUED) MEDICAL DEVICES OPHTHALMIC DEVICES Prosthetic Devices § 886.3300 Absorbable implant (scleral buckling method). (a) Identification. An absorbable implant (scleral buckling method) is a...
Handbook of Structural Stability Part I: Buckling of Flat Plates
NASA Technical Reports Server (NTRS)
Gerard, George; Becker, Herbert
1957-01-01
The various factors governing buckling of flat plates are critically reviewed and the results are summarized in a comprehensive series of charts and tables. Numerical values are presented for buckling coefficients of flat plates with various boundary conditions and applied loadings. The effects of plasticity are incorporated in non dimensional buckling charts utilizing the three-parameter description of stress-strain curves.
A nonlinear analysis of pulsatile flow in arteries.
NASA Technical Reports Server (NTRS)
Ling, S. C.; Atabek, H. B.
1972-01-01
An approximate numerical method for calculating flow profiles in arteries is developed. The theory takes into account the nonlinear terms of the Navier-Stokes equations as well as the nonlinear behaviour and large deformations of the arterial wall. Through the locally measured values of the pressure, pressure gradient, and pressure-radius function, the velocity distribution and wall shear at a given location along the artery can be determined. The computed results agree well with the corresponding experimental data.
Linear and nonlinear dynamic analysis of redundant load path bearingless rotor systems
NASA Technical Reports Server (NTRS)
Murthy, V. R.; Shultz, Louis A.
1994-01-01
The goal of this research is to develop the transfer matrix method to treat nonlinear autonomous boundary value problems with multiple branches. The application is the complete nonlinear aeroelastic analysis of multiple-branched rotor blades. Once the development is complete, it can be incorporated into the existing transfer matrix analyses. There are several difficulties to be overcome in reaching this objective. The conventional transfer matrix method is limited in that it is applicable only to linear branch chain-like structures, but consideration of multiple branch modeling is important for bearingless rotors. Also, hingeless and bearingless rotor blade dynamic characteristics (particularly their aeroelasticity problems) are inherently nonlinear. The nonlinear equations of motion and the multiple-branched boundary value problem are treated together using a direct transfer matrix method. First, the formulation is applied to a nonlinear single-branch blade to validate the nonlinear portion of the formulation. The nonlinear system of equations is iteratively solved using a form of Newton-Raphson iteration scheme developed for differential equations of continuous systems. The formulation is then applied to determine the nonlinear steady state trim and aeroelastic stability of a rotor blade in hover with two branches at the root. A comprehensive computer program is developed and is used to obtain numerical results for the (1) free vibration, (2) nonlinearly deformed steady state, (3) free vibration about the nonlinearly deformed steady state, and (4) aeroelastic stability tasks. The numerical results obtained by the present method agree with results from other methods.
Performance, robustness and sensitivity analysis of the nonlinear tuned vibration absorber
NASA Astrophysics Data System (ADS)
Detroux, T.; Habib, G.; Masset, L.; Kerschen, G.
2015-08-01
The nonlinear tuned vibration absorber (NLTVA) is a recently developed nonlinear absorber which generalizes Den Hartog's equal peak method to nonlinear systems. If the purposeful introduction of nonlinearity can enhance system performance, it can also give rise to adverse dynamical phenomena, including detached resonance curves and quasiperiodic regimes of motion. Through the combination of numerical continuation of periodic solutions, bifurcation detection and tracking, and global analysis, the present study identifies boundaries in the NLTVA parameter space delimiting safe, unsafe and unacceptable operations. The sensitivity of these boundaries to uncertainty in the NLTVA parameters is also investigated.
Analysis of Brace Stiffness Influence on Stability of the Truss
NASA Astrophysics Data System (ADS)
Krajewski, M.; Iwicki, P.
2015-02-01
The paper is devoted to the numerical and experimental research of stability of a truss with side elastic supports at the top chord. The structure is a model of a real roof truss scaled by factor 1/4. The linear buckling analysis and non-linear static analysis were carried out. The buckling length factor for the compressed top chord was calculated and the limit load for the imperfect truss shell model with respect to brace stiffness was obtained. The relation between brace normal force and loading of the truss is presented. The threshold stiffness of braces necessary to obtain the maximum buckling load was found. The truss load bearing capacity obtained from numerical analysis was compared with Eurocode 3 requirements.
Model analysis and nonlinear control of air compressors
NASA Astrophysics Data System (ADS)
Sari, Gholam-Reza
For decades, gas turbines have been important, widespread, and reliable devices in the field of power generation, petrochemical industry, and aeronautics. They employ centrifugal and axial compressors which suffer from aerodynamic instabilities, namely, surge and rotating stall. These performance limiting instabilities can cause component stress, lifespan reduction, noise, and vibration. Furthermore, in variable speed axial compressors (VSACs), speed variations affect the system stability and can lead to surge and rotating stall. This limits the rate of speed variations and results in important performance penalties. The present work firstly addresses the bifurcation analysis of VSACs' model to investigate the impact of speed dynamics on the stability of efficient operating points. Here, the rate of speed variations (acceleration rate) is defined as a new parameter of the model and a detailed numerical bifurcation analysis is provided. The results of time-domain simulations not only validate the results of bifurcation analysis, but also broaden our knowledge about the transient response of the model, which is a matter of importance as well. The analysis reveals that speed variations can lead to a fully developed rotating stall as well as the previously reported temporary stall developments. The results show that the developed instabilities depend to a great extent on the acceleration rate. The impact of other key issues such as throttle gain, viscosity factor, initial speed, final speed, and the contribution of stall modes are also explored. From the control point of view, despite reported achievements, robust control design for compression systems remains a challenging problem. In this work, at first, two nonlinear approaches are proposed to tackle the stability problem of constant-speed axial compressors (CSACs). The first approach is a robust passivity-based control and the second one is a second order sliding mode control. The approaches tackle the challenging
ERIC Educational Resources Information Center
Linting, Marielle; Meulman, Jacqueline J.; Groenen, Patrick J. F.; van der Kooij, Anita J.
2007-01-01
Principal components analysis (PCA) is used to explore the structure of data sets containing linearly related numeric variables. Alternatively, nonlinear PCA can handle possibly nonlinearly related numeric as well as nonnumeric variables. For linear PCA, the stability of its solution can be established under the assumption of multivariate…
The effect of ring distortions on buckling of blunt conical shells. [Viking mission aeroshell
NASA Technical Reports Server (NTRS)
Heard, W. L., Jr.; Anderson, M. S.; Stephens, W. B.
1975-01-01
A rigorous analytical study of cones stiffened by many thin-gage, open-section rings is presented. The results are compared with data previously obtained from uniform pressure tests of the Viking mission flight aeroshell and of the Viking structural prototype aeroshells. A conventional analysis, in which the rings are modeled as discrete rigid cross sections, is shown to lead to large, unconservative strength predictions. A more sophisticated technique of modeling the rings as shell branches leads to much more realistic strength predictions and more accurately predicts the failure modes. It is also shown that if a small initial imperfection proportional to the shape of the buckling mode is assumed, the critical buckling modes from analysis and test are in agreement. However, the reduction in buckling strength from the perfect-shell predictions is small.
Nonlinear analysis and dynamic structure in the energy market
NASA Astrophysics Data System (ADS)
Aghababa, Hajar
This research assesses the dynamic structure of the energy sector of the aggregate economy in the context of nonlinear mechanisms. Earlier studies have focused mainly on the price of the energy products when detecting nonlinearities in time series data of the energy market, and there is little mention of the production side of the market. Moreover, there is a lack of exploration about the implication of high dimensionality and time aggregation when analyzing the market's fundamentals. This research will address these gaps by including the quantity side of the market in addition to the price and by systematically incorporating various frequencies for sample sizes in three essays. The goal of this research is to provide an inclusive and exhaustive examination of the dynamics in the energy markets. The first essay begins with the application of statistical techniques, and it incorporates the most well-known univariate tests for nonlinearity with distinct power functions over alternatives and tests different null hypotheses. It utilizes the daily spot price observations on five major products in the energy market. The results suggest that the time series daily spot prices of the energy products are highly nonlinear in their nature. They demonstrate apparent evidence of general nonlinear serial dependence in each individual series, as well as nonlinearity in the first, second, and third moments of the series. The second essay examines the underlying mechanism of crude oil production and identifies the nonlinear structure of the production market by utilizing various monthly time series observations of crude oil production: the U.S. field, Organization of the Petroleum Exporting Countries (OPEC), non-OPEC, and the world production of crude oil. The finding implies that the time series data of the U.S. field, OPEC, and the world production of crude oil exhibit deep nonlinearity in their structure and are generated by nonlinear mechanisms. However, the dynamics of the non
Thermal viscoplastic buckling during the growth of silicon ribbon
NASA Technical Reports Server (NTRS)
Tsai, C. T.; Dillon, O. W., Jr.
1987-01-01
This paper is an analysis of the conditions to be satisfied in order to avoid buckling during the growth of a silicon ribbon that is being slowly pulled from the melt. A viscoplastic constitutive equation with a dislocation density effect is used to model the material behavior. The critical thicknesses and the corresponding deflection shapes are calculated by the finite element method for the cantilever boundary conditions. The value of the parameter which controls the speed of the lateral deflection is computed by using Galerkin's method. It is demonstrated that, due to the effect of viscoplasticity, some deflection shapes increase in magnitude with time and other shapes damp out.
NASA Technical Reports Server (NTRS)
Nemeth, Michael P.
1997-01-01
A parametric study of the buckling behavior of infinitely long symmetrically laminated anisotropic plates that are subjected to linearly varying edge loads, uniform shear loads, or combinations of these loads is presented. The study focuses on the effects of the shape of linearly varying edge load distribution, plate orthotropy, and plate flexural anisotropy on plate buckling behavior. In addition, the study exmines the interaction of linearly varying edge loads and uniform shear loads with plate flexural anisotropy and orthotropy. Results obtained by using a special purpose nondimensional analysis that is well suited for parametric studies of clamped and simply supported plates are presented for [+/- theta](sub s), thin graphite-epoxy laminates that are representative of spacecraft structural components. Also, numerous generic buckling-design charts are presented for a wide range of nondimensional parameters that are applicable to a broad class of laminate constructions. These charts show explicitly the effects of flexural orthotropy and flexural anisotropy on plate buckling behavior for linearly varying edge loads, uniform shear loads, or combinations of these loads. The most important finding of the present study is that specially orthotropic and flexurally anisotropic plates that are subjected to an axial edge load distribution that is tension dominated can support shear loads that are larger in magnitude than the shear buckling load.
PLANS; a finite element program for nonlinear analysis of structures. Volume 2: User's manual
NASA Technical Reports Server (NTRS)
Pifko, A.; Armen, H., Jr.; Levy, A.; Levine, H.
1977-01-01
The PLANS system, rather than being one comprehensive computer program, is a collection of finite element programs used for the nonlinear analysis of structures. This collection of programs evolved and is based on the organizational philosophy in which classes of analyses are treated individually based on the physical problem class to be analyzed. Each of the independent finite element computer programs of PLANS, with an associated element library, can be individually loaded and used to solve the problem class of interest. A number of programs have been developed for material nonlinear behavior alone and for combined geometric and material nonlinear behavior. The usage, capabilities, and element libraries of the current programs include: (1) plastic analysis of built-up structures where bending and membrane effects are significant, (2) three dimensional elastic-plastic analysis, (3) plastic analysis of bodies of revolution, and (4) material and geometric nonlinear analysis of built-up structures.
MACKEY TC; JOHNSON KI; DEIBLER JE; PILLI SP; RINKER MW; KARRI NK
2007-02-14
This report documents a detailed buckling evaluation of the primary tanks in the Hanford double-shell waste tanks (DSTs), which is part of a comprehensive structural review for the Double-Shell Tank Integrity Project. This work also provides information on tank integrity that specifically responds to concerns raised by the Office of Environment, Safety, and Health (ES&H) Oversight (EH-22) during a review of work performed on the double-shell tank farms and the operation of the aging waste facility (AWF) primary tank ventilation system. The current buckling review focuses on the following tasks: (1) Evaluate the potential for progressive I-bolt failure and the appropriateness of the safety factors that were used for evaluating local and global buckling. The analysis will specifically answer the following questions: (a) Can the EH-22 scenario develop if the vacuum is limited to -6.6-inch water gage (w.g.) by a relief valve? (b) What is the appropriate factor of safety required to protect against buckling if the EH-22 scenario can develop? (c) What is the appropriate factor of safety required to protect against buckling if the EH-22 scenario cannot develop? (2) Develop influence functions to estimate the axial stresses in the primary tanks for all reasonable combinations of tank loads, based on detailed finite element analysis. The analysis must account for the variation in design details and operating conditions between the different DSTs. The analysis must also address the imperfection sensitivity of the primary tank to buckling. (3) Perform a detailed buckling analysis to determine the maximum allowable differential pressure for each of the DST primary tanks at the current specified limits on waste temperature, height, and specific gravity. Based on the I-bolt loads analysis and the small deformations that are predicted at the unfactored limits on vacuum and axial loads, it is very unlikely that the EH-22 scenario (i.e., progressive I-bolt failure leading to global
Quantitative nonlinearity analysis of model-scale jet noise
NASA Astrophysics Data System (ADS)
Miller, Kyle G.; Reichman, Brent O.; Gee, Kent L.; Neilsen, Tracianne B.; Atchley, Anthony A.
2015-10-01
The effects of nonlinearity on the power spectrum of jet noise can be directly compared with those of atmospheric absorption and geometric spreading through an ensemble-averaged, frequency-domain version of the generalized Burgers equation (GBE) [B. O. Reichman et al., J. Acoust. Soc. Am. 136, 2102 (2014)]. The rate of change in the sound pressure level due to the nonlinearity, in decibels per jet nozzle diameter, is calculated using a dimensionless form of the quadspectrum of the pressure and the squared-pressure waveforms. In this paper, this formulation is applied to atmospheric propagation of a spherically spreading, initial sinusoid and unheated model-scale supersonic (Mach 2.0) jet data. The rate of change in level due to nonlinearity is calculated and compared with estimated effects due to absorption and geometric spreading. Comparing these losses with the change predicted due to nonlinearity shows that absorption and nonlinearity are of similar magnitude in the geometric far field, where shocks are present, which causes the high-frequency spectral shape to remain unchanged.
NASA Technical Reports Server (NTRS)
Stroud, W. J.; Greene, W. H.; Anderson, M. S.
1984-01-01
Buckling analyses used in PASCO are summarized with emphasis placed on the shear buckling analyses. The PASCO buckling analyses include the basic VIPASA analysis, which is essentially exact for longitudinal and transverse loads, and a smeared stiffener solution, which treats a stiffened panel as an orthotropic plate. Buckling results are then presented for seven stiffened panels loaded by combinations of longitudinal compression and shear. The buckling results were obtained with the PASCO, EAL, and STAGS computer programs. The EAL and STAGS solutions were obtained with a fine finite element mesh and are very accurate. These finite element solutions together with the PASCO results for pure longitudinal compression provide benchmark calculations to evaluate other analysis procedures.
Optimum single modal and bimodal buckling design of symmetric laminates
NASA Technical Reports Server (NTRS)
Qian, B.; Reiss, R.; Aung, W.
1989-01-01
Variational calculus is used to determine the design that maximizes the resistance of classical symmetric laminates against buckling. The orientations of the constituent orthotropic laminae with respect to the principal axes of the laminate are the design variables. It is shown that the optimal design may not be a point of analyticity of the buckling load. Local analytic extrema are obtained from the design derivatives of the buckling load. Nonanalytic extrema occur whenever the buckling load is a repeated eigenvalue. A novel approach, using a directional design derivative, is employed to determine nonanalytic extrema. Specific examples are presented for biaxial buckling for several different boundary conditions.
Buckling of circular cylindrical shells under dynamically applied axial loads
NASA Technical Reports Server (NTRS)
Tulk, J. D.
1972-01-01
A theoretical and experimental study was made of the buckling characteristics of perfect and imperfect circular cylindrical shells subjected to dynamic axial loading. Experimental data included dynamic buckling loads (124 data points), high speed photographs of buckling mode shapes and observations of the dynamic stability of shells subjected to rapidly applied sub-critical loads. A mathematical model was developed to describe the dynamic behavior of perfect and imperfect shells. This model was based on the Donnell-Von Karman compatibility and equilibrium equations and had a wall deflection function incorporating five separate modes of deflection. Close agreement between theory and experiment was found for both dynamic buckling strength and buckling mode shapes.
PASCO: Structural panel analysis and sizing code, capability and analytical foundations
NASA Technical Reports Server (NTRS)
Stroud, W. J.; Anderson, M. S.
1980-01-01
A computer code denoted PASCO which can be used for analyzing and sizing uniaxially-stiffened composite panels is described. Buckling and vibration analyses are carried out with a linked-plate analysis computer code denoted VIPASA, which is incorporated in PASCO. Sizing is based on nonlinear mathematical programming techniques and employs a computer code denoted CONMIN, also incorporated in PASCO. Design requirements considered are initial buckling, material strength, stiffness, and vibration frequency. The capability of the PASCO computer code and the approach used in the structural analysis and sizing are described.
Buckling tests of light-metal tubes
NASA Technical Reports Server (NTRS)
Schroeder, August
1929-01-01
I will attempt to determine mathematically the buckling-strength curves of various centrally loaded light-metal tubes which exhibit conspicuous differences of behavior under compressive loads. For this purpose I will employ Von Karman's method, after adapting it to special conditions.
Buckling of laminated composite cylinders - A review
NASA Technical Reports Server (NTRS)
Tennyson, R. C.
1975-01-01
A brief review of the available static buckling theory for both geometrically 'perfect' and 'imperfect' anisotropic composite circular cylinders is presented for various loading configurations. For comparison purposes, relevant experimental data are discussed, including recent combined loading test results and recommendations are made concerning the design of composite cylinders.
NASA Technical Reports Server (NTRS)
Noor, A. K.
1983-01-01
Advances in continuum modeling, progress in reduction methods, and analysis and modeling needs for large space structures are covered with specific attention given to repetitive lattice trusses. As far as continuum modeling is concerned, an effective and verified analysis capability exists for linear thermoelastic stress, birfurcation buckling, and free vibration problems of repetitive lattices. However, application of continuum modeling to nonlinear analysis needs more development. Reduction methods are very effective for bifurcation buckling and static (steady-state) nonlinear analysis. However, more work is needed to realize their full potential for nonlinear dynamic and time-dependent problems. As far as analysis and modeling needs are concerned, three areas are identified: loads determination, modeling and nonclassical behavior characteristics, and computational algorithms. The impact of new advances in computer hardware, software, integrated analysis, CAD/CAM stems, and materials technology is also discussed.
Computerized symbolic manipulation in nonlinear finite element analysis
NASA Technical Reports Server (NTRS)
Noor, A. K.; Andersen, C. M.
1981-01-01
The potential of using computerized symbolic manipulation in the development of nonlinear finite elements is discussed. Three tasks which can be efficiently performed using computerized symbolic manipulation are identified: (1) generation of algebraic expressions for the stiffness coefficients of nonlinear finite elements, (2) generation of FORTRAN source code for numerical evaluation of stiffness coefficients, and (3) checking the correctness of the FORTRAN statements for the arrays of coefficients. The symbolic and algebraic manipulation system MACSYMA is used in the present study. Two sample MACSYMA programs are presented for the development of the nonlinear stiffness coefficients of two-dimensional, shear-flexible, doubly-curved deep shell elements. The first program is for displacement models and the second program is for mixed models with discontinuous stress-resultant fields at interelement boundaries.
Surface subsidence prediction by nonlinear finite-element analysis
Najjar, Y. . Dept. of Civil Engineering); Zaman, M. . School of Civil Engineering and Environmental Science)
1993-11-01
An improved two-dimensional plane-strain numerical procedure based on the incremental-iterative nonlinear finite-element is developed to predict ground subsidence caused by underground mining. The procedure emphasizes the use of the following features: (1) an appropriate constitutive model that can accurately describe the nonlinear behavior of geological strata; and (2) an accurate algorithm for simulation of excavation sequences consistent with the actual underground mining process. The computer code is used to analyze a collapse that occurred in the Blue Goose Lease [number sign]1 Mine in northeastern Oklahoma. A parametric study is conducted to investigate the effects of some selected factors on the shape and extent of subsidence profiles. Analyses of the numerical results indicate that the nonlinear finite-element technique can be employed to meaningfully predict and characterize the potential for ground subsidence due to underground mining.
Perturbation analysis of a clearance-type nonlinear system
NASA Astrophysics Data System (ADS)
Zhu, Farong; Parker, Robert G.
2006-05-01
This study applies the method of multiple scales to obtain periodic solutions of a two-pulley belt system with clearance-type nonlinearity. The purpose is to explain the published numerical results and clarify how design parameters affect the system dynamics. The validity of the perturbation method for such strong nonlinearity is evaluated. The closed-form frequency-response relation is determined at the first order, and an implicit expression is obtained for the second-order approximation. The preload applied to the accessory determines the softening level of the nonlinearity. Larger preload leads to less disengagement and less softening. For a considerable range of practical parameter values, the analytical solutions well approximate the numerical results from harmonic balance.
Nonlinear shell analysis of the Space Shuttle Solid Rocket Boosters
NASA Technical Reports Server (NTRS)
Knight, N. F., Jr.; Gillian, R. E.; Nemeth, M. P.
1990-01-01
A variety of structural analyses have been performed on the Solid Rocket Boosters (SRB's) to provide information that would contribute to the understanding of the failure which destroyed the Space Shuttle Challenger. This paper describes nonlinear shell analyses that were performed to characterize the behavior of an overall SRB structure and a segment of the SRB in the vicinity of the External Tank Attachment (ETA) ring. Shell finite element models were used that would accurately reflect the global load transfer in an SRB in a manner such that nonlinear shell collapse and ovalization could be assessed. The purpose of these analyses was to calculate the overall deflection and stress distributions for these SRB models when subjected to mechanical loads corresponding to critical times during the launch sequence. Static analyses of these SRB models were performed using a 'snapshot picture' of the loads. Analytical results obtained using these models show no evidence of nonlinear shell collapse for the pre-liftoff loading cases considered.
Non-linear dynamic analysis of anisotropic cylindrical shells
Lakis, A.A.; Selmane, A.; Toledano, A.
1996-12-01
A theory to predict the influence of geometric non-linearities on the natural frequencies of an empty anisotropic cylindrical shell is presented in this paper. It is a hybrid of finite element and classical thin shell theories. Sanders-Koiter non-linear and strain-displacement relations are used. Displacement functions are evaluated using linearized equations of motion. Modal coefficients are then obtained for these displacement functions. Expressions for the mass, linear and non-linear stiffness matrices are derived through the finite element method. The uncoupled equations are solved with the help of elliptic functions. The period and frequency variations are first determined as a function of shell amplitudes and then compared with the results in the literature.
Limit cycle analysis of active disturbance rejection control system with two nonlinearities.
Wu, Dan; Chen, Ken
2014-07-01
Introduction of nonlinearities to active disturbance rejection control algorithm might have high control efficiency in some situations, but makes the systems with complex nonlinearity. Limit cycle is a typical phenomenon that can be observed in the nonlinear systems, usually causing failure or danger of the systems. This paper approaches the problem of the existence of limit cycles of a second-order fast tool servo system using active disturbance rejection control algorithm with two fal nonlinearities. A frequency domain approach is presented by using describing function technique and transfer function representation to characterize the nonlinear system. The derivations of the describing functions for fal nonlinearities and treatment of two nonlinearities connected in series are given to facilitate the limit cycles analysis. The effects of the parameters of both the nonlinearity and the controller on the limit cycles are presented, indicating that the limit cycles caused by the nonlinearities can be easily suppressed if the parameters are chosen carefully. Simulations in the time domain are performed to assess the prediction accuracy based on the describing function. PMID:24795034
Nonlinear analysis of the dielectric loaded rectangular Cerenkov maser
NASA Astrophysics Data System (ADS)
Zhao, Ding; Ding, Yaogen
2012-02-01
To deeply investigate the nonlinear interaction between the sheet beam and the slow wave mode in the dielectric loaded rectangular Cerenkov maser, a third order differential equation of the field profile function is rigorously derived. By combining with the relativistic equation of motion and using the traveling-wave boundary condition, the nonlinear phenomena, which involve with the growth rate, the electron phase bunching, the saturated power and length, etc., can be predicted through numerical calculations. An illustrative example has been given to demonstrate the validation of this method. The results show that a beam with axial momentum spread will lower the saturated power, increase the saturated length, and decrease the working bandwidth.
Handbook of structural stability part III : buckling of curved plates and shells
NASA Technical Reports Server (NTRS)
Gerard, George; Becker, Herbert
1957-01-01
Available theories and test data on buckling of curved plates and shells are reviewed. For torsion and external-pressure loadings, the test data are correlated in terms of linear buckling theories for both the elastic and inelastic ranges. The cases which exhibit a marked disagreement between linear theory and test data include those of curved plates and cylinders under axial compression, cylinders under bending, and spherical plates under external pressure. These cases have been analyzed by a unified semiempirical approach for both the elastic and inelastic ranges which is satisfactory for analysis and design purposes. The effects of internal pressure on buckling of elements under uniaxial loads are discussed and data on various combined loadings are presented in interaction form. (author)
The effect of angle of attach on the buckling of Mars entry aeroshells
NASA Technical Reports Server (NTRS)
Cohen, G. A.
1973-01-01
The buckling modes of four optimized Mars entry aeroshell configurations at angle-of-attack loadings have been calculated. The analysis is based on experimental pressure distributions and was performed with the aid of a buckling digital computer program which treats general asymmetric linearized prebuckling states of branched shells of revolution. Only zero and first harmonic pressure components are treated, these being constructed from windward and leeward meridian pressure data at a mach number of 4.63. The results showed a rather small effect of the unsymmetrical pressure component on buckling for angles of attack up to 15 deg. Comparison of the results for the 120 deg cones to previous results indicates that the common procedure of basing the design on a symmetrized pressure distribution of the windward meridian is a conservative approach.
NASA Astrophysics Data System (ADS)
Javidinejad, Amir
2012-12-01
In this paper the buckling behaviour of an I-beam under combined axial and horizontal side loading is examined. It is to shown that the actual application location of the axial loading governs the buck- ling behaviour of the long I-beam. Theoretical formulation is developed to determine the critical buckling load for such combined loading configura- tion from the elastic static theory. Both, the beam deflection theoretical model and the critical load capacity are derived for this combined loading condition. The Finite Element Analysis (FEA) is utilized to apply the axial load on the beam at various configuration locations and it is shown that this application location determines the buckling behaviour and the critical load of the buckling of the I-beam. Numerical example is given.
Hyperspectral image compression and target detection using nonlinear principal component analysis
NASA Astrophysics Data System (ADS)
Du, Qian; Wei, Wei; Ma, Ben; Younan, Nicolas H.
2013-09-01
The widely used principal component analysis (PCA) is implemented in nonlinear by an auto-associative neural network. Compared to other nonlinear versions, such as kernel PCA, such a nonlinear PCA has explicit encoding and decoding processes, and the data can be transformed back to the original space. Its data compression performance is similar to that of PCA, but data analysis performance such as target detection is much better. To expedite its training process, graphics computing unit (GPU)-based parallel computing is applied.
Thermal and Mechanical Buckling and Postbuckling Responses of Selected Curved Composite Panels
NASA Technical Reports Server (NTRS)
Breivik, Nicole L.; Hyer, Michael W.; Starnes, James H., Jr.
1998-01-01
The results of an experimental and numerical study of the buckling and postbuckling responses of selected unstiffened curved composite panels subjected to mechanical end shortening and a uniform temperature increase are presented. The uniform temperature increase induces thermal stresses in the panel when the axial displacement is constrained. An apparatus for testing curved panels at elevated temperature is described, numerical results generated by using a geometrically nonlinear finite element analysis code are presented. Several analytical modeling refinements that provide more accurate representation of the actual experimental conditions, and the relative contribution of each refinement, are discussed. Experimental results and numerical predictions are presented and compared for three loading conditions including mechanical end shortening alone, heating the panels to 250 F followed by mechanical end shortening, and heating the panels to 400 F. Changes in the coefficients of thermal expansion were observed as temperature was increased above 330 F. The effects of these changes on the experimental results are discussed for temperatures up to 400 F.
Local Influence Analysis of Nonlinear Structural Equation Models
ERIC Educational Resources Information Center
Lee, Sik-Yum; Tang, Nian-Sheng
2004-01-01
By regarding the latent random vectors as hypothetical missing data and based on the conditional expectation of the complete-data log-likelihood function in the EM algorithm, we investigate assessment of local influence of various perturbation schemes in a nonlinear structural equation model. The basic building blocks of local influence analysis…
Element-by-element Solution Procedures for Nonlinear Structural Analysis
NASA Technical Reports Server (NTRS)
Hughes, T. J. R.; Winget, J. M.; Levit, I.
1984-01-01
Element-by-element approximate factorization procedures are proposed for solving the large finite element equation systems which arise in nonlinear structural mechanics. Architectural and data base advantages of the present algorithms over traditional direct elimination schemes are noted. Results of calculations suggest considerable potential for the methods described.
Nonlinear neural mapping analysis of the adverse effects of drugs.
Domine, D; Guillon, C; Devillers, J; Lacroix, R; Lacroix, J; Doré, J C
1998-01-01
Numerous drugs have been identified as presenting adverse effects towards the driving of vehicles. A large set of these drugs was compiled and classified into ten categories. Nonlinear neural mapping (N2M) was used to derive a typology of these molecules and also to link their adverse effects to therapeutic categories and structural information. PMID:9517012
A nonlinear model for analysis of slug-test data
McElwee, C.D.; Zenner, M.A.
1998-01-01
While doing slug tests in high-permeability aquifers, we have consistently seen deviations from the expected response of linear theoretical models. Normalized curves do not coincide for various initial heads, as would be predicted by linear theories, and are shifted to larger times for higher initial heads. We have developed a general nonlinear model based on the Navier-Stokes equation, nonlinear frictional loss, non-Darcian flow, acceleration effects, radius changes in the well bore, and a Hvorslev model for the aquifer, which explains these data features. The model produces a very good fit for both oscillatory and nonoscillatory field data, using a single set of physical parameters to predict the field data for various initial displacements at a given well. This is in contrast to linear models which have a systematic lack of fit and indicate that hydraulic conductivity varies with the initial displacement. We recommend multiple slug tests with a considerable variation in initial head displacement to evaluate the possible presence of nonlinear effects. Our conclusion is that the nonlinear model presented here is an excellent tool to analyze slug tests, covering the range from the underdamped region to the overdamped region.
A Cumulant-based Analysis of Nonlinear Magnetospheric Dynamics
Jay R. Johnson; Simon Wing
2004-01-28
Understanding magnetospheric dynamics and predicting future behavior of the magnetosphere is of great practical interest because it could potentially help to avert catastrophic loss of power and communications. In order to build good predictive models it is necessary to understand the most critical nonlinear dependencies among observed plasma and electromagnetic field variables in the coupled solar wind/magnetosphere system. In this work, we apply a cumulant-based information dynamical measure to characterize the nonlinear dynamics underlying the time evolution of the Dst and Kp geomagnetic indices, given solar wind magnetic field and plasma input. We examine the underlying dynamics of the system, the temporal statistical dependencies, the degree of nonlinearity, and the rate of information loss. We find a significant solar cycle dependence in the underlying dynamics of the system with greater nonlinearity for solar minimum. The cumulant-based approach also has the advantage that it is reliable even in the case of small data sets and therefore it is possible to avoid the assumption of stationarity, which allows for a measure of predictability even when the underlying system dynamics may change character. Evaluations of several leading Kp prediction models indicate that their performances are sub-optimal during active times. We discuss possible improvements of these models based on this nonparametric approach.
Non-linear dynamic analysis of geared systems, part 2
NASA Technical Reports Server (NTRS)
Singh, Rajendra; Houser, Donald R.; Kahraman, Ahmet
1990-01-01
A good understanding of the steady state dynamic behavior of a geared system is required in order to design reliable and quiet transmissions. This study focuses on a system containing a spur gear pair with backlash and periodically time-varying mesh stiffness, and rolling element bearings with clearance type non-linearities. A dynamic finite element model of the linear time-invariant (LTI) system is developed. Effects of several system parameters, such as torsional and transverse flexibilities of the shafts and prime mover/load inertias, on free and force vibration characteristics are investigated. Several reduced order LTI models are developed and validated by comparing their eigen solution with the finite element model results. Several key system parameters such as mean load and damping ratio are identified and their effects on the non-linear frequency response are evaluated quantitatively. Other fundamental issues such as the dynamic coupling between non-linear modes, dynamic interactions between component non-linearities and time-varying mesh stiffness, and the existence of subharmonic and chaotic solutions including routes to chaos have also been examined in depth.
NASA Astrophysics Data System (ADS)
Qiu, Zhiping; Ma, Lihong; Wang, Xiaojun
2009-01-01
Effects of uncertainties on the dynamic response of the nonlinear vibration systems with general form are investigated. Based on interval mathematics, modeling the uncertain parameters as interval numbers, a non-probabilistic interval analysis method, which estimates the range of the nonlinear dynamic response with the help of Taylor series expansion, is presented, where the partial derivatives of the dynamic response with respect to uncertain parameters are considered to be interval numbers. The sensitivity matrices of dynamic response with the uncertain parameters are derived. For the presented method, only the bounds on uncertain parameters are needed, instead of probabilistic density distribution or statistical quantities. Numerical examples are used to illustrate the validity and feasibility of the presented method.
Recent Applications of Higher-Order Spectral Analysis to Nonlinear Aeroelastic Phenomena
NASA Technical Reports Server (NTRS)
Silva, Walter A.; Hajj, Muhammad R.; Dunn, Shane; Strganac, Thomas W.; Powers, Edward J.; Stearman, Ronald
2005-01-01
Recent applications of higher-order spectral (HOS) methods to nonlinear aeroelastic phenomena are presented. Applications include the analysis of data from a simulated nonlinear pitch and plunge apparatus and from F-18 flight flutter tests. A MATLAB model of the Texas A&MUniversity s Nonlinear Aeroelastic Testbed Apparatus (NATA) is used to generate aeroelastic transients at various conditions including limit cycle oscillations (LCO). The Gaussian or non-Gaussian nature of the transients is investigated, related to HOS methods, and used to identify levels of increasing nonlinear aeroelastic response. Royal Australian Air Force (RAAF) F/A-18 flight flutter test data is presented and analyzed. The data includes high-quality measurements of forced responses and LCO phenomena. Standard power spectral density (PSD) techniques and HOS methods are applied to the data and presented. The goal of this research is to develop methods that can identify the onset of nonlinear aeroelastic phenomena, such as LCO, during flutter testing.
NASA Technical Reports Server (NTRS)
Davis, D. D., Jr.; Krishnamurthy, T.; Stroud, W. J.; Mccleary, S. L.
1991-01-01
State-of-the-art nonlinear finite element analysis techniques are evaluated by applying them to a realistic aircraft structural component. A wing panel from the V-22 tiltrotor aircraft is chosen because it is a typical modern aircraft structural component for which there is experimental data for comparison of results. From blueprints and drawings, a very detailed finite element model containing 2284 9-node Assumed Natural-Coordinate Strain elements was generated. A novel solution strategy which accounts for geometric nonlinearity through the use of corotating element reference frames and nonlinear strain-displacement relations is used to analyze this detailed model. Results from linear analyses using the same finite element model are presented in order to illustrate the advantages and costs of the nonlinear analysis as compared with the more traditional linear analysis.
Nonlinear dynamic mechanism of vocal tremor from voice analysis and model simulations
NASA Astrophysics Data System (ADS)
Zhang, Yu; Jiang, Jack J.
2008-09-01
Nonlinear dynamic analysis and model simulations are used to study the nonlinear dynamic characteristics of vocal folds with vocal tremor, which can typically be characterized by low-frequency modulation and aperiodicity. Tremor voices from patients with disorders such as paresis, Parkinson's disease, hyperfunction, and adductor spasmodic dysphonia show low-dimensional characteristics, differing from random noise. Correlation dimension analysis statistically distinguishes tremor voices from normal voices. Furthermore, a nonlinear tremor model is proposed to study the vibrations of the vocal folds with vocal tremor. Fractal dimensions and positive Lyapunov exponents demonstrate the evidence of chaos in the tremor model, where amplitude and frequency play important roles in governing vocal fold dynamics. Nonlinear dynamic voice analysis and vocal fold modeling may provide a useful set of tools for understanding the dynamic mechanism of vocal tremor in patients with laryngeal diseases.
Stacking-sequence optimization for buckling of laminated plates by integer programming
NASA Technical Reports Server (NTRS)
Haftka, Raphael T.; Walsh, Joanne L.
1991-01-01
Integer-programming formulations for the design of symmetric and balanced laminated plates under biaxial compression are presented. Both maximization of buckling load for a given total thickness and the minimization of total thickness subject to a buckling constraint are formulated. The design variables that define the stacking sequence of the laminate are zero-one integers. It is shown that the formulation results in a linear optimization problem that can be solved on readily available software. This is in contrast to the continuous case, where the design variables are the thicknesses of layers with specified ply orientations, and the optimization problem is nonlinear. Constraints on the stacking sequence such as a limit on the number of contiguous plies of the same orientation and limits on in-plane stiffnesses are easily accommodated. Examples are presented for graphite-epoxy plates under uniaxial and biaxial compression using a commercial software package based on the branch-and-bound algorithm.
Some applications of NASTRAN to the buckling of thin cylindrical shells with cutouts
NASA Technical Reports Server (NTRS)
Williams, J. G.; Starnes, J. H., Jr.
1972-01-01
The buckling of isotropic and waffle-stiffened circular cylinders with and without cutouts was studied using NASTRAN's Rigid Format 5 for the case of axial compressive loading. The results obtained for the cylinders without cutouts are compared with available reference solutions. The results for the isotropic cylinders containing a single circular cutout with selected radii are compared with available experimental data. For the waffle-stiffened cyclinder, the effect of two diametrically opposed rectangular cutouts was studied. A DMAP alter sequence was used to permit the necessary application of different prebuckling and buckling boundary conditions. Advantage was taken of available symmetry planes to formulate equivalent NASTRAN model segments which reduced the associated computational cost of performing the analyses. Limitations of the applicability of NASTRAN for the solution of problems with nonlinear characteristics are discussed.
NASA Astrophysics Data System (ADS)
Riccio, A.; Di Caprio, F.; Camerlingo, F.; Scaramuzzino, F.; Gambino, B.
2013-02-01
A numerical/experimental study on the monitoring of the skin buckling phenomenon in stiffened composite panels by embedding optical fibres is presented in this paper. A numerical procedure has been introduced able to provide the most efficient embedded optical fibre path (with minimum length) fulfilling the grating sensors locations and directions requirements whilst satisfying specific embedding/integrity constraints for the optical fibre. The developed numerical procedure has been applied to a stiffened composite panel under compression load. The best location and direction of the grating sensors and the optimal optical fibre path for the monitoring of the skin buckling phenomenon have been found by performing respectively non-linear FEM analyses and optimization analyses. The procedure has been validated by means of an experimental testing activity on a stiffened panel instrumented with embedded optical fibres and back-to-back strain gauges which have been positioned according to the numerically estimated grating sensors locations and directions.
NASA Astrophysics Data System (ADS)
Shojaeian, Milad; Beni, Yaghoub Tadi; Ataei, Hossein
2016-01-01
Electromechanical buckling (EMB) of beam-type nanoelectromechanical systems (NEMSs) is investigated based on modified strain gradient theory. The system is modeled as a clamped-guided nanobeam which is under compressive or tensile axial loads as well as the effect of nonlinear electrostatic and van der Waals symmetric transverse forces. In addition, the beam is considered to be made of axially and transverse functionally graded materials. Here, FGM is Poly-SiGe, of which the general properties change gradually from silicon to germanium based on a simple power-law method. Considering the Euler-Bernoulli beam theory and using the principle of minimum potential energy, the governing equations and corresponding boundary conditions are established. After validation of results, the effects of power law index, variation of size effect parameters, length-thickness ratio and the distance between the two fixed and movable electrodes on the buckling response of the system are discussed.
Enhanced buckled-beam piezoelectric energy harvesting using midpoint magnetic force
NASA Astrophysics Data System (ADS)
Zhu, Yang; Zu, Jean W.
2013-07-01
Aiming to improve the functionality of a buckled-beam piezoelectric energy harvester, a midpoint magnetic force is utilized to enable snap-through motions under low-frequency (<30 Hz) small-amplitude (0.2 g-0.8 g) excitations. The noncontact midpoint magnetic force is introduced through a local magnetic levitation system created by neodymium magnets and is capable of triggering the second buckling mode that helps the beam easily snap through between equilibriums when subjected to excitations. Significant enhancements, along with distinct nonlinear phenomena, are observed at low frequencies in terms of large-amplitude voltage output and extended frequency bandwidth. Frequency tuning is also achievable by adjusting the separation distance between magnets.
Multiscale analysis of nonlinear systems using computational homology
Konstantin Mischaikow; Michael Schatz; William Kalies; Thomas Wanner
2010-05-24
This is a collaborative project between the principal investigators. However, as is to be expected, different PIs have greater focus on different aspects of the project. This report lists these major directions of research which were pursued during the funding period: (1) Computational Homology in Fluids - For the computational homology effort in thermal convection, the focus of the work during the first two years of the funding period included: (1) A clear demonstration that homology can sensitively detect the presence or absence of an important flow symmetry, (2) An investigation of homology as a probe for flow dynamics, and (3) The construction of a new convection apparatus for probing the effects of large-aspect-ratio. (2) Computational Homology in Cardiac Dynamics - We have initiated an effort to test the use of homology in characterizing data from both laboratory experiments and numerical simulations of arrhythmia in the heart. Recently, the use of high speed, high sensitivity digital imaging in conjunction with voltage sensitive fluorescent dyes has enabled researchers to visualize electrical activity on the surface of cardiac tissue, both in vitro and in vivo. (3) Magnetohydrodynamics - A new research direction is to use computational homology to analyze results of large scale simulations of 2D turbulence in the presence of magnetic fields. Such simulations are relevant to the dynamics of black hole accretion disks. The complex flow patterns from simulations exhibit strong qualitative changes as a function of magnetic field strength. Efforts to characterize the pattern changes using Fourier methods and wavelet analysis have been unsuccessful. (4) Granular Flow - two experts in the area of granular media are studying 2D model experiments of earthquake dynamics where the stress fields can be measured; these stress fields from complex patterns of 'force chains' that may be amenable to analysis using computational homology. (5) Microstructure Characterization
Multiscale analysis of nonlinear systems using computational homology
Konstantin Mischaikow, Rutgers University /Georgia Institute of Technology, Michael Schatz, Georgia Institute of Technology, William Kalies, Florida Atlantic University, Thomas Wanner,George Mason University
2010-05-19
This is a collaborative project between the principal investigators. However, as is to be expected, different PIs have greater focus on different aspects of the project. This report lists these major directions of research which were pursued during the funding period: (1) Computational Homology in Fluids - For the computational homology effort in thermal convection, the focus of the work during the first two years of the funding period included: (1) A clear demonstration that homology can sensitively detect the presence or absence of an important flow symmetry, (2) An investigation of homology as a probe for flow dynamics, and (3) The construction of a new convection apparatus for probing the effects of large-aspect-ratio. (2) Computational Homology in Cardiac Dynamics - We have initiated an effort to test the use of homology in characterizing data from both laboratory experiments and numerical simulations of arrhythmia in the heart. Recently, the use of high speed, high sensitivity digital imaging in conjunction with voltage sensitive fluorescent dyes has enabled researchers to visualize electrical activity on the surface of cardiac tissue, both in vitro and in vivo. (3) Magnetohydrodynamics - A new research direction is to use computational homology to analyze results of large scale simulations of 2D turbulence in the presence of magnetic fields. Such simulations are relevant to the dynamics of black hole accretion disks. The complex flow patterns from simulations exhibit strong qualitative changes as a function of magnetic field strength. Efforts to characterize the pattern changes using Fourier methods and wavelet analysis have been unsuccessful. (4) Granular Flow - two experts in the area of granular media are studying 2D model experiments of earthquake dynamics where the stress fields can be measured; these stress fields from complex patterns of 'force chains' that may be amenable to analysis using computational homology. (5) Microstructure Characterization
Geometrically nonlinear bending analysis of laminated composite plate
NASA Astrophysics Data System (ADS)
Dash, Padmanav; Singh, B. N.
2010-10-01
In this work, a transverse bending of shear deformable laminated composite plates in Green-Lagrange sense accounting for the transverse shear and large rotations are presented. Governing equations are developed in the framework of higher order shear deformation theory. All higher order terms arising from nonlinear strain-displacement relations are included in the formulation. The present plate theory satisfies zero transverse shear strains conditions at the top and bottom surfaces of the plate in von-Karman sense. A C0 isoparametric finite element is developed for the present nonlinear model. Numerical results for the laminated composite plates of orthotropic materials with different system parameters and boundary conditions are found out. The results are also compared with those available in the literature. Some new results with different parameters are also presented.