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.
Compressive buckling analysis of hat-stiffened panel
NASA Technical Reports Server (NTRS)
Ko, William L.; Jackson, Raymond H.
1991-01-01
Buckling analysis was performed on a hat-stiffened panel subjected to uniaxial compression. Both local buckling and global buckling were analyzed. It was found that the global buckling load was several times higher than the buckling load. The predicted local buckling loads compared favorably with both experimental data and finite-element analysis.
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
Shear buckling analysis of a hat-stiffened panel
NASA Technical Reports Server (NTRS)
Ko, William L.; Jackson, Raymond H.
1994-01-01
A buckling analysis was performed on a hat-stiffened panel subjected to shear loading. Both local buckling and global buckling were analyzed. The global shear buckling load was found to be several times higher than the local shear buckling load. The classical shear buckling theory for a flat plate was found to be useful in predicting the local shear buckling load of the hat-stiffened panel, and the predicted local shear buckling loads thus obtained compare favorably with the results of finite element analysis.
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 Astrophysics Data System (ADS)
Pietropaoli, Elisa; Riccio, Aniello
2012-02-01
Finite element procedures for the analysis of composite structures under compressive loads (buckling and post-buckling) generally are not deployed in books because they are still considered object of research whereas they are deemed as assessed by researchers that focus their papers on restricted audience topics. Therefore, regarding these procedures, a gap exists in literature between what researchers consider as well established and what has been already published. The aim of this paper is to contribute to close this gap by providing an insight in linear and non-linear buckling analyses and in their use with composite structures. Both modelling and analysis considerations are presented and discussed, focusing on what can be considered as best practice when dealing with this kind of problems. Applications (to a stiffened panel and to a wing box) are provided for demonstrating the effectiveness of the procedures presented.
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.
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.
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.
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 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.
Euler buckling and nonlinear kinking of double-stranded DNA
NASA Astrophysics Data System (ADS)
Fields, Alexander; Axelrod, Kevin; Cohen, Adam
2012-02-01
Bare double-stranded DNA is a stiff biopolymer with a persistence length of roughly 53 nm under physiological conditions. Cells and viruses employ extensive protein machinery to overcome this stiffness and bend, twist, and loop DNA to accomplish tasks such as packaging, recombination, gene regulation, and repair. The mechanical properties of DNA are of fundamental importance to the mechanism and thermodynamics of these processes, but physiologically relevant curvature has been difficult to access experimentally. We designed and synthesized a DNA hairpin construct in which base-pairing interactions generated a compressive force on a short segment of duplex DNA, inducing Euler buckling followed by bending to thermally inaccessible radii of curvature. The efficiency of F"orster resonance energy transfer (FRET) between two fluorophores covalently linked to the hairpin indicated the degree of buckling. Bulk and single-molecule measurements yielded distinctly different force-compression curves for intact DNA and for strands with single nicks, base pair mismatches, and damage sites. These results suggest that changes in local mechanical properties may play a significant role in the recognition of these features by DNA-binding proteins.
Johnson, Ken I.; Deibler, John E.; Karri, Naveen K.; Pilli, Siva P.; Julyk, Larry J.
2012-07-01
The U.S. Department of Energy, Office of River Protection has commissioned a structural analysis of record for the Hanford single shell tanks 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 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. This paper summarizes the structural analysis methods that were used to evaluate the limit load and buckling limit states of the underground single shell tanks at the Hanford site. The limit loads were calculated using nonlinear finite element models that capture the progressive deformation and damage to the concrete as it approaches the limit load. Both uniform and concentrated loads over the tank dome were considered, and the analysis shows how adding a penetration in the center of the tank would affect the limit loads. For uniform surface loads, the penetration does not affect the limit load because concrete crushing and rebar yielding initiates first at the top of the wall, away from the penetration. For concentrated loads, crushing initiates at the center of the
Size-dependent thermo-electrical buckling analysis of functionally graded piezoelectric nanobeams
NASA Astrophysics Data System (ADS)
Ebrahimi, Farzad; Salari, Erfan
2015-12-01
In the present study, thermo-electrical buckling characteristics of functionally graded piezoelectric (FGP) Timoshenko nanobeams subjected to in-plane thermal loads and applied electric voltage are carried out by presenting a Navier type solution for the first time. Three kinds of thermal loading, namely, uniform, linear and nonlinear temperature rises through the thickness direction are considered. Thermo-electro-mechanical properties of FGP nanobeam are supposed to vary smoothly and continuously throughout the thickness based on power-law model. Eringen’s nonlocal elasticity theory is exploited to describe the size dependency of nanobeam. Using Hamilton’s principle, the nonlocal governing equations together with corresponding boundary conditions based on Timoshenko beam theory are obtained for the thermal buckling analysis of graded piezoelectric nanobeams including size effect and they are solved applying analytical solution. According to the numerical results, it is revealed that the proposed modeling can provide accurate critical buckling temperature results of the FG nanobeams as compared some cases in the literature. In following a parametric study is accompanied to examine the effects of the several parameters such as various temperature distributions, external electric voltage, power-law index, nonlocal parameter and aspect ratio on the critical buckling temperature difference of the size-dependent FGP nanobeams in detail. It is found that the small scale effect and electrical loading have a significant effect on buckling temperatures of FGP nanobeams.
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 and modal analysis of rotationally restrained orthotropic plates
NASA Astrophysics Data System (ADS)
Villarreal, Enrique; Abajo, Daniel
2015-10-01
This paper describes a theoretical approach for the static buckling, eigenfrequency and vibration buckling analysis of typical orthotropic plates used in aeronautical constructions. The plates are constrained with any combination of simply-supported and rotationally restrained edges, and are subjected to biaxial compressive loads. The derivation of closed-form solutions is discussed, and the results are presented in the form of design charts, where the effect of the restraint stiffness is highlighted. The proposed design charts allow a more accurate initial sizing of typical aerospace structural components, like stiffened panels, where both static and dynamic buckling loads are fundamental for the final design. As compared to classical solutions based on simply-supported and clamped edges, the modeling of the edge constraint as an elastic restraint provides a more refined description of the real stringer-stiffened panel. The results demonstrate that, in contrast to the commonly adopted simply-supported boundary condition, a reduction of the design conservativeness can be achieved if the stiffness of the restraint is accounted for. A novel set of results relative to the vibration buckling is derived, illustrating that the dynamic buckling tends to increase for load frequencies higher than the first natural frequency.
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.
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.
NASA Technical Reports Server (NTRS)
Stroud, W. J.; Agranoff, N.; Anderson, M. S.
1977-01-01
A procedure is presented for designing uniaxially stiffened panels made of composite material and subjected to combined inplane loads. The procedure uses a rigorous buckling analysis and nonlinear mathematical programing techniques. Design studies carried out with the procedure consider hat-stiffened and corrugated panels made of graphite-epoxy material. Combined longitudinal compression and shear and combined longitudinal and transverse compression are the loadings used in the studies. The capability to tailor the buckling response of a panel is also explored. Finally, the adequacy of another, simpler, analysis-design procedure is examined.
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
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.
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
Dynamic Visco-elastic Buckling Analysis for Airway Model
NASA Astrophysics Data System (ADS)
Bando, Kiyoshi; Ohba, Kenkichi; Yamanoi, Yuta
In order to clarify the mechanism by which the lung airway narrows during an asthma attack, dynamic buckling analysis of the wall was conducted. The wall was modeled using a visco-elastic thin-walled circular cylinder of the Voigt model for the planestress state. A governing equation for dynamic buckling was derived, and in the equation, the contraction of smooth muscle was replaced by uniform inward transmural pressure. The non-dimensional parameters for the buckling wave number n were nondimensional retardation time τ, non-dimensional increasing velocity of inward transmural pressure β, thickness radius ratio α2, radius length ratio η, density ratio ζ, and Poisson's ratio ν. The validity of the theoretical model was confirmed by comparing the calculated wave number with that obtained from the experiment, in which a silicone rubber tube blended with silicone potting gel was used as the in vitro airway model. In addition, the wave number n increased with β. It was necessary to consider the damping effect of the tube model or the airway wall, and n increased by 1.5 to 2 due to the additional mass effect of surrounding tissues of the basement membrane in the airway wall.
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 (UNIX 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
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).
NASA Astrophysics Data System (ADS)
Haiping, Liu; Wenhua, Shi
2016-09-01
The micro-vibration from flywheel system, as one of the main disturbances, has restricted the effective use of high sensitive payloads in satellites. In order to suppress the low- frequency line spectrum from the flywheel, a novel nonlinear vibration absorber (NVA) using Euler buckled beam is developed. The proposed NVA is attached on the supporting structure of the flywheel assembly, aiming to attenuate the line spectrum introduced by the flywheel in operation. A discrete multi-degree-of-freedom dynamic model, which includes the NVA, the flywheel and the supporting structure by taking into account of the gyroscopic effect of the flywheel, is built. The NVA is represented by a linear positive stiffness spring and parallel Euler buckled beams. The systematic dynamic equations with and without the NVA under the micro-vibration from the flywheel, respectively, are solved by using fourth-order Runge-Kutta method in time-domain. In addition, the effects of initial imperfection, oblique angle and damping coefficient of the Euler buckled beam on the vibration suppression performance are studied. The calculating results reveal that a typical nonlinear dynamic absorber for controlling the micro-vibration from the flywheel is constructed successfully based on the provided designing parameters of the Euler buckled beam. Compared with the vibration responses of the combined system with and without the NVA, it can be concluded that the NVA has better attenuation performance. The initial imperfection and damping coefficient of the Euler buckled beam exist optimum values, and with the increase of the oblique angle, the vibration controlling characteristics of the NVA have been improved.
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.
Buckling and Delamination Growth Analysis of Composite Laminates Containing Embedded Delaminations
NASA Astrophysics Data System (ADS)
Hosseini-Toudeshky, H.; Hosseini, S.; Mohammadi, B.
2010-04-01
The objective of this work is to study the post buckling behavior of composite laminates, containing embedded delamination, under uniaxial compression loading. For this purpose, delamination initiation and propagation is modeled using the softening behavior of interface elements. The full layer-wise plate theory is also employed for approximating the displacement field of laminates and the interface elements are considered as a numerical layer between any two adjacent layers which delamination is expected to propagate. A finite element program was developed and the geometric non-linearity in the von karman sense is incorporated to the strain/displacement relations, to obtain the buckling behavior. It will be shown that, the buckling load, delamination growth process and buckling mode of the composite plates depends on the size of delamination and stacking sequence of the laminates.
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
Molecular dynamics analysis on buckling of defective carbon nanotubes.
Kulathunga, D D T K; Ang, K K; Reddy, J N
2010-09-01
Owing to their remarkable mechanical properties, carbon nanotubes have been employed in many diverse areas of applications. However, similar to any of the many man-made materials used today, carbon nanotubes (CNTs) are also susceptible to various kinds of defects. Understanding the effect of defects on the mechanical properties and behavior of CNTs is essential in the design of nanotube-based devices and composites. It has been found in various past studies that these defects can considerably affect the tensile strength and fracture of CNTs. Comprehensive studies on the effect of defects on the buckling and vibration of nanotubes is however lacking in the literature. In this paper, the effects of various configurations of atomic vacancy defects, on axial buckling of single-walled carbon nanotubes (SWCNTs), in different thermal environments, is investigated using molecular dynamics simulations (MDS), based on a COMPASS force field. Our findings revealed that even a single missing atom can cause a significant reduction in the critical buckling strain and load of SWCNTs. In general, increasing the number of missing atoms, asymmetry of vacancy configurations and asymmetric distribution of vacancy clusters seemed to lead to higher deterioration in buckling properties. Further, SWCNTs with a single vacancy cluster, compared to SWCNTs with two or more vacancy clusters having the same number of missing atoms, appeared to cause higher deterioration of buckling properties. However, exceptions from the above mentioned trends could be expected due to chemical instabilities of defects. Temperature appeared to have less effect on defective CNTs compared to pristine CNTs.
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.
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.
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.
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.
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
NASA Technical Reports Server (NTRS)
Britt, V. O.
1993-01-01
An approximate analysis for buckling of biaxial- and shear-loaded anisotropic panels with centrally located elliptical cutouts is presented in the present paper. The analysis is composed of two parts, a prebuckling analysis and a buckling analysis. The prebuckling solution is determined using Lekhnitskii's complex variable equations of plane elastostatics combined with a Laurent series approximation and a boundary collocation method. The buckling solution is obtained using the principle of minimum potential energy. A by-product of the minimum potential energy equation is an integral equation which is solved using Gaussian quadrature. Comparisons with documented experimental results and finite element analyses indicate that the approximate analysis accurately predicts the buckling loads of square biaxial- and shear-loaded panels having elliptical cutouts with major axes up to sixty percent of the panel width. Results of a parametric study are presented for shear- and compression-loaded rectangular anisotropic panels with elliptical cutouts. The effects of panel aspect ratio, cutout shape, cutout size, cutout orientation, laminate anisotropy, and combined loading on the buckling load are examined.
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.
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 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.
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.
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.
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.
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.
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
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.
NASA Astrophysics Data System (ADS)
Okajima, Kenji; Imai, Junichi; Tanaka, Tadatsugu; Iida, Toshiaki
Damage to piles in the liquefied ground is frequently reported. Buckling by the excess vertical load could be one of the causes of the pile damage, as well as the lateral flow of the ground and the lateral load at the pile head. The buckling mechanism is described as a complicated interaction between the pile deformation by the vertical load and the earth pressure change cased by the pile deformation. In this study, series of static buckling model tests of a pile were carried out in dried sand ground with various thickness of the layer. Finite element analysis was applied to the test results to verify the effectiveness of the elasto-plastic finite element analysis combining the implicit-explicit mixed type dynamic relaxation method with the return mapping method to the pile buckling problems. The test results and the analysis indicated the possibility that the buckling load of a pile decreases greatly where the thickness of the layer increases.
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
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.
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.
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.
NASA Astrophysics Data System (ADS)
Zhen, Wu; Wanji, Chen
2007-05-01
Buckling response of angle-ply laminated composite and sandwich plates are analyzed using the global-local higher order theory with combination of geometric stiffness matrix in this paper. This global-local theory completely fulfills the free surface conditions and the displacement and stress continuity conditions at interfaces. Moreover, the number of unknowns in this theory is independent of the number of layers in the laminate. Based on this global-local theory, a three-noded triangular element satisfying C1 continuity conditions has also been proposed. The bending part of this element is constructed from the concept of DKT element. In order to improve the accuracy of the analysis, a method of modified geometric stiffness matrix has been introduced. Numerical results show that the present theory not only computes accurately the buckling response of general laminated composite plates but also predicts the critical buckling loads of soft-core sandwiches. However, the global higher-order theories as well as first order theories might encounter some difficulties and overestimate the critical buckling loads for soft-core sandwich plates.
NASA Astrophysics Data System (ADS)
Ansari, R.; Norouzzadeh, A.
2016-10-01
The size-dependent static buckling responses of circular, elliptical and skew nanoplates made of functionally graded materials (FGMs) are investigated in this article based on an isogeometric model. The Eringen nonlocal continuum theory is implemented to capture nonlocal effects. According to the Gurtin-Murdoch surface elasticity theory, surface energy influences are also taken into account by the consideration of two thin surface layers at the top and bottom of nanoplate. The material properties vary in the thickness direction and are evaluated using the Mori-Tanaka homogenization scheme. The governing equations of buckled nanoplate are achieved by the minimum total potential energy principle. To perform the isogeometric analysis as a solution methodology, a novel matrix-vector form of formulation is presented. Numerical examples are given to study the effects of surface stress as well as other important parameters on the critical buckling loads of functionally graded nanoplates. It is found that the buckling configuration of nanoplates at small scales is significantly affected by the surface free energy.
Buckling analysis of curved composite sandwich panels subjected to inplane loadings
NASA Technical Reports Server (NTRS)
Cruz, Juan R.
1993-01-01
Composite sandwich structures are being considered for primary structure in aircraft such as subsonic and high speed civil transports. The response of sandwich structures must be understood and predictable to use such structures effectively. Buckling is one of the most important response mechanisms of sandwich structures. A simple buckling analysis is derived for sandwich structures. This analysis is limited to flat, rectangular sandwich panels loaded by uniaxial compression (N(sub x)) and having simply supported edges. In most aerospace applications, however, the structure's geometry, boundary conditions, and loading are usually very complex. Thus, a general capability for analyzing the buckling behavior of sandwich structures is needed. The present paper describes and evaluates an improved buckling analysis for cylindrically curved composite sandwich panels. This analysis includes orthotropic facesheets and first-order transverse shearing effects. Both simple support and clamped boundary conditions are also included in the analysis. The panels can be subjected to linearly varying normal loads N(sub x) and N(sub y) in addition to a constant shear load N(sub xy). The analysis is based on the modified Donnell's equations for shallow shells. The governing equations are solved by direct application of Galerkin's method. The accuracy of the present analysis is verified by comparing results with those obtained from finite element analysis for a variety of geometries, loads, and boundary conditions. The limitations of the present analysis are investigated, in particular those related to the shallow shell assumptions in the governing equations. Finally, the computational efficiency of the present analysis is considered.
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.
NASA Technical Reports Server (NTRS)
Viswanathan, A. V.; Tamekuni, M.
1973-01-01
An exact linear analysis method is presented for predicting buckling of structures with arbitrary uniform cross section. The structure is idealized as an assemblage of laminated plate-strip elements, curved and planar, and beam elements. Element edges normal to the longitudinal axes are assumed to be simply supported. Arbitrary boundary conditions may be specified on any external longitudinal edge of plate-strip elements. The structure or selected elements may be loaded in any desired combination of inplane transverse compression or tension side load and axial compression load. The analysis simultaneously considers all possible modes of instability and is applicable for the buckling of laminated composite structures. Numerical results correlate well with the results of previous analysis methods.
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
NASA Astrophysics Data System (ADS)
Kala, Zdeněk
2013-10-01
The paper deals with the statistical analysis of resistance of a hot-rolled steel IPE beam under major axis bending. The lateral-torsional buckling stability problem of imperfect beam is described. The influence of bending moments and warping torsion on the ultimate limit state of the IPE beam with random imperfections is analyzed. The resistance is calculated by means of the close form solution. The initial geometrical imperfections of the beam are considered as the formatively identical to the first eigen mode of buckling. Changes of mean values of the resistance, of mean values of internal bending moments, of the variance of resistance and of the variance of internal bending moments were studied in dependence on the beam non-dimensional slenderness. The values of non-dimensional slenderness for which the statistical characteristics of internal moments associated with random resistance are maximal were determined.
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
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.
NASA Astrophysics Data System (ADS)
Enss, Georg C.; Platz, Roland
2016-10-01
Buckling of slender load-bearing beam-columns is a crucial failure scenario in light-weight structures as it may result in the collapse of the entire structure. If axial load and load capacity are unknown, stability becomes uncertain. To compensate this uncertainty, the authors successfully developed and evaluated an approach for active buckling control for a slender beam-column, clamped at the base and pinned at the upper end. Active lateral forces are applied with two piezoelectric stack actuators in opposing directions near the beam-column' clamped base to prevent buckling. A Linear Quadratic Regulator is designed and implemented on the experimental demonstrator and statistical tests are conducted to prove effectivity of the active approach. The load capacity of the beam-column could be increased by 40% and scatter of buckling occurrences for increasing axial loads is reduced. Weibull analysis is used to evaluate the increase of the load capacity and its related uncertainty compensation.
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.
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.
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.
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.
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.
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.
NASTRAN static and buckling analysis - comparison with other large-capacity programs
NASA Technical Reports Server (NTRS)
Shah, L. C.
1973-01-01
A square plate with clamped edges under a concentrated load was modeled using NASTRAN and ASKA finite element computer programs. Deflections were computed for various width-to-thickness ratios (b/t) of the plate element, and were compared against the classical theory to determine the b/t limitations. A cylinder with simply supported ends was modeled using NASTRAN and STAGS computer programs for buckling analysis. The models were subjected to a uniform radial pressure loading. Several parameters were changed, and the effects of those variations are presented. Utilizing these data, a model which will produce results comparable to published empirical data can be constructed and processed for a minimized cost.
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.
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
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Buckle Driven Delamination in Thin Hard Film Compliant Substrate Systems
NASA Astrophysics Data System (ADS)
Moody, N. R.; Reedy, E. D.; Corona, E.; Adams, D. P.; Kennedy, M. S.; Cordill, M. J.; Bahr, D. F.
2010-06-01
behavior predicted by 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 [5] 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 (Figure 2). 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.
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
Nonlinear analysis of piezoelectric nanocomposite energy harvesting plates
NASA Astrophysics Data System (ADS)
Rafiee, M.; He, X. Q.; Liew, K. M.
2014-06-01
This paper investigates the nonlinear analysis of energy harvesting from piezoelectric functionally graded carbon nanotube reinforced composite plates under combined thermal and mechanical loadings. The excitation, which derives from harmonically varying mechanical in-plane loading, results in parametric excitation. The governing equations of the piezoelectric functionally graded carbon nanotube reinforced composite plates are derived based on classical plate theory and von Kármán geometric nonlinearity. The material properties of the nanocomposite plate are assumed to be graded in the thickness direction. The single-walled carbon nanotubes (SWCNTs) are assumed to be aligned, straight and have a uniform layout. The linear buckling and vibration behavior of the nanocomposite plates is obtained in the first step. Then, Galerkin’s method is employed to derive the nonlinear governing equations of the problem with cubic nonlinearities associated with mid-plane stretching. Periodic solutions are determined by using the Poincaré-Lindstedt perturbation scheme with movable simply supported boundary conditions. The effects of temperature change, the volume fraction and the distribution pattern of the SWCNTs on the parametric resonance, in particular the amplitude of vibration and the average harvested power of the smart functionally graded carbon nanotube reinforced composite plates, are investigated through a detailed parametric study.
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.
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
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.
Plastic buckling of cylinders under biaxial loading
NASA Astrophysics Data System (ADS)
Giezen, Jurgen J.
An experimental investigation is carried out to study the effects of nonproportional loading in the plastic range on a buckling load. The discrepancy between experimental and theoretical results points to some principal shortcoming in the analysis. The problem has been simplified by applying axial tensile load and external press to simple cylindrical shell specimen and observing the buckling load for various nonproportional load-paths. Results are compared to numerical predictions (BOSOR5) using classical type plasticity models such as [...] deformation and [...] incremental theory. Significant discrepancy was found an attributed to inadequate modeling of the nonlinear material behavior. The effects of geometrical imperfections and large deflections were found to insignificant, thereby leading to an idea [...] of the discrepancy between test and theory is due to a use of inadequate plastic model. The introduction of the Southwell plot into elastic shell buckling problem reduced the already minor effects of geometric imperfections.The Christoffersen-Hutchinson corner theory model was introduced into BOSAR5 in its simplest form as presented by Poh-Sang Lam. Results obtained with this model, which allows corners to form on an initially smooth yield surface, displayed better agreement with experimental data. However, increased computational time and problems related to abrupt changes in load-path at the corner are a major concern at this present time.
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.
Nonlinear analysis of drought dynamics
NASA Astrophysics Data System (ADS)
Ma, M.
2015-12-01
Drought is an extreme natural hazard and becomes a severe problem in the world. It arises as a result of interactions between climate input and human activity, displaying the nonlinearity and complexity. Nonlinear time series analyses open a way to study the underlying dynamic characteristics of drought, and then provide the forward knowledge to understanding the physical mechanism of drought event. The rationale behind this idea is that information about the representation of nonlinear properties could be used as an additional quality indicator. To that end, the correlation dimension method, a powerful nonlinear time series analysis method based on the chaos theory, has been suggested to assess the intrinsic dimensionality or degree of freedom of time series according to Takens (1981). It can provide an assessment of the dominant processes that is required to map the observed dynamics. In this study, daily discharge and hourly groundwater level data of 63 catchments in Germany and China were investigated with correlation dimension method. The results indicated that the correlation dimension values of studied discharge exhibited none clear spatial patterns, but showed significant correlations with the spatial heterogeneity within the catchments. In contrast, the correlation dimension values of groundwater level displayed spatial patterns due to the different aquifer conditions (confined or unconfined). High correlation dimension values indicate partly confined conditions. In addition, Hurst analysis was involved to qualify the persistence of drought. It seems that drought mechanisms can be learnt from the data themselves in an inverse manner.
NASA Astrophysics Data System (ADS)
Rouhi, S.; Ansari, R.
2012-01-01
In this article, an atomistic model is developed to study the buckling and vibration characteristics of single-layered graphene sheets (SLGSs). By treating SLGSs as space-frame structures, in which the discrete nature of graphene sheets is preserved, they are modeled using three-dimensional elastic beam elements for the bonds. The elastic moduli of the beam elements are determined via a linkage between molecular mechanics and structural mechanics. Based on this model, the critical compressive forces and fundamental natural frequencies of single-layered graphene sheets with different boundary conditions and geometries are obtained and then compared. It is indicated that the compressive buckling force decreases when the graphene sheet aspect ratio increases. At low aspect ratios, the increase of aspect ratios will result in a significant decrease in the critical buckling load. It is also indicated that increasing aspect ratio at a given side length results in the convergence of buckling envelops associated with armchair and zigzag graphene sheets. The influence of boundary conditions will be studied for different geometries. It will be shown that the influence of boundary conditions is not significant for sufficiently large SLGSs.
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.
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.
Elastic buckling of tapered circular plates
NASA Astrophysics Data System (ADS)
Wang, C. M.; Hong, G. M.; Tan, T. J.
1995-06-01
This paper is concerned with the elastic buckling of tapered circular plates. The study is prompted by the fact that results hitherto available are restricted to a narrow range of taper parameters and are somewhat different from each other. For the buckling analysis, a simple and yet accurate numerical method is presented. It is based on the shooting method and the Rayleigh-Ritz approach. Comprehensive generic buckling results of circular plates with linearly and parabolically varying thicknesses are generated. Comparison studies of the buckling results showed that some of the existing results were erroneous. Optimal values of taper parameters for such tapered plates are also given.
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…
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.
NASA Astrophysics Data System (ADS)
Jamalpoor, A.; Ahmadi-Savadkoohi, A.; Hosseini-Hashemi, Sh
2016-10-01
This paper deals with the theoretical analysis of free vibration and biaxial buckling of magneto-electro-elastic (MEE) microplate resting on Kelvin-Voigt visco-Pasternak foundation and subjected to initial external electric and magnetic potentials, using modified strain gradient theory (MSGT). Kirchhoff plate model and Hamilton’s principle are employed to extract the governing equations of motion. Governing equations were analytically solved to obtain clear closed-form expression for complex natural frequencies and buckling loads using Navier’s approach. Numerical results are presented to reveal variations of natural frequency and buckling load ratio of MEE microplate against different amounts of the length scale parameter, initial external electric and magnetic potentials, aspect ratio, damping and transverse and shear stiffness parameters of the visco-Pasternak foundation, length to thickness ratio, microplate thickness and higher modes. Numerical results of this study illustrate that by increasing thickness-to-material length scale parameter ratio, both natural frequency and buckling load ratio predicted by MSGT and modified couple stress theory are reduced because the non-dimensional length scale parameter tends to decrease the stiffness of structures and make them more flexible. In addition, results show that initial external electric and initial external magnetic potentials have no considerable influence on the buckling load ratio and frequency of MEE microplate as the microplate thickness increases.
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.
Dynamic analysis of a buckled asymmetric piezoelectric beam for energy harvesting.
Van Blarigan, Louis; Moehlis, Jeff
2016-03-01
A model of a buckled beam energy harvester is analyzed to determine the phenomena behind the transition between high and low power output levels. It is shown that the presence of a chaotic attractor is a sufficient condition to predict high power output, though there are relatively small areas where high output is achieved without a chaotic attractor. The chaotic attractor appears as a product of a period doubling cascade or a boundary crisis. Bifurcation diagrams provide insight into the development of the chaotic region as the input power level is varied, as well as the intermixed periodic windows.
Dynamic analysis of a buckled asymmetric piezoelectric beam for energy harvesting.
Van Blarigan, Louis; Moehlis, Jeff
2016-03-01
A model of a buckled beam energy harvester is analyzed to determine the phenomena behind the transition between high and low power output levels. It is shown that the presence of a chaotic attractor is a sufficient condition to predict high power output, though there are relatively small areas where high output is achieved without a chaotic attractor. The chaotic attractor appears as a product of a period doubling cascade or a boundary crisis. Bifurcation diagrams provide insight into the development of the chaotic region as the input power level is varied, as well as the intermixed periodic windows. PMID:27036185
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 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.
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.
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.
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.
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.
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.
Thin film buckling : a relation between adhesion and morphology
NASA Astrophysics Data System (ADS)
Barthel, Etienne; Faou, Jean-Yvon; Grachev, Sergey; Parry, Guillaume
2013-03-01
When thin films with low adhesion are compressively stressed, they may buckle. These buckles exhibit interesting morphologies such as the well known telephone cord. However our understanding of this form of buckling is limited because it couples the large displacement nonlinearities of plates with the subtleties of mixed-mode adhesion. Here we investigate the morphology of the thin film buckles as a function of mode mixity by a combination of experiments and simulations. We first exhibit a linear relation between the period of the telephone cord buckles and a characteristic parameter of the mixed mode adhesion. Furthermore we evidence a rich set of new buckle morphologies through experiments, and demonstrate that these morphologies can be reproduced in the simulations. We also show that we can rationalize the transitions between morphologies through a phase diagram. This excellent agreement between experimental results and numerical predictions further validates the simulation method we have developped recently.
Method for nonlinear exponential regression analysis
NASA Technical Reports Server (NTRS)
Junkin, B. G.
1972-01-01
Two computer programs developed according to two general types of exponential models for conducting nonlinear exponential regression analysis are described. Least squares procedure is used in which the nonlinear problem is linearized by expanding in a Taylor series. Program is written in FORTRAN 5 for the Univac 1108 computer.
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.
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.
NASA Technical Reports Server (NTRS)
Ng, C. F.
1988-01-01
Static postbuckling and nonlinear dynamic analysis of plates are usually accomplished by multimode analyses, although the methods are complicated and do not give straightforward understanding of the nonlinear behavior. Assuming single-mode transverse displacement, a simple formula is derived for the transverse load displacement relationship of a plate under in-plane compression. The formula is used to derive a simple analytical expression for the static postbuckling displacement and nonlinear dynamic responses of postbuckled plates under sinusoidal or random excitation. Regions with softening and hardening spring behavior are identified. Also, the highly nonlinear motion of snap-through and its effects on the overall dynamic response can be easily interpreted using the single-mode formula. Theoretical results are compared with experimental results obtained using a buckled aluminum panel, using discrete frequency and broadband point excitation. Some important effects of the snap-through motion on the dynamic response of the postbuckled plates are found.
NASA Astrophysics Data System (ADS)
Cheung, Y. K.; Kong, J.
1993-04-01
A global-local approach is proposed to analyze thick laminated plates. This approach treats a thick laminated plate as a three-dimensional inhomogeneous anisotropic elastic body. The cross-section of a laminated plate is first discretized into conventional eight-node elements. The interpolation function along the span of the plate is defined by the cubic B3-spline function. The displacement functions can be expressed as the product of the usual isoparametric shape functions and the spline function. A set of global polynomials of an appropriate order is selected to transform the nodal variables of the cross-section to a much smaller set of generalized parameters associated with the polynomials. These parameters can be obtained by means of the standard Rayleigh-Ritz technique. The total number of unknowns involved is drastically reduced with a minor sacrifice of accuracy. The six components of stresses, the fundamental natural frequencies, and the critical buckling loads can be determined with acceptable accuracy. Numerical examples are given to demonstrate the accuracy and effectiveness of the global-local procedures.
Buckling Design and Imperfection Sensitivity of Sandwich Composite Launch-Vehicle Shell Structures
NASA Technical Reports Server (NTRS)
Schultz, Marc R.; Sleight, David W.; Myers, David E.; Waters, W. Allen, Jr.; Chunchu, Prasad B.; Lovejoy, Andrew W.; Hilburger, Mark W.
2016-01-01
Composite materials are increasingly being considered and used for launch-vehicle structures. For shell structures, such as interstages, skirts, and shrouds, honeycomb-core sandwich composites are often selected for their structural efficiency. Therefore, it is becoming increasingly important to understand the structural response, including buckling, of sandwich composite shell structures. Additionally, small geometric imperfections can significantly influence the buckling response, including considerably reducing the buckling load, of shell structures. Thus, both the response of the theoretically perfect structure and the buckling imperfection sensitivity must be considered during the design of such structures. To address the latter, empirically derived design factors, called buckling knockdown factors (KDFs), were developed by NASA in the 1960s to account for this buckling imperfection sensitivity during design. However, most of the test-article designs used in the development of these recommendations are not relevant to modern launch-vehicle constructions and material systems, and in particular, no composite test articles were considered. Herein, a two-part study on composite sandwich shells to (1) examine the relationship between the buckling knockdown factor and the areal mass of optimized designs, and (2) to interrogate the imperfection sensitivity of those optimized designs is presented. Four structures from recent NASA launch-vehicle development activities are considered. First, designs optimized for both strength and stability were generated for each of these structures using design optimization software and a range of buckling knockdown factors; it was found that the designed areal masses varied by between 6.1% and 19.6% over knockdown factors ranging from 0.6 to 0.9. Next, the buckling imperfection sensitivity of the optimized designs is explored using nonlinear finite-element analysis and the as-measured shape of a large-scale composite cylindrical
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.
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.
Non-isothermal elastoviscoplastic snap-through and creep buckling of shallow arches
NASA Technical Reports Server (NTRS)
Simitses, G. J.; Riff, R.
1987-01-01
The problem of buckling of shallow arches under transient thermomechanical loads is investigated. The analysis is based on nonlinear geometric and constitutive relations, and is expressed in a rate form. The material constitutive equations are capable of reproducing all non-isothermal, elasto-viscoplastic characteristics. The solution scheme is capable of predicting response which includes pre and postbuckling with creep and plastic effects. The solution procedure is demonstrated through several examples which include both creep and snap-through behavior.
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.
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.
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.
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
Nonlinear frequency response analysis of structural vibrations
NASA Astrophysics Data System (ADS)
Weeger, Oliver; Wever, Utz; Simeon, Bernd
2014-12-01
In this paper we present a method for nonlinear frequency response analysis of mechanical vibrations of 3-dimensional solid structures. For computing nonlinear frequency response to periodic excitations, we employ the well-established harmonic balance method. A fundamental aspect for allowing a large-scale application of the method is model order reduction of the discretized equation of motion. Therefore we propose the utilization of a modal projection method enhanced with modal derivatives, providing second-order information. For an efficient spatial discretization of continuum mechanics nonlinear partial differential equations, including large deformations and hyperelastic material laws, we employ the concept of isogeometric analysis. Isogeometric finite element methods have already been shown to possess advantages over classical finite element discretizations in terms of higher accuracy of numerical approximations in the fields of linear vibration and static large deformation analysis. With several computational examples, we demonstrate the applicability and accuracy of the modal derivative reduction method for nonlinear static computations and vibration analysis. Thus, the presented method opens a promising perspective on application of nonlinear frequency analysis to large-scale industrial problems.
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.
GBT pre-buckling and buckling analyses of thin-walled members under axial and transverse loads
NASA Astrophysics Data System (ADS)
Taig, Gerard; Ranzi, Gianluca; Luongo, Angelo
2016-03-01
This paper presents an analytical approach for pre-buckling and buckling analyses of thin-walled members implemented within the framework of the Generalised Beam Theory (GBT). With the proposed GBT cross-sectional analysis, the set of deformation modes used in the analysis is represented by the dynamic modes obtained for an unrestrained frame representing the cross-section. In this manner, it is possible to account for the deformability of the cross-section in both pre-buckling and buckling analyses. Different loading conditions, including both axial and transverse arrangements, are considered in the applications to highlight under which circumstances the use of the GBT deformation modes is required for an adequate representation of the pre-buckling and buckling response. The numerical results have been validated against those determined using a shell element model developed in the finite element software ABAQUS.
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.
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.
Micro-buckling in the nanocomposite structure of biological materials
NASA Astrophysics Data System (ADS)
Su, Yewang; Ji, Baohua; Hwang, Keh-Chih; Huang, Yonggang
2012-10-01
Nanocomposite structure, consisting of hard mineral and soft protein, is the elementary building block of biological materials, where the mineral crystals are arranged in a staggered manner in protein matrix. This special alignment of mineral is supposed to be crucial to the structural stability of the biological materials under compressive load, but the underlying mechanism is not yet clear. In this study, we performed analytical analysis on the buckling strength of the nanocomposite structure by explicitly considering the staggered alignment of the mineral crystals, as well as the coordination among the minerals during the buckling deformation. Two local buckling modes of the nanostructure were identified, i.e., the symmetric mode and anti-symmetric mode. We showed that the symmetric mode often happens at large aspect ratio and large volume fraction of mineral, while the anti-symmetric happens at small aspect ratio and small volume fraction. In addition, we showed that because of the coordination of minerals with the help of their staggered alignment, the buckling strength of these two modes approached to that of the ideally continuous fiber reinforced composites at large aspect ratio given by Rosen's model, insensitive to the existing "gap"-like flaws between mineral tips. Furthermore, we identified a mechanism of buckling mode transition from local to global buckling with increase of aspect ratio, which was attributed to the biphasic dependence of the buckling strength on the aspect ratio. That is, for small aspect ratio, the local buckling strength is smaller than that of global buckling so that it dominates the buckling behavior of the nanocomposite; for comparatively larger aspect ratio, the local buckling strength is higher than that of global buckling so that the global buckling dominates the buckling behavior. We also found that the hierarchical structure can effectively enhance the buckling strength, particularly, this structural design enables
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 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.
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 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.
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
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.
NASA Astrophysics Data System (ADS)
Gruttmann, F.; Pham, V. D.
2008-02-01
The delamination process of thin films on rigid substrates is investigated. Such systems are typically subject to high residual compression and modest adhesion causing them to buckling driven blisters. In certain cases buckles with the shape of telephone cords are observed. A finite element model for quasi-static delamination growth is developed. Applying a Reissner-Mindlin shell kinematic for the film allows C 0- continuous shape functions. The traction vector at the film-substrate interface is obtained from the derivative of a cohesive free energy. Incorporation of loading and unloading conditions is considered for the irreversible process. The equilibrium state is computed iteratively in dependence of the compressive residual stresses. The computed telephone cord delaminations are stable asymmetric configurations whereas the symmetric configurations are unstable.
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.
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)
Nemeth, Michael P.; Young, Richard D.; Collins, Timothy J.; Starnes, James H., Jr.
2002-01-01
The results of an analytical study of the elastic buckling and nonlinear behavior of the liquid-oxygen tank for the new Space Shuttle superlightweight external fuel tank are presented. Selected results that illustrate three distinctly different types of non-linear response phenomena for thin-walled shells which are subjected to combined mechanical and thermal loads are presented. These response phenomena consist of a bifurcation-type buckling response, a short-wavelength non-linear bending response and a non-linear collapse or "snap-through" response associated with a limit point. The effects of initial geometric imperfections on the response characteristics are emphasized. The results illustrate that the buckling and non-linear response of a geometrically imperfect shell structure subjected to complex loading conditions may not be adequately characterized by an elastic linear bifurcation buckling analysis, and that the traditional industry practice of applying a buckling-load knock-down factor can result in an ultraconservative design. Results are also presented that show that a fluid-filled shell can be highly sensitive to initial geometric imperfections, and that the use a buckling-load knock-down factor is needed for this case.
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.
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.
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.
Tissue morphogenesis: a surface buckling mechanism.
Volokh, Konstantin Y
2006-01-01
Surface patterns can emerge during growth of anisotropic tissues because of surface buckling. This morphogenetic scenario is examined in the present paper based on a simple phenomenological theory of tissue growth. In particular, we show that constrained growth can lead to tissue compression, which in turn may result in surface buckling of the tissue. The latter means the appearance of wavy patterns on the surface. These patterns decay away from the surface. It is interesting that the critical magnitude of the parameter of mass supply, which corresponds to surface buckling, is independent of the pattern wavelength and various patterns can generally be generated in growth. Results of theoretical analysis show that the surface buckling scenario is realistic if the growing tissue matches the following two conditions. First, compression should appear during tissue growth. Second, the tissue should exhibit strong anisotropy. The former condition does not necessarily mean geometric constraints: inhomogeneous growth or material inhomogeneity and anisotropy can lead to the appearance of compressive stresses. The latter condition is typical of some tissues with fiber reinforcement in planes parallel to the surface. In the latter case, the tissue material is much softer in the out-of-plane direction than in plane. The creation of patterns by restraining tissue growth and forcing the surface to buckle represents a challenging experimental problem.
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
Buckle propagation in tubular structures
Nogueira, A.C.; Tassoulas, J.L.
1995-12-01
A novel method for the analysis of buckle propagation in tubes such as tendons of tension leg platforms and pipelines for deep-water applications is presented. Results are reported for the propagation pressure and state deformation in tubes of various materials (SS-304, CS-1010 and X-52 steel tubes) with a wide range of values of the diameter-to-thickness ratio (D/t). Not only the method overcomes the prohibitive computational demands of earlier procedures, but also it is in excellent agreement with experimental data for all values of D/t investigated (from D/t = 78 to as low as D/t = 12.8).
NASA Technical Reports Server (NTRS)
Budiansky, B.
1976-01-01
The papers deal with such topics as the buckling and post-buckling behavior of plates and shells; methods of calculating critical buckling and collapse loads; finite element representations for thin-shell instability analysis; theory and experiment in the creep buckling of plates and shells; creep instability of thick shell structures; analytical and numerical studies of the influence of initial imperfections on the elastic buckling of columns; mode interaction in stiffened panels under compression; imperfection-sensitivity in the interactive buckling of stiffened plates; buckling of stochastically imperfect structures; and the Liapunov stability of elastic dynamic systems. A special chapter is devoted to design problems, including the design of a Mars entry 'aeroshell', and buckling design in vehicle structures. Individual items are announced in this issue.
Stability Analysis of Nonlinear Systems with Slope Restricted Nonlinearities
Du, Jiajia
2014-01-01
The problem of absolute stability of Lur'e systems with sector and slope restricted nonlinearities is revisited. Novel time-domain and frequency-domain criteria are established by using the Lyapunov method and the well-known Kalman-Yakubovich-Popov (KYP) lemma. The criteria strengthen some existing results. Simulations are given to illustrate the efficiency of the results. PMID:24592160
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.
Euler buckling of geothermal well casing
Rechard, R.P.; Schuler, K.W.
1983-02-01
Geothermal well operators have expressed concern over the vulnerability of unsupported casing to buckling from thermal elongation. Preliminary numerical and theoretical calculations are presented, which indicate the buckling phenomenon should not be serious in N-80 casing if the string is tension preloaded. Buckling would be detrimental for K-55 casing. The effect of wall contact was found to be beneficial for closely confined pipe strings and of no detriment when hole gaps are large. The weakness of API screw joints in bending appears to be the structural limitation. The analysis assumed stresses above yield constituted failure, that thermal expansion was strain controlled, and that the casing was continuous. Excessive internal pressure instability was ignored. The temperature variation considered was between cementing conditions of 100 to 200/sup 0/F (40 to 95/sup 0/C) and shut-in conditions of 425 to 450/sup 0/F (220 to 230/sup 0/C).
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
Spectral analysis of noisy nonlinear maps
Hirshman, S.P.; Whitson, J.C.
1982-01-01
A path integral equation formalism is developed to obtain the frequency spectrum of nonlinear mappings exhibiting chaotic behavior. The one-dimensional map, x/sub n+1/ = f(x/sub n/), where f is nonlinear and n is a discrete time variable, is analyzed in detail. This map is introduced as a paradigm of systems whose exact behavior is exceedingly complex, and therefore irretrievable, but which nevertheless possess smooth, well-behaved solutions in the presence of small sources of external noise. A Boltzmann integral equation is derived for the probability distribution function p(x,n). This equation is linear and is therefore amenable to spectral analysis. The nonlinear dynamics in f(x) appear as transition probability matrix elements, and the presence of noise appears simply as an overall multiplicative scattering amplitude. This formalism is used to investigate the band structure of the logistic equation and to analyze the effects of external noise on both the invariant measure and the frequency spectrum of x/sub n/ for several values of lambda epsilon (0,1).
On the interaction of thermal buckling and debonding of patched structures
NASA Astrophysics Data System (ADS)
Carabetta, Pamela Marie
The widespread use of patched assemblies in engineering structures creates the need for better fundamental understanding of the failure phenomena of such structures to ensure their safe and effective usage. A structure possessing two substructures, the "patch" and "baseplate", with mismatched coefficients of thermal expansion is studied under thermal loading for two extreme edge conditions. The composite structure is taken as initially flawed, such that partial separation exists at the edges of the patch between the two substructures. Two relevant failure mechanisms are sling-shot buckling and edge debonding (separation). Sling-shot buckling, first observed for perfectly intact structures under thermal loads, occurs when the structure dynamically slings from one equilibrium configuration to another in an opposite sense of deflection at a critical load. It is desired to be able to predict and characterize buckling of the structure, and its coupling with debonding. The geometrically nonlinear problem is formulated via a variational formulation, which allows the boundaries of the domains of the structure to vary in addition to the displacements. The vanishing of the first variation of the potential energy yields governing equilibrium equations, boundary/matching conditions, and transversality conditions. The transversality condition yields a Griffith type delamination criterion. A closed-form solution is obtained after recasting the problem in a mixed formulation. A stability analysis is performed using the second variation of the potential energy functional. The partially debonded structure is seen to possess a "dual nature", where it is structurally different depending on the deflection, due to the existence of the initial flaw. It experiences sling-shot buckling, which, coupled with the structure's duality leads to what we refer to as "Buckle Trapping." It is suggested that, for certain critical temperature fields, the structure oscillates dynamically between
Nonlinear dynamic analysis of sandwich panels
NASA Technical Reports Server (NTRS)
Lush, A. M.
1984-01-01
Two analytical techniques applicable to large deflection dynamic response calculations for pressure loaded composite sandwich panels are demonstrated. One technique utilizes finite element modeling with a single equivalent layer representing the face sheets and core. The other technique utilizes the modal analysis computer code DEPROP which was recently modified to include transverse shear deformation in a core layer. The example problem consists of a simply supported rectangular sandwich panel. Included are comparisons of linear and nonlinear static response calculations, in addition to dynamic response calculations.
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)
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.
Nonlinear peculiar-velocity analysis and PCA
Dekel, A.
2001-02-20
We allow for nonlinear effects in the likelihood analysis of peculiar velocities, and obtain {approximately}35%-lower values for the cosmological density parameter and for the amplitude of mass-density fluctuations. The power spectrum in the linear regime is assumed to be of the flat {Lambda}CDM model (h = 0:65, n = 1) with only {Omega}{sub m} free. Since the likelihood is driven by the nonlinear regime, we break the power spectrum at k{sub b} {approximately} 0.2 (h{sup {minus}1} Mpc){sup {minus}1} and fit a two-parameter power-law at k > k{sub b} . This allows for an unbiased fit in the linear regime. Tests using improved mock catalogs demonstrate a reduced bias and a better fit. We find for the Mark III and SFI data {Omega}{sub m} = 0.35 {+-} 0.09 with {sigma}{sub 8}{Omega}P{sub m}{sup 0.6} = 0.55 {+-} 0.10 (90% errors). When allowing deviations from {Lambda}CDM, we find an indication for a wiggle in the power spectrum in the form of an excess near k {approximately} 0.05 and a deficiency at k {approximately} 0.1 (h{sup {minus}1} Mpc){sup {minus}1}--a cold flow which may be related to a feature indicated from redshift surveys and the second peak in the CMB anisotropy. A {chi}{sup 2} test applied to principal modes demonstrates that the nonlinear procedure improves the goodness of fit. The Principal Component Analysis (PCA) helps identifying spatial features of the data and fine-tuning the theoretical and error models. We address the potential for optimal data compression using PCA.
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.
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.
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
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.
Buckling of dislocation in graphene
NASA Astrophysics Data System (ADS)
Yao, Yin; Wang, Shaofeng; Bai, Jianhui; Wang, Rui
2016-10-01
The buckling of dislocation in graphene is discussed through the lattice theory of dislocation and elastic theory. The approximate solution of the buckling is obtained based on the inner stress distribution caused by different structure of dislocations and is proved to be suitable by the simulation. The position of the highest buckling is predicted to be at the vertex of the pentagon far away from the heptagon. The buckling is strongly influenced by the internal stress and the distance between the extrusive area and stretching area, as well as the critical stress σc. The SW defect is proved to be unbuckled due to its strong interaction between extrusion and stretching.
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.
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.
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.
Bifurcation analysis method of nonlinear traffic phenomena
NASA Astrophysics Data System (ADS)
Ai, Wenhuan; Shi, Zhongke; Liu, Dawei
2015-03-01
A new bifurcation analysis method for analyzing and predicting the complex nonlinear traffic phenomena based on the macroscopic traffic flow model is presented in this paper. This method makes use of variable substitution to transform a traditional traffic flow model into a new model which is suitable for the stability analysis. Although the substitution seems to be simple, it can extend the range of the variable to infinity and build a relationship between the traffic congestion and the unstable system in the phase plane. So the problem of traffic flow could be converted into that of system stability. The analysis identifies the types and stabilities of the equilibrium solutions of the new model and gives the overall distribution structure of the nearby equilibrium solutions in the phase plane. Then we deduce the existence conditions of the models Hopf bifurcation and saddle-node bifurcation and find some bifurcations such as Hopf bifurcation, saddle-node bifurcation, Limit Point bifurcation of cycles and Bogdanov-Takens bifurcation. Furthermore, the Hopf bifurcation and saddle-node bifurcation are selected as the starting point of density temporal evolution and it will be helpful for improving our understanding of stop-and-go wave and local cluster effects observed in the free-way traffic.
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.
Analysis of orthotropic plates with nonlinear shear characteristics
Raouf, R.A.
1994-12-31
This paper presents an analytical study of the response of orthotropic plates with nonlinear shear characteristics to transverse loading. The shear stress-shear strain relationship is based on experimental results available in the literature. It is nonlinear and of the polynomial type. The symbolic manipulator Mathematics is used to implement a Rayleigh-Ritz procedure to derive a set of approximate nonlinear algebraic equations of equilibrium for the plate under a uniformly distributed load. The equations of equilibrium show that the nonlinearity introduces a coupling between the in-plane displacements and the transverse displacement. The studied case shows that the nonlinearity has a hardening effect on the transverse displacements but a softening effect on the in-plane displacements. Moreover, the studied case shows that the linear solution underestimates the magnitude of shear stress. The nonlinear solution indicates that the in-plane shear stress predicted by the nonlinear analysis is higher than those predicted by the linear theory.
Buckling of offshore structures
Walker, A.C.; Ellinas, C.P.; Supple, W.J.
1984-01-01
This new handbook gives detailed design guidance for a wide range of structural components and types of loading related to the buckling of offshore structures. It presents many hundreds of test results that have been examined and collated to give a common base of comparison, and its surveys all the relevant national and international design codes, comparing the relative accuracy of their predictions against the available test results. Contents are: unstiffened cord and bracing elements; ring-stiffened cylinders; stringer-stiffened and orthogonally-stiffened cylinders; flat panels; and end-closures and transition shells.
Buckle up for Interesting Times
ERIC Educational Resources Information Center
Myers, Miles
2011-01-01
Those who are involved in the current Common Core Standards should buckle up for a rocky ride. Some of the same issues that churned within the National Council of Teachers of English (NCTE) during the standards movement of the 1990s (1989-1997) are here once again. The author's buckle is pulled tight, having already had his standards report…
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 of polymerized monomolecular films
NASA Astrophysics Data System (ADS)
Bourdieu, L.; Daillant, J.; Chatenay, D.; Braslau, A.; Colson, D.
1994-03-01
The buckling of a two-dimensional polymer network at the air-water interface has been evidenced by grazing incidence x-ray scattering. A comprehensive description of the inhomogeneous octadecyltrichlorosilane polymerized film was obtained by atomic force microscopy and x-ray scattering measurements. The buckling occurs with a characteristic wavelength ~=10 μm.
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
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.
Nonlinear filtering properties of detrended fluctuation analysis
NASA Astrophysics Data System (ADS)
Kiyono, Ken; Tsujimoto, Yutaka
2016-11-01
Detrended fluctuation analysis (DFA) has been widely used for quantifying long-range correlation and fractal scaling behavior. In DFA, to avoid spurious detection of scaling behavior caused by a nonstationary trend embedded in the analyzed time series, a detrending procedure using piecewise least-squares fitting has been applied. However, it has been pointed out that the nonlinear filtering properties involved with detrending may induce instabilities in the scaling exponent estimation. To understand this issue, we investigate the adverse effects of the DFA detrending procedure on the statistical estimation. We show that the detrending procedure using piecewise least-squares fitting results in the nonuniformly weighted estimation of the root-mean-square deviation and that this property could induce an increase in the estimation error. In addition, for comparison purposes, we investigate the performance of a centered detrending moving average analysis with a linear detrending filter and sliding window DFA and show that these methods have better performance than the standard DFA.
Using the Hypergeometric Model to analyze the buckling of drillstrings in curved boreholes
Sampaio, J.H.B. Jr.; Eustes, A.W. III
1998-12-31
Current methodologies for analytically determining the onset of buckling of drillstrings within curved boreholes are limited. In this paper, the Hypergeometric Model is shown to be an effective model to determine drillstring buckling within curved boreholes. With the Hypergeometric Model, the analysis of drillstring buckling results in curves expressing the local buckling force versus the angle of inclination. The local buckling force alone, however, does not contain all the information required for a practical analysis. From the local buckling force curve, the positional buckling force is derived. The positional buckling force considers the distributed weight of the drillstring and the friction between the drillstring and the borehole wall. From this curve, the point of minimum resistance to buckling of the drillstring is determined. Using the local and positional buckling force curves, experimental results and simulations are presented. When multiple configurations exist (for example tapered drillstrings, tapered boreholes, multi-curved boreholes, or any combination of these), the analysis procedure uses superposition of two or more single configuration curves and a graphical algorithm. The Hypergeometric Model permits the optimization of the position of the crossing points (cross-over positioning, casing-shoe positioning, and change of curvature) to achieve extended reach with less risk and cost. The procedure for this model and examples are presented in this paper.
Energy minimization versus pseudo force technique for nonlinear structural analysis
NASA Technical Reports Server (NTRS)
Kamat, M. P.; Hayduk, R. J.
1980-01-01
The effectiveness of using minimization techniques for the solution of nonlinear structural analysis problems is discussed and demonstrated by comparison with the conventional pseudo force technique. The comparison involves nonlinear problems with a relatively few degrees of freedom. A survey of the state-of-the-art of algorithms for unconstrained minimization reveals that extension of the technique to large scale nonlinear systems is possible.
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 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 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 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 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.
Adhesion-driven buckling of single-walled carbon nanotube bundles
NASA Astrophysics Data System (ADS)
Ke, Changhong; Zheng, Meng; Bae, In-Tae; Zhou, Guangwen
2010-05-01
Buckling of a thin single-walled carbon nanotube (SWNT) bundle that is partially bound on another straight free-standing SWNT bundle is reported. The buckling of the SWNT bundle is purely due to the adhesion interaction between two SWNT bundles. The deformation curvature of the buckled SWNT bundle is experimentally measured by transmission electron microscopy, and is theoretically modeled by a continuum model based on nonlinear elastica theory. Our results reveal that the binding strength of the bundle interface and the bulk elastic modulus of the SWNT bundle can be associated by its buckling curvature. Our results show that the bulk elastic moduli of the tested SWNT bundles are significantly lower than the Young's modulus of individual SWNTs. The reported adhesion-driven nanotube buckling provides a potential new approach to quantify the elastic modulus and the binding strength of bundled nanotubes.
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.
Khang, Dahl-Young; Xiao, Jianliang; Kocabas, Coskun; MacLaren, Scott; Banks, Tony; Jiang, Hanqing; Huang, Yonggang Y; Rogers, John A
2008-01-01
We have studied the scaling of controlled nonlinear buckling processes in materials with dimensions in the molecular range (i.e., approximately 1 nm) through experimental and theoretical studies of buckling in individual single-wall carbon nanotubes on substrates of poly(dimethylsiloxane). The results show not only the ability to create and manipulate patterns of buckling at these molecular scales, but also, that analytical continuum mechanics theory can explain, quantitatively, all measurable aspects of this system. Inverse calculation applied to measurements of diameter-dependent buckling wavelengths yields accurate values of the Young's moduli of individual SWNTs. As an example of the value of this system beyond its use in this type of molecular scale metrology, we implement parallel arrays of buckled SWNTs as a class of mechanically stretchable conductor.
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.
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)
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.
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.
A Second Generation Nonlinear Factor Analysis.
ERIC Educational Resources Information Center
Etezadi-Amoli, Jamshid; McDonald, Roderick P.
1983-01-01
Nonlinear common factor models with polynomial regression functions, including interaction terms, are fitted by simultaneously estimating the factor loadings and common factor scores, using maximum likelihood and least squares methods. A Monte Carlo study gives support to a conjecture about the form of the distribution of the likelihood ratio…
Nonlinear transient analysis of joint dominated structures
NASA Technical Reports Server (NTRS)
Chapman, J. M.; Shaw, F. H.; Russell, W. C.
1987-01-01
A residual force technique is presented that can perform the transient analyses of large, flexible, and joint dominated structures. The technique permits substantial size reduction in the number of degrees of freedom describing the nonlinear structural models and can account for such nonlinear joint phenomena as free-play and hysteresis. In general, joints can have arbitrary force-state map representations but these are used in the form of residual force maps. One essential feature of the technique is to replace the arbitrary force-state maps describing the nonlinear joints with residual force maps describing the truss links. The main advantage of this replacement is that the incrementally small relative displacements and velocities across a joint are not monitored directly thereby avoiding numerical difficulties. Instead, very small and 'soft' residual forces are defined giving a numerically attractive form for the equations of motion and thereby permitting numerically stable integration algorithms. The technique was successfully applied to the transient analyses of a large 58 bay, 60 meter truss having nonlinear joints. A method to perform link testing is also presented.
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.
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.
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.
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 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.
NASA Astrophysics Data System (ADS)
Kiani, Keivan
2015-06-01
The axial buckling behavior of magnetically affected current-carrying nanowires is studied accounting for the surface energy effect. Using Euler-Bernoulli beam theory, the Lorentz force on the nanowire is determined and the governing equations are established. By application of the Galerkin approach and assumed mode method, the critical axial compressive load of the nanostructure is evaluated in the cases of simply supported and fully clamped ends. The effects of surface energy, electric current, strength of the magnetic field, slenderness ratio, and nanowire’s radius on the axial buckling loads are comprehensively discussed. The obtained results reveal that both the electric current and exerted magnetic field endanger the axial stability of the nanowire. For high levels of electric current or magnetic field strength, the surface effect becomes significant in the axial buckling performance of the nanostructure.
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 chaotic component extraction for postural stability analysis.
Snoussi, Hichem; Hewson, David; Duchêne, Jacques
2009-01-01
This paper proposes a nonlinear analysis of the human postural steadiness system. The analyzed signal is the displacement of the centre of pressure (COP) collected from a force plate used for measuring postural sway. Instead of analyzing the classical nonlinear parameters on the whole signal, the proposed method consists of analyzing the nonlinear dynamics of the intrinsic mode functions (IMF) of the COP signal. Based on the computation of the IMFs Lyapunov exponents, it is shown that pre-processing the COP signal with the Empirical Mode Decomposition allows an efficient extraction of its chaotic component.
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.
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.
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.
A hybrid transfinite element approach for nonlinear transient thermal analysis
NASA Technical Reports Server (NTRS)
Tamma, Kumar K.; Railkar, Sudhir B.
1987-01-01
A new computational approach for transient nonlinear thermal analysis of structures is proposed. It is a hybrid approach which combines the modeling versatility of contemporary finite elements in conjunction with transform methods and classical Bubnov-Galerkin schemes. The present study is limited to nonlinearities due to temperature-dependent thermophysical properties. Numerical test cases attest to the basic capabilities and therein validate the transfinite element approach by means of comparisons with conventional finite element schemes and/or available solutions.
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.
Suprachoroidal Buckling: Technique and Indications
El Rayes, Ehab N; Elborgy, Ebrahim
2013-01-01
The authors herein report the feasibility of suprachoroidal buckling (SCB) procedure as a new approach for treating different forms of retinal detachment (RD) by creating suprachoroidal indentation (buckling effect). With this technique, specially designed devices, i.e. a catheter or cannula, are guided in the suprachoroidal space to reach the target area. Then, a suprachoroidal filler (long lasting hyaluronic acid) is injected to indent the choroid creating SCB, thereby closing retinal tears and supporting the overlying retina. This procedure was performed to treat both myopic tractional maculopathy (MTM), including myopic macular holes, as well as peripheral retinal breaks. SCB may be used alone or in conjunction with vitrectomy. In myopic patients, restoration of retinal layers was achieved in all eyes with myopic foveoschisis. Most eyes with macular hole detachments demonstrated closure of the holes. All peripheral retinal breaks were adequately buckled and closed in a single procedure. The buckling effect was long enough in duration to seal the tears and promote adequate chorioretinal scarring. The procedure was safe and relatively simple in terms of reaching the treatment area and injecting the filler. SCB adds to our surgical options for treating selected cases of peripheral retinal tears and rhegmatogenous RD, and avoids potential problems of episcleral buckles. Moreover it may avoid vitrectomy in selected cases of rhegmatogenous RD. PMID:24653830
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
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.
NASA Astrophysics Data System (ADS)
Taffetani, M.; Ciarletta, P.
2015-08-01
Soft cylindrical gels can develop a long-wavelength peristaltic pattern driven by a competition between surface tension and bulk elastic energy. In contrast to the Rayleigh-Plateau instability for viscous fluids, the macroscopic shape in soft solids evolves toward a stable beading, which strongly differs from the buckling arising in compressed elastic cylinders. This work proposes a novel theoretical and numerical approach for studying the onset and the non-linear development of the elasto-capillary beading in soft cylinders, made of neo-Hookean hyperelastic material with capillary energy at the free surface, subjected to axial stretch. Both a theoretical study, deriving the linear and the weakly non-linear stability analyses for the problem, and numerical simulations, investigating the fully non-linear evolution of the beaded morphology, are performed. The theoretical results prove that an axial elongation can not only favour the onset of beading, but also determine the nature of the elastic bifurcation. The fully non-linear phase diagrams of the beading are also derived from finite element numerical simulations, showing two peculiar morphological transitions when varying either the axial stretch or the material properties of the gel. Since the bifurcation is found to be subcritical for very slender cylinders, an imperfection sensitivity analysis is finally performed. In this case, it is shown that a surface sinusoidal imperfection can resonate with the corresponding marginally stable solution, thus selecting the emerging beading wavelength. In conclusion, the results of this study provide novel guidelines for controlling the beaded morphology in different experimental conditions, with important applications in micro-fabrication techniques, such as electrospun fibres.
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.
PASCO: Structural panel analysis and sizing code: Users manual - Revised
NASA Technical Reports Server (NTRS)
Anderson, M. S.; Stroud, W. J.; Durling, B. J.; Hennessy, K. W.
1981-01-01
A computer code denoted PASCO is described for analyzing and sizing uniaxially stiffened composite panels. Buckling and vibration analyses are carried out with a linked plate analysis computer code denoted VIPASA, which is included in PASCO. Sizing is based on nonlinear mathematical programming techniques and employs a computer code denoted CONMIN, also included in PASCO. Design requirements considered are initial buckling, material strength, stiffness and vibration frequency. A user's manual for PASCO is presented.
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…
Torque-induced buckling behavior in stretched intertwined DNAs
NASA Astrophysics Data System (ADS)
Brahmachari, Sumitabha; Marko, John F.
Two intertwined DNA molecules (a DNA 'braid') is a common occurrence in the cell and is a relevant substrate for the study of topoisomerase and recombination enzymes. Single molecule experiments have observed the signature of a buckling transition in braids under tensile and torsional stress. We present a free energy model for braided DNA to investigate the mechanical properties of these structures. Our model is based on the semi-flexible polymer model for double helix DNA and is in quantitative accord with the experiments. We identify coexistence of a force-extended state with a plectonemically buckled state, which is reminiscent of single supercoiled DNA behavior. However, the absence of an intrinsic twist modulus in braided DNA results in unique mechanical properties such as non-linear torque in the extended state. At the buckling transition, we predict a jump in the braid extension due to the plectoneme end loop which acts as a nucleation barrier. We investigate the effect of salt concentration on the mechanical response of braids, e.g. we find that buckling starts at a lower linking number for lower salt concentration, the opposite of what is seen for single supercoiled DNAs. Also, concentrations less than 20 mM monovalent salt favor formation of multiple plectoneme domains. NSF Grant: DMR-9734178.
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.
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.
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 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.
Concurrent algorithms for transient nonlinear FE analysis
NASA Technical Reports Server (NTRS)
Ortiz, M.
1987-01-01
A two-parameter class of time-stepping algorithms for nonlinear structural dynamics is investigated. What sets the present method apart from other concurrent algorithms is the fact that it can be used to some advantage in sequential machines as well. Thus, substantial speed-ups are obtained on a single processor as the number of subdomains is increased. An additional O(p) speed-up is obtained when p processors are utilized. The test case discussed is being repeated for a mesh comprising four times as many elements, in an effort to understand how the large scale asymptotic speed-ups are attained. A three dimensional example involving finite deformations and free body motions is also being pursued. A code optimized for concurrency in the Alliant FX8 computer is being finalized. This will provide the means for testing the performance of the algorithm in a multiprocessor environment.
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
The effect of collagenase on the critical buckling pressure of arteries.
Martinez, Ricky; Han, Hai-Chao
2012-03-01
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 effects of collagen degradation on the mechanical stability of arteries are 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 400 U/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 of 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.
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.
Symmetry analysis for nonlinear time reversal methods applied to nonlinear acoustic imaging
NASA Astrophysics Data System (ADS)
Dos Santos, Serge; Chaline, Jennifer
2015-10-01
Using symmetry invariance, nonlinear Time Reversal (TR) and reciprocity properties, the classical NEWS methods are supplemented and improved by new excitations having the intrinsic property of enlarging frequency analysis bandwidth and time domain scales, with now both medical acoustics and electromagnetic applications. The analysis of invariant quantities is a well-known tool which is often used in nonlinear acoustics in order to simplify complex equations. Based on a fundamental physical principle known as symmetry analysis, this approach consists in finding judicious variables, intrinsically scale dependant, and able to describe all stages of behaviour on the same theoretical foundation. Based on previously published results within the nonlinear acoustic areas, some practical implementation will be proposed as a new way to define TR-NEWS based methods applied to NDT and medical bubble based non-destructive imaging. This paper tends to show how symmetry analysis can help us to define new methodologies and new experimental set-up involving modern signal processing tools. Some example of practical realizations will be proposed in the context of biomedical non-destructive imaging using Ultrasound Contrast Agents (ACUs) where symmetry and invariance properties allow us to define a microscopic scale-invariant experimental set-up describing intrinsic symmetries of the microscopic complex system.
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.
Computer analysis of ring stiffened shells of revolution
NASA Technical Reports Server (NTRS)
Cohen, G. A.
1973-01-01
The equations and method of solution for a series of five compatible computer programs for structural analysis of axisymmetric shell structures are presented. These programs, designated as the SRA programs, apply to a common structural model but analyze different modes of structural response. They are: (1) linear asymmetric static response (SRA 100), (2) buckling of linearized asymmetric equilibrium states (SRA 101), (3) nonlinear axisymmetric static response (SRA 200), (4) buckling of nonlinear axisymmetric equilibrium states(SRA 201), and (5) vibrations about nonlinear axisymmetric equilibrium state (SRA 300).
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.
Nonlinear analysis of helix traveling wave tubes
Freund, H.P.; Zaidman, E.G.; Mankofsky, A.; Vanderplaats, N.R.; Kodis, M.A.
1995-10-01
A time-dependent nonlinear formulation of the interaction in the helix traveling wave tube is presented for a configuration in which an electron beam propagates through a sheath helix surrounded by a conducting wall. In order to describe both the variation in the wave dispersion and in the transverse inhomogeneity of the electromagnetic field with wave number, the field is represented as a superposition of waves in a vacuum sheath helix. An overall explicit sinusoidal variation of the form exp({ital ikz}{minus}{ital i}{omega}{ital t}) is assumed (where {omega} denotes the angular frequency corresponding to the wave number {ital k} in the vacuum sheath helix), and the polarization and radial variation of each wave is determined by the boundary conditions in a vacuum sheath helix. Thus, while the field is three-dimensional in nature, it is azimuthally symmetric. The propagation of each wave {ital in} {ital vacuo} as well as the interaction of each wave with the electron beam is included by allowing the amplitudes of the waves to vary in {ital z} and {ital t}. A dynamical equation for the field amplitudes is derived analogously to Poynting`s equation, and solved in conjunction with the three-dimensional Lorentz force equations for an ensemble of electrons. Numerical examples are presented corresponding to both single- and multiwave interactions. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.
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.
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
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.
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"
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.
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.
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.
Optimal stabilization of indefinite plate buckling problems
NASA Astrophysics Data System (ADS)
Chase, J. Geoffrey; Bhashyam, Srinivas
2001-08-01
Indefinite plate buckling problems arise when the applied load case results in buckling loads which are not all of the same sign. Examples include the important cases of shear buckling and general combinations of tensile and compressive in-plane edge loads. Optimal controllers which actively stabilize these general, indefinite plate buckling problems, by transforming them into a system of definite plate buckling problems, are presented. Important features of this approach include the ability to select the designed closed loop critical buckling load, and to pre-determine what load cases a given controller will stabilize when the exact load combination varies or is unknown. This last result enables the control designer to know exactly, by design, what load combinations will be stabilized. A numerical example is presented where the controllers developed are employed to stabilize multiple, definite and indefinite buckling modes for laminated composite plates similar to aircraft wing skins.
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)
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.
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.
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 Time Series Analysis of Sunspot Data
NASA Astrophysics Data System (ADS)
Suyal, Vinita; Prasad, Awadhesh; Singh, Harinder P.
2009-12-01
This article deals with the analysis of sunspot number time series using the Hurst exponent. We use the rescaled range ( R/ S) analysis to estimate the Hurst exponent for 259-year and 11 360-year sunspot data. The results show a varying degree of persistence over shorter and longer time scales corresponding to distinct values of the Hurst exponent. We explain the presence of these multiple Hurst exponents by their resemblance to the deterministic chaotic attractors having multiple centers of rotation.
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.
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.
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.
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.
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.
Advances in Shell Buckling: Theory and Experiments
NASA Astrophysics Data System (ADS)
Thompson, J. Michael T.
In a recent feature article in this journal, coauthored by Gert van der Heijden, I described the static-dynamic analogy and its role in understanding the localized post-buckling of shell-like structures, looking exclusively at integrable systems. We showed the true significance of the Maxwell energy criterion load in predicting the sudden onset of "shock sensitivity" to lateral disturbances. The present paper extends the survey to cover nonintegrable systems, such as thin compressed shells. These exhibit spatial chaos, generating a multiplicity of localized paths (and escape routes) with complex snaking and laddering phenomena. The final theoretical contribution shows how these concepts relate to the response and energy barriers of an axially compressed cylindrical shell. After surveying NASA's current shell-testing programme, a new nondestructive technique is proposed to estimate the "shock sensitivity" of a laboratory specimen that is in a compressed metastable state before buckling. A probe is used to measure the nonlinear load-deflection characteristic under a rigidly applied lateral displacement. Sensing the passive resisting force, it can be plotted in real time against the displacement, displaying an equilibrium path along which the force rises to a maximum and then decreases to zero: having reached the free state of the shell that forms a mountain-pass in the potential energy. The area under this graph gives the energy barrier against lateral shocks. The test is repeated at different levels of the overall compression. If a symmetry-breaking bifurcation is encountered on the path, computer simulations show how this can be suppressed by a controlled secondary probe tuned to deliver zero force on the shell.
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.
Nonlinear Pressure Wave Analysis by Concentrated Mass Model
NASA Astrophysics Data System (ADS)
Ishikawa, Satoshi; Kondou, Takahiro; Matsuzaki, Kenichiro
A pressure wave propagating in a tube often changes to a shock wave because of the nonlinear effect of fluid. Analyzing this phenomenon by the finite difference method requires high computational cost. To lessen the computational cost, a concentrated mass model is proposed. This model consists of masses, connecting nonlinear springs, connecting dampers, and base support dampers. The characteristic of a connecting nonlinear spring is derived from the adiabatic change of fluid, and the equivalent mass and equivalent damping coefficient of the base support damper are derived from the equation of motion of fluid in a cylindrical tube. Pressure waves generated in a hydraulic oil tube, a sound tube and a plane-wave tube are analyzed numerically by the proposed model to confirm the validity of the model. All numerical computational results agree very well with the experimental results carried out by Okamura, Saenger and Kamakura. Especially, the numerical analysis reproduces the phenomena that a pressure wave with large amplitude propagating in a sound tube or in a plane tube changes to a shock wave. Therefore, it is concluded that the proposed model is valid for the numerical analysis of nonlinear pressure wave problem.
NASA Astrophysics Data System (ADS)
Kurt, Mehmet; Eriten, Melih; McFarland, D. Michael; Bergman, Lawrence A.; Vakakis, Alexander F.
2014-03-01
We consider a linear cantilever beam attached to ground through a strongly nonlinear stiffness at its free boundary, and study its dynamics computationally by the assumed-modes method. The nonlinear stiffness of this system has no linear component, so it is essentially nonlinear and nonlinearizable. We find that the strong nonlinearity mostly affects the lower-frequency bending modes and gives rise to strongly nonlinear beat phenomena. Analysis of these beats proves that they are caused by internal resonance interactions of nonlinear normal modes (NNMs) of the system. These internal resonances are not of the classical type since they occur between bending modes whose linearized natural frequencies are not necessarily related by rational ratios; rather, they are due to the strong energy-dependence of the frequency of oscillation of the corresponding NNMs of the beam (arising from the strong local stiffness nonlinearity) and occur at energy ranges where the frequencies of these NNMs are rationally related. Nonlinear effects start at a different energy level for each mode. Lower modes are influenced at lower energies due to larger modal displacements than higher modes and thus, at certain energy levels, the NNMs become rationally related, which results in internal resonance. The internal resonances of NNMs are studied using a reduced order model of the beam system. Then, a nonlinear system identification method is developed, capable of identifying this type of strongly nonlinear modal interactions. It is based on an adaptive step-by-step application of empirical mode decomposition (EMD) to the measured time series, which makes it valid for multi-frequency beating signals. Our work extends an earlier nonlinear system identification approach developed for nearly mono-frequency (monochromatic) signals. The extended system identification method is applied to the identification of the strongly nonlinear dynamics of the considered cantilever beam with the local strong
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.
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.
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.
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.
Determination of the critical buckling pressure of blood vessels using the energy approach.
Han, Hai-Chao
2011-03-01
The stability of blood vessels under lumen blood pressure is essential to the maintenance of normal vascular function. Differential buckling equations have been established recently for linear and nonlinear elastic artery models. However, the strain energy in bent buckling and the corresponding energy method have not been investigated for blood vessels under lumen pressure. The purpose of this study was to establish the energy equation for blood vessel buckling under internal pressure. A buckling equation was established to determine the critical pressure based on the potential energy. The critical pressures of blood vessels with small tapering along their axis were estimated using the energy approach. It was demonstrated that the energy approach yields both the same differential equation and critical pressure for cylindrical blood vessel buckling as obtained previously using the adjacent equilibrium approach. Tapering reduced the critical pressure of blood vessels compared to the cylindrical ones. This energy approach provides a useful tool for studying blood vessel buckling and will be useful in dealing with various imperfections of the vessel wall.
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.
Slope Stability Analysis Using Limit Equilibrium Method in Nonlinear Criterion
Lin, Hang; Zhong, Wenwen; Xiong, Wei; Tang, Wenyu
2014-01-01
In slope stability analysis, the limit equilibrium method is usually used to calculate the safety factor of slope based on Mohr-Coulomb criterion. However, Mohr-Coulomb criterion is restricted to the description of rock mass. To overcome its shortcomings, this paper combined Hoek-Brown criterion and limit equilibrium method and proposed an equation for calculating the safety factor of slope with limit equilibrium method in Hoek-Brown criterion through equivalent cohesive strength and the friction angle. Moreover, this paper investigates the impact of Hoek-Brown parameters on the safety factor of slope, which reveals that there is linear relation between equivalent cohesive strength and weakening factor D. However, there are nonlinear relations between equivalent cohesive strength and Geological Strength Index (GSI), the uniaxial compressive strength of intact rock σci, and the parameter of intact rock mi. There is nonlinear relation between the friction angle and all Hoek-Brown parameters. With the increase of D, the safety factor of slope F decreases linearly; with the increase of GSI, F increases nonlinearly; when σci is relatively small, the relation between F and σci is nonlinear, but when σci is relatively large, the relation is linear; with the increase of mi, F decreases first and then increases. PMID:25147838
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.
Investigation of nonlinear pupil dynamics by recurrence quantification analysis.
Mesin, L; Monaco, A; Cattaneo, R
2013-01-01
Pupil is controlled by the autonomous nervous system (ANS). It shows complex movements and changes of size even in conditions of constant stimulation. The possibility of extracting information on ANS by processing data recorded during a short experiment using a low cost system for pupil investigation is studied. Moreover, the significance of nonlinear information contained in the pupillogram is investigated. We examined 13 healthy subjects in different stationary conditions, considering habitual dental occlusion (HDO) as a weak stimulation of the ANS with respect to the maintenance of the rest position (RP) of the jaw. Images of pupil captured by infrared cameras were processed to estimate position and size on each frame. From such time series, we extracted linear indexes (e.g., average size, average displacement, and spectral parameters) and nonlinear information using recurrence quantification analysis (RQA). Data were classified using multilayer perceptrons and support vector machines trained using different sets of input indexes: the best performance in classification was obtained including nonlinear indexes in the input features. These results indicate that RQA nonlinear indexes provide additional information on pupil dynamics with respect to linear descriptors, allowing the discrimination of even a slight stimulation of the ANS. Their use in the investigation of pathology is suggested. PMID:24187665
Dynamic Delamination Buckling In Composite Laminates
NASA Technical Reports Server (NTRS)
Grady, Joseph E.; Chamis, Christos C.; Aiello, Robert A.
1989-01-01
Procedure for mathematical modeling of dynamic delamination buckling and propagation of delamination, with plate bending elements and multipoint constraints, developed and incorporated into finite-element computer program. Predicts time at which delamination buckling occurs, shape of dynamic-buckling mode, and strain-energy-release rate due to extension of delamination crack. Method extended to handle such other defects as transply and edge cracks.
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.
Predictability of global surface temperature by means of nonlinear analysis
NASA Astrophysics Data System (ADS)
Gimeno, L.; García, R.; Pacheco, J. M.; Hernández, E.; Ribera, P.
2001-01-01
The time series of annually averaged global surface temperature anomalies for the years 1856-1998 is studied through nonlinear time series analysis with the aim of estimating the predictability time. Detection of chaotic behaviour in the data indicates that there is some internal structure in the data; the data may be considered to be governed by a deterministic process and some predictability is expected. Several tests are performed on the series, with results indicating possible chaotic behaviour.
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.
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.
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
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.
Compressive buckling of rectangular composite plates with a free-edge delamination
NASA Astrophysics Data System (ADS)
Suemasu, Hiroshi; Gozu, Katsuhisa; Hayashi, Kunio; Ishikawa, Takashi
1995-02-01
An experimental and analytical investigation is conducted on the compressive buckling behavior of orthotropic plates with a delamination. The plates, which have three simply supported edges and one free edge, are a simplified model of stiffener plates of a stiffened panel. A uniform width delamination is located at their free edges over the whole length. In the analysis, the Rayleigh-Ritz approximation method is adopted. A constrained point is introduced to allow the contact between the two delaminated surfaces. Imaginary springs about relative displacement and two relative slopes are introduced at the constrained point. With the constraint, buckling loads of physically admissible buckling modes can be obtained by ordinary buckling analysis. The global buckling load reduction is found to be significant and almost proportional to the delamination width. Local delamination buckling is found to occur when the delamination is located near the surface and its size is relatively large compared with that of the plate. The local buckling mode is different from the global one, and more wave number in loading direction and constrained points are necessary to obtain physically admissible solutions. The analytical results agree well with the experimental ones.
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.
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.
Bifurcation techniques for nonlinear dynamic analysis of compressor stall phenomena
NASA Technical Reports Server (NTRS)
Razavi, H. C.; Mehra, R. K.
1985-01-01
Compressor stall phenomena is analyzed from nonlinear control theory viewpoint, 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; furthermore it suggests strategies for recovery from stall. 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 effect is shown to exist in the stall/recovery process. Surge cycles are observed to develop for some critical parameter values. It is shown that the oscillatory behavior is due to development of limit cycles, generated by Hopf bifurcation of solutions. Both stable and unstable limit cycles are observed. To further illustrate the usefulness of the methodology some partial computation of domains of attraction of equilibria is carried out, and parameter sensitivity analysis is performed.
Diagnosis of nonlinear systems using kernel principal component analysis
NASA Astrophysics Data System (ADS)
Kallas, M.; Mourot, G.; Maquin, D.; Ragot, J.
2014-12-01
Technological advances in the process industries during the past decade have resulted in increasingly complicated processes, systems and products. Therefore, recent researches consider the challenges in their design and management for successful operation. While principal component analysis (PCA) technique is widely used for diagnosis, its structure cannot describe nonlinear related variables. Thus, an extension to the case of nonlinear systems is presented in a feature space for process monitoring. Working in a high-dimensional feature space, it is necessary to get back to the original space. Hence, an iterative pre-image technique is derived to provide a solution for fault diagnosis. The relevance of the proposed technique is illustrated on artificial and real dataset.
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.
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.
Effects of multiple delaminations on compressive buckling behaviors of composite panels
NASA Astrophysics Data System (ADS)
Suemasu, Hiroshi
1993-01-01
Compressive buckling stability of composite panels with through-width, equally spaced multiple delaminations are investigated analytically and experimentally. An analytical method is formulated on the basis of Rayleigh-Ritz approximation technique. Timoshenko type shear effects are included. An experiment and a finite element analysis are also conducted on the present model. The analytical results agree very well with the experimental and finite element results. The buckling load, which is the compressive strength of the panel in the case of the present model, reduces significantly due to the existence of multiple delaminations. The mechanism causing the significant loss of the compressive buckling load due to the delaminations is well explained.
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.
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.
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.
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 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.
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
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
Analysis of a non-linear structure by considering two non-linear formulations
NASA Astrophysics Data System (ADS)
Majed, R.; Raynaud, J. L.
2003-03-01
In recent years, modal synthesis methods have been extended for solving non-linear dynamic problems subjected to harmonic excitation. These methods are based on the notion of non-linear or linearized modes and exploited in the case of structures affected by localized non-linearity. Actually, the experimental tests executed on non-linear structures are time consuming, particularly when repeated experimental tests are needed. It is often preferable to consider new non-linear methods with a view to decrease significantly the number of attempts during prototype tests and improving the accuracy of the dynamic behaviour. This article describes two fundamental non-linear formulations based on two different strategies. The first formulation exploits the eigensolutions of the associated linear system and the dynamics characteristics of each localized non-linearity. The second formulation is based on the exploitation of the linearized eigensolutions obtained using an iterative process. This article contains a numerical and an experimental study which examines the non-linear behaviour of the structure affected by localized non-linearities. The study is intended to validate the numerical algorithm and to evaluate the problems arising from the introduction of non-linearities. The complex responses are evaluated using the iterative Newton-Raphson method and for a series of discrete frequencies. The theory has been applied to a bi-dimensional structure and consists of evaluating the harmonic responses obtained using the proposed formulations by comparing measured and calculated transfer functions.
Sequential buckling of an elastic wall
NASA Astrophysics Data System (ADS)
Bico, Jose; Bense, Hadrien; Keiser, Ludovic; Roman, Benoit; Melo, Francisco; Abkarian, Manouk
A beam under quasistatic compression classically buckles beyond a critical threshold. In the case of a free beam, the lowest buckling mode is selected. We investigate the case of a long ``wall'' grounded of a compliant base and compressed in the axial compression. In the case of a wall of slender rectangular cross section, the selected buckling mode adopts a nearly fixed wavelength proportional to the height of the wall. Higher compressive loads only increase the amplitude of the buckle. However if the cross section has a sharp shape (such as an Eiffel tower profile), we observe successive buckling modes of increasing wavelength. We interpret this unusual evolution in terms of scaling arguments. At small scales, this variable periodicity might be used to develop tunable optical devices. We thank ECOS C12E07, CNRS-CONICYT, and Fondecyt Grant No. N1130922 for partially funding this work.
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.
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.
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.
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.
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.
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.
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
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 thin-walled cylinder under axial compression and internal pressure
NASA Technical Reports Server (NTRS)
Lo, Hsu; Crate, Harold; Schwartz, Edward B
1951-01-01
An investigation was made of a thin-walled cylinder under axial compression and various internal pressures to study the effect of the internal pressure on the compressive buckling stress of the cylinder. A theoretical analysis based on a large-deflection theory was also made. The theoretically predicted increase of compressive buckling stress due to internal pressure agrees fairly well with the experimental results. (author)
Perturbation and Nonlinear Dynamic Analysis of Different Singing Styles
Butte, Caitlin J.; Zhang, Yu; Song, Huangqiang; Jiang, Jack J.
2012-01-01
Summary 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 (D2) 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 D2 = 2.14), jazz (median D2 = 2.24), pop (median D2 = 2.60), MT (median D2 = 2.73), and soul (mean D2 = 3.26). Correlation dimension was significantly higher in opera (P < 0.001) with median D2 = 6.19. In this study, acoustic analysis in opera singing gave significantly high values for shimmer and D2, 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
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.
Geometric Nonlinear Finite Element Analysis of Active Fibre Composite Bimorphs
NASA Astrophysics Data System (ADS)
Kernaghan, Robert
Active fibre composite-actuated bimorphic actuators were studied in order to measure deflection performance. The deflection of the actuators was a function of the actuating electric potential applied to the active material as well as the magnitude of the axial preload applied to the bimorphic structure. This problem required the use of geometric nonlinear modeling techniques. Geometric nonlinear finite element analysis was undertaken to determine the deflection performance of Macro Fibre Composite (MFC)- and Hollow Active Fibre (HAFC)-actuated bimorphic structures. A physical prototype MFC-actuated bimorphic structure was manufactured in order to verify the results obtained by the finite element analysis. Theses analyses determined that the bimorphic actuators were capable of significant deflection. The analyses determined that the axial preload of the bimorphic actuators significantly amplified the deflection performance of the bimorphic actuators. The deflection performance of the bimorphic actuators suggest that they could be candidates to act as actuators for the morphing wing of a micro unmanned air vehicle.
On a numerical solution of the plastic buckling problem of structures
NASA Technical Reports Server (NTRS)
Gupta, K. K.
1978-01-01
An automated digital computer procedure is presented for the accurate and efficient solution of the plastic buckling problem of structures. This is achieved by a Sturm sequence method employing a bisection strategy, which eliminates the need for having to solve the buckling eigenvalue problem at each incremental (decremental) loading stage that is associated with the usual solution techniques. The plastic buckling mode shape is determined by a simple inverse iteration process, once the buckling load has been established. Numerical results are presented for plate problems with various edge conditions. The resulting computer program written in FORTRAN V for the JPL UNIVAC 1108 machine proves to be most economical in comparison with other existing methods of such analysis.
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.
NASA Technical Reports Server (NTRS)
Heard, W. L., Jr.; Anderson, M. S.; Slysh, P.
1976-01-01
An engineering procedure is presented for calculating the compressive buckling strength of isogrid cylinders using shell of revolution techniques and accounting for loading beyond the material proportional limit and/or local buckling of the skin prior to general buckling. A general nondimensional chart is presented which can be used in conjunction with formulas based on simple deformation plasticity theory to calculate postbuckling stiffnesses of the skin. The stiffening grid system is treated as an equivalent isotropic grid layer. Stiffnesses are determined for this grid layer, when loaded beyond the proportional limit, by the same plasticity theory used for the skin and a nonlinear stress-strain curve constructed from simple isogrid-handbook formulas and standard-reference-manual stress-strain curves for the material involved. Comparison of prebuckling strains and buckling results obtained by this procedure with data from a large isogrid-cylinder test is excellent with the calculated buckling load no more than 4 percent greater than the test value.
Modifying PASVART to solve singular nonlinear 2-point boundary problems
NASA Technical Reports Server (NTRS)
Fulton, James P.
1988-01-01
To study the buckling and post-buckling behavior of shells and various other structures, one must solve a nonlinear 2-point boundary problem. Since closed-form analytic solutions for such problems are virtually nonexistent, numerical approximations are inevitable. This makes the availability of accurate and reliable software indispensable. In a series of papers Lentini and Pereyra, expanding on the work of Keller, developed PASVART: an adaptive finite difference solver for nonlinear 2-point boundary problems. While the program does produce extremely accurate solutions with great efficiency, it is hindered by a major limitation. PASVART will only locate isolated solutions of the problem. In buckling problems, the solution set is not unique. It will contain singular or bifurcation points, where different branches of the solution set may intersect. Thus, PASVART is useless precisely when the problem becomes interesting. To resolve this deficiency we propose a modification of PASVART that will enable the user to perform a more complete bifurcation analysis. PASVART would be combined with the Thurston bifurcation solution: as adaptation of Newton's method that was motivated by the work of Koiter 3 are reinterpreted in terms of an iterative computational method by Thurston.
BOOK REVIEW: Nonlinear Continuum Mechanics for Finite Element Analysis
NASA Astrophysics Data System (ADS)
Bialek, James M.
1998-05-01
Nonlinear continuum mechanics of solids is a fascinating subject. All the assumptions inherited from an overexposure to linear behaviour and analysis must be re-examined. The standard definitions of strain designed for small deformation linear problems may be totally misleading when finite motion or large deformations are considered. Nonlinear behaviour includes phenomena like `snap-through', where bifurcation theory is applied to engineering design. Capabilities in this field are growing at a fantastic speed; for example, modern automobiles are presently being designed to crumple in the most energy absorbing manner in order to protect the occupants. The combination of nonlinear mechanics and the finite element method is a very important field. Most engineering designs encountered in the fusion effort are strictly limited to small deformation linear theory. In fact, fusion devices are usually kept in the low stress, long life regime that avoids large deformations, nonlinearity and any plastic behaviour. The only aspect of nonlinear continuum solid mechanics about which the fusion community now worries is that rare case where details of the metal forming process must be considered. This text is divided into nine sections: introduction, mathematical preliminaries, kinematics, stress and equilibrium, hyperelasticity, linearized equilibrium equations, discretization and solution, computer implementation and an appendix covering an introduction to large inelastic deformations. The authors have decided to use vector and tensor notation almost exclusively. This means that the usual maze of indicial equations is avoided, but most readers will therefore be stretched considerably to follow the presentation, which quickly proceeds to the heart of nonlinear behaviour in solids. With great speed the reader is led through the material (Lagrangian) and spatial (Eulerian) co-ordinates, the deformation gradient tensor (an example of a two point tensor), the right and left Cauchy
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
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
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
Vibration and buckling of super elliptical plates
NASA Astrophysics Data System (ADS)
Wang, C. M.; Wang, L.; Liew, K. M.
1994-03-01
This paper is concerned with the vibration and buckling of a new class of plates, the periphery shape of which is defined by a super elliptical function. Such a plate shape has practical applications, as the advantageous curved corners help to diffuse stress concentrations. The loading considered for the buckling problem is that of in-plane uniform pressure along the periphery. Accurate frequency and buckling factors are tabulated for such plates with either simply supported or clamped edges. The solutions are obtained using the pb - 2 Rayleigh-Ritz method.
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.
NASA Astrophysics Data System (ADS)
Haddadzadeh Hendou, Ramtin; Karami Mohammadi, Ardeshir
2014-11-01
In this paper an Euler-Bernoulli model has been used for vibration analysis of micro-beams with large transverse deflection. Thermoelastic damping is considered to be the dominant damping mechanism and introduced as imaginary stiffness into the equation of motion by evaluating temperature profile as a function of lateral displacement. The obtained equation of motion is analyzed in the case of pure single mode motion by two methods; nonlinear normal mode theory and the Galerkin procedure. In contrast with the Galerkin procedure, nonlinear normal mode analysis introduces a nonconventional nonlinear damping term in modal oscillator which results in strong damping in case of large amplitude vibrations. Evaluated modal oscillators are solved using harmonic balance method and tackling damping terms introduced as an imaginary stiffness is discussed. It has been shown also that nonlinear modal analysis of micro-beam with thermoelastic damping predicts parameters such as inverse quality factor, and frequency shift, to have an extrema point at certain amplitude during transient response due to the mentioned nonlinear damping term; and the effect of system's characteristics on this critical amplitude has also been discussed.
Carnivorous Utricularia: the buckling scenario.
Vincent, Olivier; Marmottant, Philippe
2011-11-01
We review recent results about the functioning of aquatic carnivorous traps from the genus Utricularia. The use of high speed cameras has helped to elucidate the mechanism at the origin of the ultra fast capture process of Utricularia, at a millisecond time scale. As water is pumped out of the trap, pressure decreases inside the trap and elastic energy is stored due to the change of shape of the trap body. This energy is suddenly released when the trap is fired: the trap door undergoes an elastical instability--buckling--which allows its fast and passive opening and closure. This mechanism is used by Utricularia both to catch preys touching its trigger hairs and to fire spontaneously at regular time intervals. The results leading to this interpretation are reviewed and discussed and suggestions for further work are briefly presented.
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.
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.
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.
Hybrid perturbation/Bubnov-Galerkin technique for nonlinear thermal analysis
NASA Technical Reports Server (NTRS)
Noor, A. K.; Balch, C. D.
1983-01-01
A two step hybrid analysis technique to predict the nonlinear steady state temperature distribution in structures and solids is presented. The technique is based on the regular perturbation expansion and the classical Bubnov-Galerkin approximation. The functions are obtained by using the regular perturbation method. These functions are selected as coordinate functions and the classical Bubnov-Galerkin technique is used to compute their amplitudes. The potential of the proposed hybrid technique for the solution of nonlinear thermal problems is discussed. The effectiveness of this technique is demonstrated by the effects of conduction, convection, and radiation modes of heat transfer. It is indicated that the hybrid technique overcomes the two major drawbacks of the classical techniques: (1) the requirement of using a small parameter in the regular perturbation method; and (2) the arbitrariness in the choice of the coordinate functions in the Bubnov-Galerkin technique. The proposed technique extends the range of applicability of the regular perturbation method and enhances the effectiveness of the Bubnov-Galerkin technique.
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.
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.
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.
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.
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.
Use of quadratic components for buckling calculations
Dohrmann, C.R.; Segalman, D.J.
1996-12-31
A buckling calculation procedure based on the method of quadratic components is presented. Recently developed for simulating the motion of rotating flexible structures, the method of quadratic components is shown to be applicable to buckling problems with either conservative or nonconservative loads. For conservative loads, stability follows from the positive definiteness of the system`s stiffness matrix. For nonconservative loads, stability is determined by solving a nonsymmetric eigenvalue problem, which depends on both the stiffness and mass distribution of the system. Buckling calculations presented for a cantilevered beam are shown to compare favorably with classical results. Although the example problem is fairly simple and well-understood, the procedure can be used in conjunction with a general-purpose finite element code for buckling calculations of more complex systems.
Thermal-structural panel buckling tests
NASA Astrophysics Data System (ADS)
Thompson, Randolph C.; Richards, W. L.
A titanium-matrix-composite (TMC) hat-stiffened panel of 61 cm sq area and 3.175 cm thick was nondestructively tested to 649 C to examine its buckling characteristics. Compressive loads were applied to the panel in a 978.6 kN uniaxial load frame system. High-temperature testing was performed using quartz lamp heating. A single-strain-age force/stiffness buckling prediction technique was developed to predict panel buckling loads. For the monolithic panel, these test predictions correlated within 10 percent with a finite-element buckling analyses performed elsewhere. Comparisons between force/stiffness predictions and analyses for the TMC panel are in progress.
Thermal-structural panel buckling tests
NASA Technical Reports Server (NTRS)
Thompson, Randolph C.; Richards, W. L.
1991-01-01
A titanium-matrix-composite (TMC) hat-stiffened panel of 61 cm sq area and 3.175 cm thick was nondestructively tested to 649 C to examine its buckling characteristics. Compressive loads were applied to the panel in a 978.6 kN uniaxial load frame system. High-temperature testing was performed using quartz lamp heating. A single-strain-age force/stiffness buckling prediction technique was developed to predict panel buckling loads. For the monolithic panel, these test predictions correlated within 10 percent with a finite-element buckling analyses performed elsewhere. Comparisons between force/stiffness predictions and analyses for the TMC panel are in progress.
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.
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.
Probability bounds analysis for nonlinear population ecology models.
Enszer, Joshua A; Andrei Măceș, D; Stadtherr, Mark A
2015-09-01
Mathematical models in population ecology often involve parameters that are empirically determined and inherently uncertain, with probability distributions for the uncertainties not known precisely. Propagating such imprecise uncertainties rigorously through a model to determine their effect on model outputs can be a challenging problem. We illustrate here a method for the direct propagation of uncertainties represented by probability bounds though nonlinear, continuous-time, dynamic models in population ecology. This makes it possible to determine rigorous bounds on the probability that some specified outcome for a population is achieved, which can be a core problem in ecosystem modeling for risk assessment and management. Results can be obtained at a computational cost that is considerably less than that required by statistical sampling methods such as Monte Carlo analysis. The method is demonstrated using three example systems, with focus on a model of an experimental aquatic food web subject to the effects of contamination by ionic liquids, a new class of potentially important industrial chemicals.
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.
Nonlinear analysis of anesthesia dynamics by Fractal Scaling Exponent.
Gifani, P; Rabiee, H R; Hashemi, M R; Taslimi, P; Ghanbari, M
2006-01-01
The depth of anesthesia estimation has been one of the most research interests in the field of EEG signal processing in recent decades. In this paper we present a new methodology to quantify the depth of anesthesia by quantifying the dynamic fluctuation of the EEG signal. Extraction of useful information about the nonlinear dynamic of the brain during anesthesia has been proposed with the optimum Fractal Scaling Exponent. This optimum solution is based on the best box sizes in the Detrended Fluctuation Analysis (DFA) algorithm which have meaningful changes at different depth of anesthesia. The Fractal Scaling Exponent (FSE) Index as a new criterion has been proposed. The experimental results confirm that our new Index can clearly discriminate between aware to moderate and deep anesthesia levels. Moreover, it significantly reduces the computational complexity and results in a faster reaction to the transients in patients' consciousness levels in relations with the other algorithms.
Discriminative Non-Linear Stationary Subspace Analysis for Video Classification.
Baktashmotlagh, Mahsa; Harandi, Mehrtash; Lovell, Brian C; Salzmann, Mathieu
2014-12-01
Low-dimensional representations are key to the success of many video classification algorithms. However, the commonly-used dimensionality reduction techniques fail to account for the fact that only part of the signal is shared across all the videos in one class. As a consequence, the resulting representations contain instance-specific information, which introduces noise in the classification process. In this paper, we introduce non-linear stationary subspace analysis: a method that overcomes this issue by explicitly separating the stationary parts of the video signal (i.e., the parts shared across all videos in one class), from its non-stationary parts (i.e., the parts specific to individual videos). Our method also encourages the new representation to be discriminative, thus accounting for the underlying classification problem. We demonstrate the effectiveness of our approach on dynamic texture recognition, scene classification and action recognition. PMID:26353144
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.
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
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.
NASA Astrophysics Data System (ADS)
Xiong, Liuyang; Tang, Lihua; Ding, Hu; Chen, Liqun; Mace, Brian
2016-04-01
Nonlinear internal resonance mechanism is exploited in piezoelectric vibration energy harvesting (PVEH) for the purpose of broadening the resonance band. Conventional linear energy harvester has narrow operating bandwidth. In this research, a buckled piezoelectric beam structure with preload under transverse excitation is investigated to demonstrate the superiority of internal resonance. The condition for 2:1 internal resonance could be established by truncating the continuum beam with geometrical nonlinearity. Integro-partial-differential equations are derived for governing transverse motion measured from a stable equilibrium position. At specific initial axial compressive force, two modes are coupled through the internal resonance interaction. For weak nonlinear perturbations, multiple scales method is used to explore the amplitude-frequency responses of the buckled beam system under primary resonance with 2:1 internal resonance. Numerical examples demonstrate that the resonance bandwidth is broadened thanks to the coexistence of softening and hardening nonlinear characteristics. Moreover, validity of the approximate analytical method is demonstrated by comparing with simulation. Furthermore, the optimal resistance is discussed with a pure resistive load. This research on the internal resonance of buckled beam provides a basis for structure design and optimization in broadband PVEH.
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.
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.
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
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.
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.
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.
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.
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.
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.
Nonlinear Time Series Analysis of White Dwarf Light Curves
NASA Astrophysics Data System (ADS)
Jevtic, N.; Zelechoski, S.; Feldman, H.; Peterson, C.; Schweitzer, J.
2001-12-01
We use nonlinear time series analysis methods to examine the light intensity curves of white dwarf PG1351+489 obtained by the Whole Earth Telescope (WET). Though these methods were originally introduced to study chaotic systems, when a clear signature of determinism is found for the process generating an observable and it couples the active degrees of freedom of the system, then the notion of phase space provides a framework for exploring the system dynamics of nonlinear systems in general. With a pronounced single frequency, its harmonics and other frequencies of lower amplitude on a broadband background, the PG1351 light curve lends itself to the use of time delay coordinates. Our phase space reconstruction yields a triangular, toroidal three-dimensional shape. This differs from earlier results of a circular toroidal representation. We find a morphological similarity to a magnetic dynamo model developed for fast rotators that yields a union of both results: the circular phase space structure for the ascending portion of the cycle, and the triangular structure for the declining portion. The rise and fall of the dynamo cycle yield both different phase space representations and different correlation dimensions. Since PG1351 is known to have no significant fields, these results may stimulate the observation of light curves of known magnetic white dwarfs for comparison. Using other data obtained by the WET, we compare the phase space reconstruction of DB white dwarf PG1351 with that of GD 358 which has a more complex power spectrum. We also compare these results with those for PG1159. There is some general similarity between the results of the phase space reconstruction for the DB white dwarfs. As expected, the difference between the results for the DB white dwarfs and PG1159 is great.
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…
Robust simulation of buckled structures using reduced order modeling
NASA Astrophysics Data System (ADS)
Wiebe, R.; Perez, R. A.; Spottswood, S. M.
2016-09-01
Lightweight metallic structures are a mainstay in aerospace engineering. For these structures, stability, rather than strength, is often the critical limit state in design. For example, buckling of panels and stiffeners may occur during emergency high-g maneuvers, while in supersonic and hypersonic aircraft, it may be induced by thermal stresses. The longstanding solution to such challenges was to increase the sizing of the structural members, which is counter to the ever present need to minimize weight for reasons of efficiency and performance. In this work we present some recent results in the area of reduced order modeling of post- buckled thin beams. A thorough parametric study of the response of a beam to changing harmonic loading parameters, which is useful in exposing complex phenomena and exercising numerical models, is presented. Two error metrics that use but require no time stepping of a (computationally expensive) truth model are also introduced. The error metrics are applied to several interesting forcing parameter cases identified from the parametric study and are shown to yield useful information about the quality of a candidate reduced order model. Parametric studies, especially when considering forcing and structural geometry parameters, coupled environments, and uncertainties would be computationally intractable with finite element models. The goal is to make rapid simulation of complex nonlinear dynamic behavior possible for distributed systems via fast and accurate reduced order models. This ability is crucial in allowing designers to rigorously probe the robustness of their designs to account for variations in loading, structural imperfections, and other uncertainties.
Telephone cord buckles-A relation between wavelength and adhesion
NASA Astrophysics Data System (ADS)
Faou, Jean-Yvon; Parry, Guillaume; Grachev, Sergey; Barthel, Etienne
2015-02-01
Thin films with low adhesion and large residual stresses may buckle. The resulting morphologies are varied, but one of the most commonly observed is an intriguing oscillating pattern - the so-called "telephone cord" - which has been extensively investigated in the recent years. We have studied the kinematics of formation of telephone cords using a geometrically non-linear plate model and mode dependent interfacial toughness, captured via a cohesive zone. Through extensive Finite Element Simulations, we have demonstrated a simple, non-trivial relation between telephone cord wavelength and interfacial toughness. To validate this prediction, highly stressed Mo thin films were deposited on Si wafers, with a well defined interface and very reproducible adhesion. Studying the morphology of the resulting buckles for different film thicknesses and stresses, we observed a trend which was fully consistent with our simulation results. From the data fit, an adhesion energy of 0.58±0.04 J m-2 for the SiO2/Ag interface was inferred, which compares well with literature estimates.
Flutter of buckled shape memory alloy reinforced laminates
NASA Astrophysics Data System (ADS)
Kuo, Shih-Yao; Shiau, Le-Chung; Lai, Chin-Hsin
2012-03-01
The effect of shape memory alloys (SMA) on the linear and nonlinear flutter behaviors of buckled cross-ply and angle-ply laminates was investigated in the frequency and time domains using the finite element method. In particular, this study takes the first move toward examining the effect of varying the SMA fiber spacing. Von Karman large deformation assumptions and quasi-steady aerodynamic theory were employed. The flutter boundary, stability boundary, time history response, and phase plane plots of SMA reinforced cross-ply and angle-ply laminates are presented. The numerical results show that increase in the SMA fiber volume fraction and prestrain may generate more recovery stress, and increase the stiffness of the SMA reinforced laminates. Therefore, the flutter boundary and critical load of the plate may be increased significantly. All five types of panel behavior, namely flat, buckled, limit-cycle, periodic, and chaotic motion, are clearly displayed and successively identified. This study sheds light on improving the flutter boundary efficiently by increasing the SMA fiber volume fraction to reinforce the center of the plate.
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 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.
Independent vector analysis using subband and subspace nonlinearity
NASA Astrophysics Data System (ADS)
Na, Yueyue; Yu, Jian; Chai, Bianfang
2013-12-01
Independent vector analysis (IVA) is a recently proposed technique, an application of which is to solve the frequency domain blind source separation problem. Compared with the traditional complex-valued independent component analysis plus permutation correction approach, the largest advantage of IVA is that the permutation problem is directly addressed by IVA rather than resorting to the use of an ad hoc permutation resolving algorithm after a separation of the sources in multiple frequency bands. In this article, two updates for IVA are presented. First, a novel subband construction method is introduced, IVA will be conducted in subbands from high frequency to low frequency rather than in the full frequency band, the fact that the inter-frequency dependencies in subbands are stronger allows a more efficient approach to the permutation problem. Second, to improve robustness and against noise, the IVA nonlinearity is calculated only in the signal subspace, which is defined by the eigenvector associated with the largest eigenvalue of the signal correlation matrix. Different experiments were carried out on a software suite developed by us, and dramatic performance improvements were observed using the proposed methods. Lastly, as an example of real-world application, IVA with the proposed updates was used to separate vibration components from high-speed train noise data.
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.
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.
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: Catastrophe Theory Modeling and Cobb's Cusp Surface Analysis Program.
ERIC Educational Resources Information Center
Allen, Bradford D.; Carifio, James
1995-01-01
Cobb's Cusp Surface Analysis Program (CUSP) provides a way to estimate empirically and test a nonlinear cusp catastrophe model. A model of emotion during problem solving is used to introduce catastrophe theory modeling and is discussed in conjunction with how to run and interpret CUSP. (SLD)
The static nonlinear analysis of shells of revolution (SNASOR II)
NASA Technical Reports Server (NTRS)
Stricklin, J. A.; Haisler, W. E.
1974-01-01
Utilizing stiffness matrices and supplying as input the loading and boundary conditions, program generates equilibrium equations for structure. Nonlinear strain energy terms result in pseudogeneralized forces which are combined with applied generalized forces. Resulting set of nonlinear algebraic equilibrium equations is solved by one of several methods.
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
Mathematical Methods in Wave Propagation: Part 2--Non-Linear Wave Front Analysis
ERIC Educational Resources Information Center
Jeffrey, Alan
1971-01-01
The paper presents applications and methods of analysis for non-linear hyperbolic partial differential equations. The paper is concluded by an account of wave front analysis as applied to the piston problem of gas dynamics. (JG)
Buckling instability in ordered bacterial colonies
NASA Astrophysics Data System (ADS)
Boyer, Denis; Mather, William; Mondragón-Palomino, Octavio; Orozco-Fuentes, Sirio; Danino, Tal; Hasty, Jeff; Tsimring, Lev S.
2011-04-01
Bacterial colonies often exhibit complex spatio-temporal organization. This collective behavior is affected by a multitude of factors ranging from the properties of individual cells (shape, motility, membrane structure) to chemotaxis and other means of cell-cell communication. One of the important but often overlooked mechanisms of spatio-temporal organization is direct mechanical contact among cells in dense colonies such as biofilms. While in natural habitats all these different mechanisms and factors act in concert, one can use laboratory cell cultures to study certain mechanisms in isolation. Recent work demonstrated that growth and ensuing expansion flow of rod-like bacteria Escherichia coli in confined environments leads to orientation of cells along the flow direction and thus to ordering of cells. However, the cell orientational ordering remained imperfect. In this paper we study one mechanism responsible for the persistence of disorder in growing cell populations. We demonstrate experimentally that a growing colony of nematically ordered cells is prone to the buckling instability. Our theoretical analysis and discrete-element simulations suggest that the nature of this instability is related to the anisotropy of the stress tensor in the ordered cell colony.
Buckled diamond-like carbon nanomechanical resonators
NASA Astrophysics Data System (ADS)
Tomi, Matti; Isacsson, Andreas; Oksanen, Mika; Lyashenko, Dmitry; Kaikkonen, Jukka-Pekka; Tervakangas, Sanna; Kolehmainen, Jukka; Hakonen, Pertti J.
2015-08-01
We have developed capacitively-transduced nanomechanical resonators using sp2-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.We have developed capacitively-transduced nanomechanical resonators using sp2-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. Electronic supplementary information (ESI) available: Detailed transmission measurements, discussion about mechanical contacts and surface roughness, derivation of the equations describing the eigenspectrum of a buckled beam under electrostatic load. See DOI: 10.1039/c5nr02820e
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.
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)
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.
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
Fast nonlinear regression method for CT brain perfusion analysis.
Bennink, Edwin; Oosterbroek, Jaap; Kudo, Kohsuke; Viergever, Max A; Velthuis, Birgitta K; de Jong, Hugo W A M
2016-04-01
Although computed tomography (CT) perfusion (CTP) imaging enables rapid diagnosis and prognosis of ischemic stroke, current CTP analysis methods have several shortcomings. We propose a fast nonlinear regression method with a box-shaped model (boxNLR) that has important advantages over the current state-of-the-art method, block-circulant singular value decomposition (bSVD). These advantages include improved robustness to attenuation curve truncation, extensibility, and unified estimation of perfusion parameters. The method is compared with bSVD and with a commercial SVD-based method. The three methods were quantitatively evaluated by means of a digital perfusion phantom, described by Kudo et al. and qualitatively with the aid of 50 clinical CTP scans. All three methods yielded high Pearson correlation coefficients ([Formula: see text]) with the ground truth in the phantom. The boxNLR perfusion maps of the clinical scans showed higher correlation with bSVD than the perfusion maps from the commercial method. Furthermore, it was shown that boxNLR estimates are robust to noise, truncation, and tracer delay. The proposed method provides a fast and reliable way of estimating perfusion parameters from CTP scans. This suggests it could be a viable alternative to current commercial and academic methods. PMID:27413770
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.
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.
Analytic Sensitivity and Approximation of Skin Buckling Constraints in Wing-Shape Synthesis
NASA Technical Reports Server (NTRS)
Livne, Eli; Milosavljevic, Radomir
1995-01-01
Explicit expressions for terms of the stiffness and geometric stiffness matrices are derived for the buckling analysis of trapezoidal fiber composite wing skin panels. The formulation is based on Ritz analysis using simple polynomials, and leads to explicit expressions for the analytic sensitivities of the stiffness and geometric stiffness matrices with respect to layer thickness, fiber directions, and panel shape. Integration with wing box analysis using either the equivalent plate approach or the finite element method, makes it possible to obtain sensitivities of panel buckling constraints with respect to wing planform shape or locations of internal ribs and spars. The analytic sensitivities are used to construct approximations of panel buckling constraints for integrated wing/panel design synthesis.
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
Elastoswellability: Will it bend or will it buckle?
NASA Astrophysics Data System (ADS)
Holmes, Douglas; Pandey, Anupam
2013-03-01
Soft mechanical structures such as biological tissues and gels exhibit motion, instabilities, and large morphological changes when subjected to external stimuli. Swelling is a robust approach for inducing structural change as it occurs naturally in humid environments and can be easily adapted for industrial design. Small volumes of fluid that interact favorably with a material can cause large, dramatic, and geometrically nonlinear deformations including beam bending, plate buckling, and surface wrinkling. In this talk we address an overarching question regarding swelling-induced deformations: will the structural change occur globally, or will it be confined to the material's surface? We introduce a materials and geometry defined transition point that describes a fluid-structure's characteristic ``elastoswellability'' lengthscale. By locally swelling unconstrained slender beams and plates with solvents of varying solubility, we identify a transition between local surface wrinkling and global structural bending.
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.
Buckling instability in amorphous carbon films
NASA Astrophysics Data System (ADS)
Zhu, X. D.; Narumi, K.; Naramoto, H.
2007-06-01
In this paper, we report the buckling instability in amorphous carbon films on mirror-polished sapphire (0001) wafers deposited by ion beam assisted deposition at various growth temperatures. For the films deposited at 150 °C, many interesting stress relief patterns are found, which include networks, blisters, sinusoidal patterns with π-shape, and highly ordered sinusoidal waves on a large scale. Starting at irregular buckling in the centre, the latter propagate towards the outer buckling region. The maximum length of these ordered patterns reaches 396 µm with a height of ~500 nm and a wavelength of ~8.2 µm. However, the length decreases dramatically to 70 µm as the deposition temperature is increased to 550 °C. The delamination of the film appears instead of sinusoidal waves with a further increase of the deposition temperature. This experimental observation is correlated with the theoretic work of Crosby (1999 Phys. Rev. E 59 R2542).
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.
Nonlinear analysis of a simply-supported composite beam under random excitations
Eslami, H.; Gudmundson, S.
1994-12-31
Nonlinear analysis of composite laminated beams subjected-to random excitation is studied here. The forcing function is a stationary Gaussian type random excitation. The governing partial differential equations of motion are obtained by considering the Von Karman type geometrical nonlinearity. These partial differential equations are transformed into nonlinear Ordinary differential equations of Duffing type by applying the Galerkin`s method. The resulting nonlinear ODE are first solved by using the equivalent linearization method and the numerical integration (Runge Kutta) method. The equations are reduced to that of isotropic beam and results are also compared with the previously published ones.
NASA Astrophysics Data System (ADS)
Zhu, F. H.; Fu, Y. M.
2008-12-01
By considering the effect of interfacial damage and using the variation principle, three-dimensional nonlinear dynamic governing equations of the laminated plates with interfacial damage are derived based on the general six-degrees-of-freedom plate theory towards the accurate stress analysis. The solutions of interlaminar stress and nonlinear dynamic response for a simply supported laminated plate with interfacial damage are obtained by using the finite difference method, and the results are validated by comparison with the solution of nonlinear finite element method. In numerical calculations, the effects of interfacial damage on the stress in the interface and the nonlinear dynamic response of laminated plates are discussed.
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.
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.
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 %.
Selective buckling via states of self-stress in topological metamaterials.
Paulose, Jayson; Meeussen, Anne S; Vitelli, Vincenzo
2015-06-23
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.
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 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.
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…
Nonlinear System Of Equations For Multicomponent Analysis Of Artificial Food Coloring
NASA Astrophysics Data System (ADS)
Santosa, I. E.; Budiasih, L. K.
2010-12-01
In multicomponent analysis of artificial food coloring (AFC), nonlinear relation of the absorbance and the concentration forms a nonlinear system of equations. The Newton's method based algorithm has been used to calculate individual AFC concentration in the mixture of two AFCs. The absorbance was measured using a spectrophotometer at two different wavelengths.
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
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.
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.
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
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
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.
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
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.
Simple models for quorum sensing: Nonlinear dynamical analysis
NASA Astrophysics Data System (ADS)
Chiang, Wei-Yin; Li, Yue-Xian; Lai, Pik-Yin
2011-10-01
Quorum sensing refers to the change in the cooperative behavior of a collection of elements in response to the change in their population size or density. This behavior can be observed in chemical and biological systems. These elements or cells are coupled via chemicals in the surrounding environment. Here we focus on the change of dynamical behavior, in particular from quiescent to oscillatory, as the cell population changes. For instance, the silent behavior of the elements can become oscillatory as the system concentration or population increases. In this work, two simple models are constructed that can produce the essential representative properties in quorum sensing. The first is an excitable or oscillatory phase model, which is probably the simplest model one can construct to describe quorum sensing. Using the mean-field approximation, the parameter regime for quorum sensing behavior can be identified, and analytical results for the detailed dynamical properties, including the phase diagrams, are obtained and verified numerically. The second model consists of FitzHugh-Nagumo elements coupled to the signaling chemicals in the environment. Nonlinear dynamical analysis of this mean-field model exhibits rich dynamical behaviors, such as infinite period bifurcation, supercritical Hopf, fold bifurcation, and subcritical Hopf bifurcations as the population parameter changes for different coupling strengths. Analytical result is obtained for the Hopf bifurcation phase boundary. Furthermore, two elements coupled via the environment and their synchronization behavior for these two models are also investigated. For both models, it is found that the onset of oscillations is accompanied by the synchronized dynamics of the two elements. Possible applications and extension of these models are also discussed.
Post buckling behaviour of stiffened composite panels loaded in cyclic compression and shear
NASA Astrophysics Data System (ADS)
Segal, A.; Frostig, Y.; Shalev, D.; Weller, T.; Sheinman, Y.
1993-02-01
This paper presents the summary of a multiphase experimental - analytical study of the post-buckling mechanical behavior of a graphite/epoxy integrally stiffened panel. The first phase of the study included cyclic compression tests in the post-buckling regime of flat panels stiffened by either 'I' or 'J' shaped stiffeners. Static residual strength of the panels after 250,000 cycles was greater than the reference strength; however, some stiffness loss was observed. A series of tests of individual stiffeners, identical to those in the panels, was also carried out and the results showed the same trends as had been observed in the panels. There were no cases of early failure during the cyclic tests. The second phase included an experimental study of the post-buckling behavior of cylindrical panels integrally stiffened in the axial and transverse directions. Panels were tested in cyclic compression, cyclic torsion, and in combinations of both. The panels were stressed through 40,000 cycles, damage was inflicted, and an additional 40,000 cycles were imposed. No damage development was observed. The third phase of the study included an analytical effort for the development of a computer code, PBCOMP, for the buckling and post-buckling analysis of stiffened laminated flat and curved panels. The results of this study clearly show a great potential for the safe use of stiffened graphite/epoxy panels in aircraft structures.
Buckling behavior of long symmetrically laminated plates subjected to combined loadings
NASA Technical Reports Server (NTRS)
Nemeth, Michael P.
1992-01-01
A parametric study is presented of the buckling behavior of infinitely long, symmetrically laminated anisotropic plates subjected to combined loadings. The loading conditions considered are axial tension and compression transverse tension and compression, and shear. Results obtained using a special-purpose analysis, well-suited for parametric studies, are presented for clamped and simply supported plates. Moreover, results are presented for some common laminate constructions, and generic buckling design charts are presented for a wide range of parameters. The generic design charts are presented in terms of useful nondimensional parameters, and the dependence of the nondimensional parameters on laminate fiber orientation, stacking sequence, and material properties is discussed. An important finding of the study is that the effects of anisotropy are much more pronounced in shear-loaded plates than in compression-loaded plates. In addition, the effects of anisotropy on plates subjected to combined loadings are generally manifested as a phase shift of self-similar buckling interaction curves. A practical application of this phase shift is that the buckling resistance of long plates can be improved by applying a shear loading with a specific orientation. In all cases considered in the study, the buckling coefficients of infinitely long plates are found to be independent of the bending stiffness ratio (D sub 11/D sub 22)(1/4).
Buckling behavior of long symmetrically laminated plates subjected to combined loads
NASA Technical Reports Server (NTRS)
Nemeth, Michael P.
1992-01-01
A parametric study of the buckling behavior of infinitely long symmetrically laminated anisotropic plates subjected to combined loadings is presented. The loading conditions considered are axial tension and compression, transverse tension and compression, and shear. Results obtained using a special purpose analysis, well suited for parametric studies are presented for clamped and simply supported plates. Moreover, results are presented for some common laminate constructions, and generic buckling design charts are presented for a wide range of parameters. The generic design charts are presented in terms of useful nondimensional parameters, and dependence of the nondimensional parameters on laminate fiber orientation, stacking sequence, and material properties is discussed. An important finding of the study is that the effects of anisotropy are much more pronounced in shear-loaded plates than in compression loaded plates. In addition, the effects of anisotropy on plates subjected to combined loadings are generally manifested as a phase shift of self-similar buckling interaction curves. A practical application of this phase shift is the buckling resistance of long plates can be improved by applying a shear loading with a specific orientation. In all cases considered, it is found that the buckling coefficients of infinitely long plates are independent of the bending stiffness ratio (D sub 11/D sub 22) sup 1/4.
Nonlinear aeroelastic analysis of airfoils: bifurcation and chaos
NASA Astrophysics Data System (ADS)
Lee, B. H. K.; Price, S. J.; Wong, Y. S.
1999-04-01
Different types of structural and aerodynamic nonlinearities commonly encountered in aeronautical engineering are discussed. The equations of motion of a two-dimensional airfoil oscillating in pitch and plunge are derived for a structural nonlinearity using subsonic aerodynamics theory. Three classical nonlinearities, namely, cubic, freeplay and hysteresis are investigated in some detail. The governing equations are reduced to a set of ordinary differential equations suitable for numerical simulations and analytical investigation of the system stability. The onset of Hopf-bifurcation, and amplitudes and frequencies of limit cycle oscillations are investigated, with examples given for a cubic hardening spring. For various geometries of the freeplay, bifurcations and chaos are discussed via the phase plane, Poincaré maps, and Lyapunov spectrum. The route to chaos is investigated from bifurcation diagrams, and for the freeplay nonlinearity it is shown that frequency doubling is the most commonly observed route. Examples of aerodynamic nonlinearities arising from transonic flow and dynamic stall are discussed, and special attention is paid to numerical simulation results for dynamic stall using a time-synthesized method for the unsteady aerodynamics. The assumption of uniform flow is usually not met in practice since perturbations in velocities are encountered in flight. Longitudinal atmospheric turbulence is introduced to show its effect on both the flutter boundary and the onset of Hopf-bifurcation for a cubic restoring force.
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.
Sasanpour, Pezhman; Shahmansouri, Afsaneh; Rashidian, Bizhan
2010-11-01
Third order nonlinear effects and its enhancement in gold nanostructures has been numerically studied. Analysis method is based on computationally solving nonlinear Maxwell's equations, considering dispersion behavior of permittivity described by Drude model and third order nonlinear susceptibility. Simulation is done by method of nonlinear finite difference time domain method, in which nonlinear equations of electric field are solved by Newton-Raphshon method. As the main outcomes of third order nonlinear susceptibility, four wave mixing and third harmonic generation terms are produced around gold nanostructures. Results of analysis on different geometries and structures show that third order nonlinearity products are more enhanced in places where electric field enhancement is occurred due to surface plasmons. Results indicates that enhancement of nonlinearities is strongly occurred in structures whose interface is dielectric. According to analysis results, nonlinear effects are highly concentrated in the vicinity of nanostructures. Hence this approach can be used in applications where localized ultraviolet light is required.
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
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.
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.
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.
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.
Buckling modes of elastic thin films on elastic substrates
NASA Astrophysics Data System (ADS)
Mei, Haixia; Huang, Rui; Chung, Jun Young; Stafford, Christopher M.; Yu, Hong-Hui
2007-04-01
Two buckling modes have been observed in thin films: buckle delamination and wrinkling. This letter identifies the conditions for selecting the favored buckling modes for elastic films on elastic substrates. Transition from one buckling mode to another is predicted as the stiffness ratio between the substrate and the film or is predicted for variation of the stiffness ratio between the substrate and the film or variation of theinterfacial defect size. The theoretical results are demonstrated experimentally by observing the coexistence of both buckling modes and mode transition in one film-substrate system.
Stability analysis and limit cycle in fractional system with Brusselator nonlinearities
NASA Astrophysics Data System (ADS)
Gafiychuk, V.; Datsko, B.
2008-07-01
The investigation of limit cycles in the fractional dynamical systems with Brusselator nonlinearities is considered. We present analysis of the stability domains as well as possible solutions realizing at different system parameters.
The use of non-linear analysis for differentiating the biomagnetic activity in ovarian lesions.
Anninos, P A; Anastasiadis, P; Kotini, A
1999-05-01
In this study we investigated the biomagnetic activity measured with the superconducting quantum interference device (SQUID) in benign and malignant ovarian lesions using non-linear analysis. We used a single channel biomagnetometer SQUID in order to measure the magnetic field emitted from benign and malignant ovarian lesions. We can differentiate such biomagnetic activities using non-linear analysis. Using the application of non-linear analysis in the ovarian lesions together with the use of dimensional calculations we have observed a clear saturation value for the dimension of malignant ovarian lesions and non-saturation for benign ovarian lesions. The biomagnetic measurements with the SQUID and the application of non-linear analysis in benign and malignant ovarian lesions, is a promising procedure in assessing and differentiating ovarian tumours. PMID:15512296
NASA Astrophysics Data System (ADS)
Ciampa, Francesco; Meo, Michele
2012-04-01
In this research work, an imaging method of the nonlinear signature in a reverberant complex anisotropic structure with hysteretic behaviour is reported. The proposed technique relies on a combination of phase symmetry analysis with frequency modulation excitation and nonlinear time reversal, and it is applied to a number of waveforms containing the nonlinear impulse responses of the medium. Phase symmetry analysis was used to characterize the third order nonlinearity of the structure due to delamination and cracks, by exploiting its invariant properties with the phase angle of the input waveforms. Then, a "virtual" reciprocal time reversal imaging process, using only two sensors in pitch-catch mode, was used to "illuminate" the damage. Taking advantage of multiple linear scattering, this methodology allows achieving the optimal focalization at the nonlinear source by a compensation of the distortion effects in a dissipative medium. The robustness of this technique was experimentally demonstrated on a damaged sandwich panel undergone to low-velocity impact loading. The nonlinear source was retrieved with a high level of accuracy with little computational time (less than 1 sec). Its minimal processing requirements make this method a valid alternative to the traditional nonlinear elastic wave spectroscopy techniques for materials showing either classical or non-classical nonlinear behaviour.
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)
Unilateral buckling of elastically restrained rectangular mild steel plates
NASA Astrophysics Data System (ADS)
Smith, S. T.; Bradford, M. A.; Oehlers, D. J.
This paper considers the elastic unilateral buckling of rectangular mild steel plates that are restrained elastically and subjected to bending and axial actions. A variational formulation of the Ritz method using linear combinations of harmonic functions for the buckling deformations is used to establish an eigenproblem to determine the plate local buckling coefficients. The motivation for the study is the retrofit of reinforced concrete beams by gluing and then bolting steel plates to the sides of the beam. Such plates, when acting compositely with the concrete beam, are subjected to predominantly bending and axial actions which may cause unilateral local buckling. Whereas the bolts provide complete restraint against buckling at discrete points, the glue may also inhibit local buckling between these nodal points since it acts as a continuous elastic restraint. The influence of the glue stiffness, support conditions and plate proportions on the unilateral buckling of such plates are assessed.
Dynamic nonlinear analysis of shells of revolution (DYNASOR II)
NASA Technical Reports Server (NTRS)
Tillerson, J. R.; Haisler, W. E.
1974-01-01
Equations of motion of shell are solved using Houbolt's numerical procedure with nonlinear terms being moved to right-hand side of equilibrium equations and treated as generalized loads. Program was written in FORTRAN IV for IBM 360 or CDC 6000 series computers.
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.
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.
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.
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…
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.
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.
Ultrashort laser-driven stable-buckling of blisters in chirped mirror
NASA Astrophysics Data System (ADS)
Li Chen, Shun; An Zhao, Yuan; Da Shao, Jian; Zhi Wang, Yan; Fang, Zhou; Feng Liu, Xiao; Hang Hu, Guo; Xin Leng, Yu; Xu, Yi
2013-02-01
Multilayer dielectric mirrors (niobium pentoxide/silica) were irradiated by single 800 nm-38fs laser pulses. A circular blister feature appeared in the chirped mirrors at a wide range of laser fluence, while only existed above a few percent of the damage threshold for the high-reflector. Absorptive source of laser energy can be determined by combining theoretical simulation with focused ion beam technology. Mechanical analysis with a linear-elastic buckling model reveals the blister evolution belonging to a stable-buckling process until the blister radius confined by limited laser spot size.
The buckling response of symmetrically laminated composite plates having a trapezoidal planform area
NASA Astrophysics Data System (ADS)
Radloff, H. D., II; Hyer, M. W.; Nemeth, M. P.
1994-08-01
The focus of this work is the buckling response of symmetrically laminated composite plates having a planform area in the shape of an isosceles trapezoid. The loading is assumed to be inplane and applied perpendicular to the parallel ends of the plate. The tapered edges of the plate are assumed to have simply supported boundary conditions, while the parallel ends are assumed to have either simply supported or clamped boundary conditions. A semi-analytic closed-form solution based on energy principles and the Trefftz stability criterion is derived and solutions are obtained using the Rayleigh-Ritz method. Intrinsic in this solution is a simplified prebuckling analysis which approximates the inplane force resultant distributions by the forms Nx=P/W(x) and Ny=Nxy=0, where P is the applied load and W(x) is the plate width which, for the trapezoidal planform, varies linearly with the lengthwise coordinate x. The out-of-plane displacement is approximated by a double trigonometric series. This analysis is posed in terms of four nondimensional parameters representing orthotropic and anisotropic material properties, and two nondimensional parameters representing geometric properties. For comparison purposes, a number of specific plate geometry, ply orientation, and stacking sequence combinations are investigated using the general purpose finite element code ABAQUS. Comparison of buckling coefficients calculated using the semi-analytical model and the finite element model show agreement within 5 percent, in general, and within 15 percent for the worst cases. In order to verify both the finite element and semi-analytical analyses, buckling loads are measured for graphite/epoxy plates having a wide range of plate geometries and stacking sequences. Test fixtures, instrumentation system, and experimental technique are described. Experimental results for the buckling load, the buckled mode shape, and the prebuckling plate stiffness are presented and show good agreement with the
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.
Non-linear substructure approach for dynamic analysis of rigid-flexible multibody systems
NASA Astrophysics Data System (ADS)
Liu, A. Q.; Liew, K. M.
1994-04-01
This paper presents a substructure synthesis method (SSM) for nonlinear analysis of multibody systems. The detailed derivation of the equation of motion which takes into account the geometric nonlinear effects of large rotation undergoing small strain elastic deformation is presented. Using the substructure synthesis approach, the equation of motion is condensed through the boundary conditions at the interface between the flexible and rigid substructures. As a result, equations of motion for multi-flexible-body systems including the geometric non-linear effects of large rotation are derived. To demonstrate the applicability and accuracy of the proposed approach, an example of a two-link manipulator was chosen for this presentation. The results using the linear and nonlinear models are presented to highlight the effects of geometric nonlinearities.
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.
Nonlinear dynamic mechanism of vocal tremor from voice analysis and model simulations
Zhang, Yu; Jiang, Jack J.
2009-01-01
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. PMID:22505778
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.
Mullineux, G; Hicks, B J; Berry, C
2012-04-28
Understanding what happens in terms of delamination during buckling of laminate materials is of importance across a range of engineering sectors. Normally concern is that the strength of the material is not significantly impaired. Carton-board is a material with a laminate structure and, in the initial creation of carton nets, the board is creased in order to weaken the structure. This means that when the carton is eventually folded into its three-dimensional form, correct folding occurs along the weakened crease lines. Understanding what happens during creasing and folding is made difficult by the nonlinear nature of the material properties. This paper considers a simplified approach which extends the idea of minimizing internal energy so that the effects of delamination can be handled. This allows a simulation which reproduces the form of buckling-delamination observed in practice and the form of the torque-rotation relation.
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)
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, 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
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
Nonlinear Aeroelastic Analysis of UAVs: Deterministic and Stochastic Approaches
NASA Astrophysics Data System (ADS)
Sukut, Thomas Woodrow
Aeroelastic aspects of unmanned aerial vehicles (UAVs) is analyzed by treatment of a typical section containing geometrical nonlinearities. Equations of motion are derived and numerical integration of these equations subject to quasi-steady aerodynamic forcing is performed. Model properties are tailored to a high-altitude long-endurance unmanned aircraft. Harmonic balance approximation is employed based on the steady-state oscillatory response of the aerodynamic forcing. Comparisons are made between time integration results and harmonic balance approximation. Close agreement between forcing and displacement oscillatory frequencies is found. Amplitude agreement is off by a considerable margin. Additionally, stochastic forcing effects are examined. Turbulent flow velocities generated from the von Karman spectrum are applied to the same nonlinear structural model. Similar qualitative behavior is found between quasi-steady and stochastic forcing models illustrating the importance of considering the non-steady nature of atmospheric turbulence when operating near critical flutter velocity.
Nonlinear structural analysis on distributed-memory computers
NASA Technical Reports Server (NTRS)
Watson, Brian C.; Noor, Ahmed K.
1995-01-01
A computational strategy is presented for the nonlinear static and postbuckling analyses of large complex structures on massively parallel computers. The strategy is designed for distributed-memory, message-passing parallel computer systems. The key elements of the proposed strategy are: (1) a multiple-parameter reduced basis technique; (2) a nested dissection (or multilevel substructuring) ordering scheme; (3) parallel assembly of global matrices; and (4) a parallel sparse equation solver. The effectiveness of the strategy is assessed by applying it to thermo-mechanical postbuckling analyses of stiffened composite panels with cutouts, and nonlinear large-deflection analyses of HSCT models on Intel Paragon XP/S computers. The numerical studies presented demonstrate the advantages of nested dissection-based solvers over traditional skyline-based solvers on distributed memory machines.
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.
Applications Of Nonlinear Principal Components Analysis To Behavioral Data.
Hicks, M M
1981-07-01
A quadratic function was derived from variables believed to be nonlinearly related. The method was suggested by Gnanadesikan (1977) and based on an early paper of Karl Pearson (1901) (which gave rise to principal components), in which Pearson demonstrated that a plane of best fit to a system of points could be elicited from the elements of the eigenvector associated with the smallest eigenvalue of the covariance matrix. PMID:26815595
Nonlinear analysis and prediction of pulsatile hormone secretion
Prank, K. |; Kloppstech, M.; Nowlan, S.J.; Harms, H.M.; Brabant, G.; Hesch, R.; Sejnowski, T.J.
1996-06-01
Pulsatile hormone secretion is observed in almost every hormonal system. The frequency of episodic hormone release ranges from approximately 10 to 100 pulses in 24 hours. This temporal mode of secretion is an important feature of intercellular information transfer in addition to a dose-response dependent regulation. It has been demonstrated in a number of experiments that changes in the temporal pattern of pulsatile hormone secretion specifically regulate cellular and organ function and structure. Recent evidence links osteoporosis, a disease characterized by loss of bone mass and structure, to changes in the dynamics of pulsatile parathyroid hormone (PTH) secretion. In our study we applied nonlinear and linear time series prediction to characterize the secretory dynamics of PTH in both healthy human subjects and patients with osteoporosis. Osteoporotic patients appear to lack periods of high predictability found in normal humans. In contrast to patients with osteoporosis patients with hyperparathyroidism, a condition which despite sometimes reduced bone mass has a preserved bone architecture, show periods of high predictability of PTH secretion. Using stochastic surrogate data sets which match certain statistical properties of the original time series significant nonlinear determinism could be found for the PTH time series of a group of healthy subjects. Using classical nonlinear analytical techniques we could demonstrate that the irregular pattern of pulsatile PTH secretion in healthy men exhibits characteristics of deterministic chaos. Pulsatile secretion of PTH in healthy subjects seems to be a first example of nonlinear determinism in an apparently irregular hormonal rhythm in human physiology. {copyright} {ital 1996 American Institute of Physics.}
Slave finite elements: The temporal element approach to nonlinear analysis
NASA Technical Reports Server (NTRS)
Gellin, S.
1984-01-01
A formulation method for finite elements in space and time incorporating nonlinear geometric and material behavior is presented. The method uses interpolation polynomials for approximating the behavior of various quantities over the element domain, and only explicit integration over space and time. While applications are general, the plate and shell elements that are currently being programmed are appropriate to model turbine blades, vanes, and combustor liners.
Nonlinearity correction and dispersion analysis in FMCW laser radar
NASA Astrophysics Data System (ADS)
Zhao, Hao; Liu, Bingguo; Liu, Guodong; Chen, Fengdong; Zhuang, Zhitao; Yu, Yahui; Gan, Yu
2014-12-01
Frequency Modulated Continuous Wave laser radar is one of the most important ways to measure the large-size targets , combining the advantages of laser with conventional FMCW radar. Dispersion compensation and non-linear calibration are two key aspects in FMCW laser radar measurement. The paper studies the method of frequency-sampling to correct the Nonlinearity and analyzes the importance of dispersion compensation. We set up experimental verification platform, choose 1550nm band continuously tunable external cavity infrared laser as the light source, use all-fiber optical device structures, choose balanced detectors as photoelectric conversion, and finally acquire data with high speed PCI-E data acquisition card, write a measurement software with Labview. We measured the gage block 1 meter away. The experiment results show that the frequency sampling method correct the Nonlinearity well and there is a significant impact on the accuracy because of the fiber dispersion, dispersion must be compensated to obtain high accuracy. The experiment lays the foundation for further research on FMCW Laser radar.
Nonlinear finite-element analysis of nanoindentation of viral capsids
NASA Astrophysics Data System (ADS)
Gibbons, Melissa M.; Klug, William S.
2007-03-01
Recent atomic force microscope (AFM) nanoindentation experiments measuring mechanical response of the protein shells of viruses have provided a quantitative description of their strength and elasticity. To better understand and interpret these measurements, and to elucidate the underlying mechanisms, this paper adopts a course-grained modeling approach within the framework of three-dimensional nonlinear continuum elasticity. Homogeneous, isotropic, elastic, thick-shell models are proposed for two capsids: the spherical cowpea chlorotic mottle virus (CCMV), and the ellipsocylindrical bacteriophage ϕ29 . As analyzed by the finite-element method, these models enable parametric characterization of the effects of AFM tip geometry, capsid dimensions, and capsid constitutive descriptions. The generally nonlinear force response of capsids to indentation is shown to be insensitive to constitutive particulars, and greatly influenced by geometric and kinematic details. Nonlinear stiffening and softening of the force response is dependent on the AFM tip dimensions and shell thickness. Fits of the models capture the roughly linear behavior observed in experimental measurements and result in estimates of Young’s moduli of ≈280-360MPa for CCMV and ≈4.5GPa for ϕ29 .
NASA Astrophysics Data System (ADS)
Weil, Arlo; Gutiérrez-Alonso, Gabriel; Johnston, Stephen; Pastor Galán, Daniel
2013-04-01
The Paleozoic Variscan orogeny was a large-scale collisional event involving amalgamation of multiple continents and micro-continents. Existing data, suggests oroclinal buckling of an originally near-linear convergent margin during the last stages of Variscan deformation in the late Paleozoic. Closure of the Rheic Ocean resulted in E-W shortening (present-day coordinates) in the Carboniferous, producing a near linear N-S trending, east-verging belt. Subsequent N-S shortening near the Carb-Permian boundary resulted in oroclinal buckling. This late-stage orogenic event remains an enigmatic part of final Pangea amalgamation. The present-day arc curvature of the Variscan has inspired many tectonic models, with little agreement between them. While there is general consensus that two separate phases of deformation occurred, various models consider that curvature was caused by: dextral transpression around a Gondwana indentor; strike-slip wrench tectonics; or a change in tectonic transport direction due to changing stress fields. More recent models explain the curvature as an orocline, with potentially two opposite-facing bends, caused by secondary rotations. Deciphering the kinematic history of curved orogens is difficult, and requires establishment of two deformation phases: an initial compressive phase that forms a relatively linear belt, and a second phase that causes vertical-axis rotation of the orogenic limbs. Historically the most robust technique to accurately quantify vertical axis-rotation in curved orogens is paleomagnetic analysis, but recently other types of data, including fracture, geochemical, petrologic, paleo-current and calcite twin data, have been used to corroborate secondary buckling. A review of existing and new Variscan data from Iberia is presented that argues for secondary buckling of an originally linear orogenic system. Together, these data constrain oroclinal buckling of the Cantabrian Orocline to have occurred in about 10 Ma during the
The Mexican hat effect on the delamination buckling of a compressed thin film
NASA Astrophysics Data System (ADS)
Zhang, Yin; Liu, Yun
2014-12-01
Because of the interaction between film and substrate, the film buckling stress can vary significantly, depending on the delamination geometry, the film and substrate mechanical properties. The Mexican hat effect indicates such interaction. An analytical method is presented, and related dimensional analysis shows that a single dimensionless parameter can effectively evaluate the effect.
The Search for an Effective Clinical Behavior Analysis: The Nonlinear Thinking of Israel Goldiamond
ERIC Educational Resources Information Center
Layng, T. V. Joe
2009-01-01
This paper has two purposes; the first is to reintroduce Goldiamond's constructional approach to clinical behavior analysis and to the field of behavior analysis as a whole, which, unfortunately, remains largely unaware of his nonlinear functional analysis and its implications. The approach is not simply a set of clinical techniques; instead it…
Linear versus Nonlinear Analysis in the Measurement of Effects in a Quasi-Experimental Design.
ERIC Educational Resources Information Center
Vooijs, Marcel W.; Van der Kamp, Leo J. T.
1991-01-01
A two-step procedure is developed for the analysis of pretest-posttest data. Nonlinear canonical correlation analysis is followed by covariance analysis of optimally scaled pretest and posttest measures. The procedure is available in the computer program CANALS. Advantages of the two-step procedure are discussed. (SLD)
A new continuum approach for nonlinear kinetic simulation and transport analysis
Dai, Zongliang Wang, Shaojie; Xu, Yingfeng; Ye, Lei; Xiao, Xiaotao
2015-02-15
A numerical code based on the I-transform approach is developed to solve the nonlinear Vlasov equation and carry out the transport analysis. The numerical results given by the I-transform approach agree with the conservative semi-Lagrangian approach in the Landau damping case and the bump-on-tail instability case. The diffusivities induced by the random fields and the quasilinear transport are also successfully demonstrated by using the new approach. It is found that the nonlinear transport in the one-dimensional Langmuir turbulence cannot be well-described by a simple diffusion model, due to the strong particle trapping at the nonlinear stage.
Nonlinear analysis of a closed-loop tractor-semitrailer vehicle system with time delay
NASA Astrophysics Data System (ADS)
Liu, Zhaoheng; Hu, Kun; Chung, Kwok-wai
2016-08-01
In this paper, a nonlinear analysis is performed on a closed-loop system of articulated heavy vehicles with driver steering control. The nonlinearity arises from the nonlinear cubic tire force model. An integration method is employed to derive an analytical periodic solution of the system in the neighbourhood of the critical speed. The results show that excellent accuracy can be achieved for the calculation of periodic solutions arising from Hopf bifurcation of the vehicle motion. A criterion is obtained for detecting the Bautin bifurcation which separates branches of supercritical and subcritical Hopf bifurcations. The integration method is compared to the incremental harmonic balance method in both supercritical and subcritical scenarios.
Phenomenology and control of buckling dynamics in multicomponent colloidal droplets
NASA Astrophysics Data System (ADS)
Pathak, Binita; Basu, Saptarshi
2015-06-01
Self-assembly of nano sized particles during natural drying causes agglomeration and shell formation at the surface of micron sized droplets. The shell undergoes sol-gel transition leading to buckling at the weakest point on the surface and produces different types of structures. Manipulation of the buckling rate with inclusion of surfactant (sodium dodecyl sulphate, SDS) and salt (anilinium hydrochloride, AHC) to the nano-sized particle dispersion (nanosilica) is reported here in an acoustically levitated single droplet. Buckling in levitated droplets is a cumulative, complicated function of acoustic streaming, chemistry, agglomeration rate, porosity, radius of curvature, and elastic energy of shell. We put forward our hypothesis on how buckling occurs and can be suppressed during natural drying of the droplets. Global precipitation of aggregates due to slow drying of surfactant-added droplets (no added salts) enhances the rigidity of the shell formed and hence reduces the buckling probability of the shell. On the contrary, adsorption of SDS aggregates on salt ions facilitates the buckling phenomenon with an addition of minute concentration of the aniline salt to the dispersion. Variation in the concentration of the added particles (SDS/AHC) also leads to starkly different morphologies and transient behaviour of buckling (buckling modes like paraboloid, ellipsoid, and buckling rates). Tuning of the buckling rate causes a transition in the final morphology from ring and bowl shapes to cocoon type of structure.
NASA Technical Reports Server (NTRS)
Young, Richard D.; Nemeth, Michael P.; Collins, Timothy J.; Starnes, James H., Jr.
1998-01-01
Results of linear bifurcation and nonlinear analyses of the Space Shuttle superlightweight (SLWT) external liquid-oxygen (LO2) tank for an important early booster ascent loading condition are presented. These results for thin-walled linear elastic shells that are subjected to combined mechanical and thermal loads illustrate an important type of response mode that may be encountered in the design of other liquid-fuel launch vehicles. Linear bifurcation analyses are presented that predict several nearly equal eigenvalues that correspond to local buckling modes in the forward ogive section of the LO2 tank. In contrast, the nonlinear response phenomenon is shown to consist of short-wavelength bending deformations in the forward ogive and barrel sections of the LO2 tank that growing amplitude in a stable manner increasing load. Imperfection sensitivity analyses are presented that show that the presence of several nearly equal eigenvalues does not lead to a premature general instability mode for the forward ogive section. For the linear bifurcation and nonlinear analyses, the results show that accurate predictions of the response of the shield generally require a large-scale, high-fidelity finite-element model. Results are also presented that show that the SLWT LO2 tank can support loads in excess of approximately 2.6 times the values of the operational loads considered.
Nonlinearity detection for condition monitoring utilizing higher-order spectral analysis diagnostics
NASA Astrophysics Data System (ADS)
Park, Hyeonsu
In this dissertation, we investigate the theory and application of higher-order spectral analysis techniques to condition monitoring in shipboard electrical power systems. Monitoring and early detection of faults in rotating machines, such as induction motors, are essential for both preventive maintenance and to avoid potentially severe damage. As machines degrade, they often tend to become more nonlinear. This increased nonlinearity results in the introduction of new frequencies which satisfy particular frequency selection rules; the exact selection rule depends on the order of the nonlinearity. In addition, the phases of the newly generated frequencies satisfy a similar phase selection rule. This results in a phase coherence, or phase coupling, between the "original" interacting frequencies and the "new" frequencies. This phase coupling is a true signature of nonlinearity. Since the classical auto-power spectrum contains no phase information, the phase coupling signature associated with nonlinear interactions is not available. However, various higher-order spectra (HOS) are capable of detecting such nonlinear-induced phase coupling. The efficacy of the various proposed HOS-based methodologies is investigated using real-world vibration time-series data from a faulted induction motor driving a dc generator. The fault is controlled by varying a resistor placed in one phase of the three-phase line to the induction motor. First, we propose a novel method using a bispectral change detection (BCD) for condition monitoring. Even though the bicoherence is dominant and powerful in the detection of phase coupling of nonlinearly interacting frequencies, it has some difficulties in its application to machine condition monitoring. Basically, the bicoherence may not be able to distinguish between intrinsic nonlinearities associated with healthy machines and fault-induced nonlinearities. Therefore, the ability to discriminate the fault-only nonlinearities from the intrinsic
Multipolar tensor analysis of second-order nonlinear optical response of surface and bulk of glass.
Rodríguez, Francisco J; Wang, Fu X; Canfield, Brian K; Cattaneo, Stefano; Kauranen, Martti
2007-07-01
We use two-beam second-harmonic generation to perform a quantitative tensor analysis of the effective dipolar surface nonlinearity and the separable multipolar bulk nonlinearity for BK7 glass. The most straightforward, self-consistent interpretation of the results is obtained when the effective surface response is assumed to have approximate Kleinman symmetry and the bulk contribution is dominated by magnetic, rather than quadrupole, effects.
Stability analysis of nonlinear autonomous systems - General theory and application to flutter
NASA Technical Reports Server (NTRS)
Smith, L. L.; Morino, L.
1975-01-01
The analysis makes use of a singular perturbation method, the multiple time scaling. Concepts of stable and unstable limit cycles are introduced. The solution is obtained in the form of an asymptotic expansion. Numerical results are presented for the nonlinear flutter of panels and airfoils in supersonic flow. The approach used is an extension of a method for analyzing nonlinear panel flutter reported by Morino (1969).
Buckled silicene formation on Ir(111).
Meng, Lei; Wang, Yeliang; Zhang, Lizhi; Du, Shixuan; Wu, Rongting; Li, Linfei; Zhang, Yi; Li, Geng; Zhou, Haitao; Hofer, Werner A; Gao, Hong-Jun
2013-02-13
Silicene, a two-dimensional (2D) honeycomb structure similar to graphene, has been successfully fabricated on an Ir(111) substrate. It is characterized as a (√7×√7) superstructure with respect to the substrate lattice, as revealed by low energy electron diffraction and scanning tunneling microscopy. Such a superstructure coincides with the (√3×√3) superlattice of silicene. First-principles calculations confirm that this is a (√3×√3)silicene/(√7×√7)Ir(111) configuration and that it has a buckled conformation. Importantly, the calculated electron localization function shows that the silicon adlayer on the Ir(111) substrate has 2D continuity. This work provides a method to fabricate high-quality silicene and an explanation for the formation of the buckled silicene sheet.
Buckling Design Studies of Inverted, Oblate Bulkheads for a Propellant Tank
NASA Technical Reports Server (NTRS)
Smeltzer, Stanley S., III; Bowman, Lynn M.
2002-01-01
An investigation of the deformation and buckling characteristics of a composite, oblate bulkhead that has an inverted geometry and is subjected to pressure-only loading is presented for three bulkhead geometries and thicknesses. The effects of a stiffening support ring at the bulkhead to cylinder interface are also evaluated. Buckling analyses conducted using the axisymmetric shell code BOSOR4 are discussed for several bulkhead configurations. These results are analytically verified using results from the Structural Analysis of General Shells (STAGS) code for a selected bulkhead configuration. The buckling characterization of an inverted, oblate bulkhead requires careful attention as small changes in bulkhead parameters can have a significant effect on the critical buckling load. Comparison of BOSOR4 and STAGS results provided a very good correlation between the two analysis methods. In addition, the analysis code BOSOR4 was found to be an efficient sizing tool that is useful during the preliminary design stage of a practical shell structure. Together, these two aspects should give the design engineer confidence in sizing these stability critical structures. Additional characterization is warranted, especially for a composite tank structure, since only one bulkhead configuration was examined closely.
Buckling Behavior of Long Anisotropic Plates Subjected to Elastically Restrained Thermal Expansion
NASA Technical Reports Server (NTRS)
Nemeth, Michael P.
2002-01-01
An approach for synthesizing buckling results for, and behavior of, 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, 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 and compliance coefficients are derived that are used to determine critical temperatures in terms of physically intuitive mechanical-buckling coefficients. The effects of membrane orthotropy and membrane anisotropy are included in the general formulation. Many results are presented for some common laminates that are intended to facilitate a structural designer's transition to the use of 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 generic design curves. The analysis approach and generic results indicate the effects and characteristics of elastically restrained laminate thermal expansion or contraction, membrane orthotropy and anisotropy, and flexural orthotropy and anisotropy in a very general and unifying manner.
NASA Technical Reports Server (NTRS)
Przekop, Adam; Wu, Hsi-Yung T.; Shaw, Peter
2014-01-01
The Environmentally Responsible Aviation Project aims to develop aircraft technologies enabling significant fuel burn and community noise reductions. Small incremental changes to the conventional metallic alloy-based 'tube and wing' configuration are not sufficient to achieve the desired metrics. One of the airframe concepts that might dramatically improve aircraft performance is a composite-based hybrid wing body configuration. Such a concept, however, presents inherent challenges stemming from, among other factors, the necessity to transfer wing loads through the entire center fuselage section which accommodates a pressurized cabin confined by flat or nearly flat panels. This paper discusses a nonlinear finite element analysis of a large-scale test article being developed to demonstrate that the Pultruded Rod Stitched Efficient Unitized Structure concept can meet these challenging demands of the next generation airframes. There are specific reasons why geometrically nonlinear analysis may be warranted for the hybrid wing body flat panel structure. In general, for sufficiently high internal pressure and/or mechanical loading, energy related to the in-plane strain may become significant relative to the bending strain energy, particularly in thin-walled areas such as the minimum gage skin extensively used in the structure under analysis. To account for this effect, a geometrically nonlinear strain-displacement relationship is needed to properly couple large out-of-plane and in-plane deformations. Depending on the loading, this nonlinear coupling mechanism manifests itself in a distinct manner in compression- and tension-dominated sections of the structure. Under significant compression, nonlinear analysis is needed to accurately predict loss of stability and postbuckled deformation. Under significant tension, the nonlinear effects account for suppression of the out-of-plane deformation due to in-plane stretching. By comparing the present results with the previously
Torsion and buckling of open sections
NASA Technical Reports Server (NTRS)
Wagner, Herbert
1936-01-01
In this paper is a discussion of the general principles for open sections of any shape. In what follows the torsion will be computed and on the basis of the results it will be possible to obtain a proper design of section in each case. The torsion of buckling members for the case where they are centrally loaded, leads to a problem in pure stability and is similar to that of stressed beams.
Inclusion Analysis and Absorption Measurement in Nonlinear Crystals
Smith, L L
2005-08-26
Yttrium calcium oxyborate (YCOB) is a newly developed nonlinear optical crystal used for second harmonic generation in the Mercury laser. As with any new crystal, optical characterization of the material properties needs to be fully investigated. We are developing two new techniques to detect inclusions and measure optical absorption. With the side illuminating detection examination (SIDE) method, we hope to identify and map the size, density, and the morphology of inclusions. The multi-pass absorption technique (MPAT) will be used to help determine the absorption coefficient of various finished crystalline pieces at near-infrared wavelengths.
Frequency analysis of nonlinear oscillations via the global error minimization
NASA Astrophysics Data System (ADS)
Kalami Yazdi, M.; Hosseini Tehrani, P.
2016-06-01
The capacity and effectiveness of a modified variational approach, namely global error minimization (GEM) is illustrated in this study. For this purpose, the free oscillations of a rod rocking on a cylindrical surface and the Duffing-harmonic oscillator are treated. In order to validate and exhibit the merit of the method, the obtained result is compared with both of the exact frequency and the outcome of other well-known analytical methods. The corollary reveals that the first order approximation leads to an acceptable relative error, specially for large initial conditions. The procedure can be promisingly exerted to the conservative nonlinear problems.
Nonlinear analysis using a modal based reduction technique
NASA Astrophysics Data System (ADS)
Shalev, D.; Unger, A.
1993-02-01
A solution to nonlinear formulated problems using eigenfunctions computed by a linear free vibration solution is presented. The system of equations is extremely reduced compared with the finite element method. The solution is unique in its formulation as the governing equations represent the problem continuously and do not require an iterational solution over a tangent stiffness. Energy consideration is used and the Ritz method is applied to render the governing equations. The eigenfunctions are computed by a linear finite element code: MSC/NASTRAN. Several numerical examples are presented and compared with examples from the literature.
Nonlinear displacement analysis of advanced propeller structures using NASTRAN
NASA Technical Reports Server (NTRS)
Lawrence, C.; Kielb, R. E.
1984-01-01
The steady state displacements of a rotating advanced turboprop are computed using the geometrically nonlinear capabilities of COSMIC NASTRAN Rigid Format 4 and MSC NASTRAN Solution 64. A description of the modified Newton-Raphson algorithm used by Solution 64 and the iterative scheme used by Rigid Format 4 is provided. A representative advanced turboprop, SR3, was used for the study. Displacements for SR3 are computed for rotational speeds up to 10,000 rpm. The results show Solution 64 to be superior for computating displacements of flexible rotating structures. This is attributed to its ability to update the displacement dependent centrifugal force during the solution process.
Evaluation of Inelastic Constitutive Models for Nonlinear Structural Analysis
NASA Technical Reports Server (NTRS)
Kaufman, A.
1983-01-01
The influence of inelastic material models on computed stress-strain states, and therefore predicted lives, was studied for thermomechanically loaded structures. Nonlinear structural analyses were performed on a fatigue specimen which was subjected to thermal cycling in fluidized beds and on a mechanically load cycled benchmark notch specimen. Four incremental plasticity creep models (isotropic, kinematic, combined isotropic-kinematic, combined plus transient creep) were exercised. Of the plasticity models, kinematic hardening gave results most consistent with experimental observations. Life predictions using the computed strain histories at the critical location with a Strainrange Partitioning approach considerably overpredicted the crack initiation life of the thermal fatigue specimen.
Nonlinear potential analysis techniques for supersonic-hypersonic aerodynamic design
NASA Technical Reports Server (NTRS)
Shankar, V.; Clever, W. C.
1984-01-01
Approximate nonlinear inviscid theoretical techniques for predicting aerodynamic characteristics and surface pressures for relatively slender vehicles at supersonic and moderate hypersonic speeds were developed. Emphasis was placed on approaches that would be responsive to conceptual configuration design level of effort. Second order small disturbance and full potential theory was utilized to meet this objective. Numerical codes were developed for relatively general three dimensional geometries to evaluate the capability of the approximate equations of motion considered. Results from the computations indicate good agreement with experimental results for a variety of wing, body, and wing-body shapes.
Buckled graphene for efficient energy harvest, storage and conversion
NASA Astrophysics Data System (ADS)
Jiang, Jin-Wu
2016-10-01
Buckling is one of the most common phenomena in atom-thick layered structures like graphene. While the buckling phenomenon usually causes disaster for most nanodevices, we illustrate one positive application of buckled graphene for energy harvest, storage and conversion. More specifically, we perform molecular dynamical simulations to show that buckled graphene can be used to collect wasted mechanical energy and store the energy in the form of internal knotting potential. Through strain engineering, the knotting potential can be converted into useful kinetic (thermal) energy that is highly concentrated at the free edges of buckled graphene. The present study demonstrates potential applications of buckled graphene for converting dispersed wasted mechanical energy into concentrated useful kinetic (thermal) energy.
Dynamic buckling behavior of thin metal film lines from substrate
NASA Astrophysics Data System (ADS)
Wu, Dan; Xie, Huimin; Wang, Heling; Zhang, Jie; Li, Chuanwei
2014-10-01
The dynamic buckling behavior of thin films from substrate is studied in this work. The experimental results show that the buckling morphology of the constantan film lines from the polymer substrate is inconsistent and non-sinusoidal, which is different from the sinusoidal form of the buckling morphology under static loads. The plastic deformation of the film lines results in the non-sinusoidal buckling morphology and residual deformation when unloaded. Finite element modeling results with regard to the plastic dissipation of the constantan film lines reveal that the plastic dissipation suppresses the buckling-driven delaminating under impact loads. This study will give some new perspectives on the buckling behavior of thin film from substrate.