Pseudo-nonlinear dynamic analysis of buckled pipes
NASA Astrophysics Data System (ADS)
Gültekin Sınır, B.
2013-02-01
In this study, the post-divergence behavior of fluid-conveying pipes supported at both ends is investigated using the nonlinear equations of motion. The governing equation exhibits a cubic nonlinearity arising from mid-plane stretching. Exact solutions for post-buckling configurations of pipes with fixed-fixed, fixed-hinged, and hinged-hinged boundary conditions are investigated. The pipe is stable at its original static equilibrium position until the flow velocity becomes high enough to cause a supercritical pitchfork bifurcation, and the pipe loses stability by static divergence. In the supercritical fluid velocity regime, the equilibrium configuration becomes unstable and bifurcates into multiple equilibrium positions. To investigate the vibrations that occur in the vicinity of a buckled equilibrium position, the pseudo-nonlinear vibration problem around the first buckled configuration is solved precisely using a new solution procedure. By solving the resulting eigenvalue problem, the natural frequencies and the associated mode shapes of the pipe are calculated. The dynamic stability of the post-buckling configurations obtained in this manner is investigated. The first buckled shape is a stable equilibrium position for all boundary conditions. The buckled configurations beyond the first buckling mode are unstable equilibrium positions. The natural frequencies of the lowest vibration modes around each of the first two buckled configurations are presented. Effects of the system parameters on pipe behavior as well as the possibility of a subcritical pitchfork bifurcation are also investigated. The results show that many internal resonances might be activated among the vibration modes around the same or different buckled configurations.
Nonlinear analysis of hydraulic buckling instability of ANS involute fuel plates
Sartory, W.K.
1993-03-01
The hydraulic buckling instability of the involute fuel plates and hydraulic coolant channels in the Advanced Neutron Source (ANS) uranium fission reactor is analyzed nonlinearly using the commercial ABAQUS finite element computer program for the fuel plates in conjunction with a user-written element for the two-dimensional fluid flow in the coolant channels. This methodology has been used for several purposes, including determination of the effect of the aluminum-clad plate plastic behavior and the effect of three-dimensional plate temperature distributions on hydraulic buckling. The present report concentrates on a study of the effect of hydraulic channel imperfections on buckling. The specific form of imperfection considered is an error in fluid channel thickness that is uniform within any one channel but that varies from one channel to the next. The calculated bifurcation (linear buckling) coolant velocity is about 45 m/s, whereas the present design coolant velocity is 25 m/s. At the design velocity, the calculated fluid-induced plate deflection due to the imperfection is somewhat less in magnitude and opposite in direction from the imperfection itself.
NASA Technical Reports Server (NTRS)
Nemeth, Michael P.
2014-01-01
Nonlinear and bifurcation buckling equations for elastic, stiffened, geometrically perfect, right-circular cylindrical, anisotropic shells subjected to combined loads are presented that are based on Sanders' shell theory. Based on these equations, a three-parameter approximate Rayleigh-Ritz solution and a classical solution to the buckling problem are presented for cylinders with simply supported edges. Extensive comparisons of results obtained from these solutions with published results are also presented for a wide range of cylinder constructions. These comparisons include laminated-composite cylinders with a wide variety of shell-wall orthotropies and anisotropies. Numerous results are also given that show the discrepancies between the results obtained by using Donnell's equations and variants of Sanders' equations. For some cases, nondimensional parameters are identified and "master" curves are presented that facilitate the concise representation of results.
Cooperative buckling and the nonlinear mechanics of nematic semiflexible networks
NASA Astrophysics Data System (ADS)
Foucard, L. C.; Price, J. K.; Klug, W. S.; Levine, A. J.
2015-09-01
We review the nonlinear mechanics of cross-linked networks of stiff filaments with a quenched anisotropic (nematic) alignment. A combination of numerical simulations and analytic calculations shows that the broken rotational symmetry of the filament orientational distribution leads to a dramatic nonlinear softening of the network at very small strain (on the order of 0.1%). We argue that one can understand this softening in terms of Euler buckling, i.e. the loss of further load-carrying capacity in compression within the network. With increasing shear strain, this source of geometric nonlinearity appears as heterogeneous nucleation (originating in particularly fragile regions, which may be identified by a linear stability analysis) and subsequently grows into ‘buckling scars’ that eventually spread throughout the system. We develop a simple mean-field model for the nonlinear mechanics of such networks and suggest applications of these ideas to a variety of fiber networks and biopolymer systems.
NASA Astrophysics Data System (ADS)
Kala, Zdeněk; Kala, Jiří
2012-09-01
The paper deals with the influence of correlation length, of Gauss random field, and of yield strength of a hotrolled I-beam under bending on the ultimate load carrying capacity limit state. Load carrying capacity is an output random quantity depending on input random imperfections. Latin Hypercube Sampling Method is used for sampling simulation. Load carrying capacity is computed by the programme ANSYS using shell finite elements and nonlinear computation methods. The nonlinear FEM computation model takes into consideration the effect of lateral-torsional buckling on the ultimate limit state.
On Buckling, Kink Boundaries and Kinking Nonlinear Elastic Solids
NASA Astrophysics Data System (ADS)
Shamma, Mohamed
The mechanical behavior of materials has been under investigation for decades. However, there is always unknown information to be researched and characterized. Extensive research has been performed on materials deforming by slip and twin mechanisms due to their presence in a lot of materials used in practical applications. Conversely, much less attention was directed to investigating the dislocation mechanism responsible for the fully reversible energy dissipating mechanical response of Kinking Nonlinear Elastic (KNE) solids. Herein, the buckling dislocation mechanism responsible for the KNE mechanical behavior of MAX phases is investigated. The main features of the buckling dislocation mechanism are identified that are globally applicable for layered structured materials as well. This was done by analyzing the deformation of a single crystal layered structure. The single crystal layered structure is a setup consisting of a pile of paper supported by sponge and ply wood in which paper buckles during compression. The displacement of the paper layers is studied in relation to dislocation nucleation across the layers called dislocation walls (DW). Schmid factor maps where developed that recognize the shape and progress of traction applied on the layers during deformation. Hence, the evolution of buckling dislocation mechanism that occurs in layered structures has been discovered distinguishing between two possible buckling modes (extrusion and indentation) that depend on the layered structure surrounding support and constraints. In situ neutron diffraction and ultrasonic bias stress techniques were used to perform in situ experiments on selected MAX phases to obtain information about the dislocation mechanism during its activity. Linear elastic Ti 2SC was investigated as well for comparison with Ti3SiC 2 and Ti2AlC MAX phases which demonstrate KNE mechanical response in bulk. The in situ ND results of textured Ti2AlC showed typical results except for the (0004) grains
Buckling Design and Analysis of a Payload Fairing One-Sixth Cylindrical Arc-Segment Panel
NASA Technical Reports Server (NTRS)
Kosareo, Daniel N.; Oliver, Stanley T.; Bednarcyk, Brett A.
2013-01-01
Design and analysis results are reported for a panel that is a 16th arc-segment of a full 33-ft diameter cylindrical barrel section of a payload fairing structure. Six such panels could be used to construct the fairing barrel, and, as such, compression buckling testing of a 16th arc-segment panel would serve as a validation test of the buckling analyses used to design the fairing panels. In this report, linear and nonlinear buckling analyses have been performed using finite element software for 16th arc-segment panels composed of aluminum honeycomb core with graphiteepoxy composite facesheets and an alternative fiber reinforced foam (FRF) composite sandwich design. The cross sections of both concepts were sized to represent realistic Space Launch Systems (SLS) Payload Fairing panels. Based on shell-based linear buckling analyses, smaller, more manageable buckling test panel dimensions were determined such that the panel would still be expected to buckle with a circumferential (as opposed to column-like) mode with significant separation between the first and second buckling modes. More detailed nonlinear buckling analyses were then conducted for honeycomb panels of various sizes using both Abaqus and ANSYS finite element codes, and for the smaller size panel, a solid-based finite element analysis was conducted. Finally, for the smaller size FRF panel, nonlinear buckling analysis was performed wherein geometric imperfections measured from an actual manufactured FRF were included. It was found that the measured imperfection did not significantly affect the panel's predicted buckling response
Buckling analysis of Big Dee Vacuum Vessel
Lightner, S.; Gallix, R.
1983-12-01
A simplified three-dimensional shell buckling analysis of the GA Technologies Inc., Big Dee Vacuum Vessel (V/V) was performed using the finite element program TRICO. A coarse-mesh linear elastic model, which accommodated the support boundary conditions, was used to determine the buckling mode shape under a uniform external pressure. Using this buckling mode shape, refined models were used to calculate the linear buckling load (P/sub crit/) more accurately. Several different designs of the Big Dee V/V were considered in this analysis. The supports for the V/V were equally-spaced radial pins at the outer diameter of the mid-plane. For all the cases considered, the buckling mode was axisymmetric in the toroidal direction. Therefore, it was possible to use only a small angular sector of a toric shell for the refined analysis. P/sub crit/ for the Big Dee is about 60 atm for a uniform external pressure. Also investigated in this analysis were the effects of geometrical imperfections and non-uniform pressure distributions.
Nonlinear contact between inner walls of deep sea pipelines in buckling process
NASA Astrophysics Data System (ADS)
Ma, Weilin; Yu, Jianxing; Zhou, Qingji; Xie, Bin; Cao, Jing; Li, Zhibo
2015-02-01
In order to study buckling propagation mechanism in deep sea pipelines, the contact between pipeline's inner walls in buckling process was studied. A two-dimensional ring model was used to represent the pipeline and a nonlinear spring model was adopted to simulate the contact between inner walls. Based on the elastoplastic constitutive relationship and the principle of virtual work theory, the coupling effect of pipeline's nonlinear large deformation and wall contact was included in the theoretical analysis with the aid of MATLAB, and the application scope of the theoretical model was also discussed. The calculated results show that during the loading process, the change in external pressure is closely related to the distribution of section stress, and once the walls are contacting each other, the external pressure increases and then remains stable after it reaches a specific value. Without fracture, the pipeline section will stop showing deformation. The results of theoretical calculations agree well with those of numerical simulations. Finally, in order to ensure reliability and accuracy of the theoretical results, the collapse pressure and propagation pressure were both verified by numerical simulations and experiments. Therefore, the theoretical model can be used to analyze pipeline's buckling deformation and contact between pipeline's inner walls, which forms the basis for further research on three-dimensional buckling propagation.
NASA Technical Reports Server (NTRS)
Hoff, N J; Klein, Bertram
1944-01-01
In the present part I of a series of reports on the inward bulge type buckling of monocoque cylinders the buckling load in combined bending and compression is first derived. Next the reduction in the buckling load because of a nonlinear direct stress distribution is determined. In experiments nonlinearity may result from an inadequate stiffness of the end attachments in actual airplanes from the existence of concentrated loads or cut-outs. The effect of a shearing force upon the critical load is investigated through an analysis of the results of tests carried out at GALCIT with 55 reinforced monocoque cylinders. Finally, a simple criterion of general instability is presented in the form of a buckling inequality which should be helpful to the designer of a monocoque in determining the sizes of the rings required for excluding the possibility of inward bulge type buckling.
Nonlinear buckling analyses of a small-radius carbon nanotube
NASA Astrophysics Data System (ADS)
Liu, Ning; Wang, Yong-Gang; Li, Min; Jia, Jiao
2014-04-01
Carbon nanotube (CNT) was first discovered by Sumio Iijima. It has aroused extensive attentions of scholars from all over the world. Over the past two decades, we have acquired a lot of methods to synthesize carbon nanotubes and learn their many incredible mechanical properties such as experimental methods, theoretical analyses, and computer simulations. However, the studies of experiments need lots of financial, material, and labor resources. The calculations will become difficult and time-consuming, and the calculations may be even beyond the realm of possibility when the scale of simulations is large, as for computer simulations. Therefore, it is necessary for us to explore a reasonable continuum model, which can be applied into nano-scale. This paper attempts to develop a mathematical model of a small-radius carbon nanotube based on continuum theory. An Isotropic circular cross-section, Timoshenko beam model is used as a simplified mechanical model for the small-radius carbon nanotube. Theoretical part is mainly based on modified couple stress theory to obtain the numerical solutions of buckling deformation. Meanwhile, the buckling behavior of the small radius carbon nanotube is simulated by Molecular Dynamics method. By comparing with the numerical results based on modified couple stress theory, the dependence of the small-radius carbon nanotube mechanical behaviors on its elasticity constants, small-size effect, geometric nonlinearity, and shear effect is further studied, and an estimation of the small-scale parameter of a CNT (5, 5) is obtained.
Euler buckling and nonlinear kinking of double-stranded DNA.
Fields, Alexander P; Meyer, Elisabeth A; Cohen, Adam E
2013-11-01
The bending stiffness of double-stranded DNA (dsDNA) at high curvatures is fundamental to its biological activity, yet this regime has been difficult to probe experimentally, and literature results have not been consistent. We created a 'molecular vise' in which base-pairing interactions generated a compressive force on sub-persistence length segments of dsDNA. Short dsDNA strands (<41 base pairs) resisted this force and remained straight; longer strands became bent, a phenomenon called 'Euler buckling'. We monitored the buckling transition via Förster Resonance Energy Transfer (FRET) between appended fluorophores. For low-to-moderate concentrations of monovalent salt (up to ∼150 mM), our results are in quantitative agreement with the worm-like chain (WLC) model of DNA elasticity, without the need to invoke any 'kinked' states. Greater concentrations of monovalent salts or 1 mM Mg(2+) induced an apparent softening of the dsDNA, which was best accounted for by a kink in the region of highest curvature. We tested the effects of all single-nucleotide mismatches on the DNA bending. Remarkably, the propensity to kink correlated with the thermodynamic destabilization of the mismatched DNA relative the perfectly complementary strand, suggesting that the kinked state is locally melted. The molecular vise is exquisitely sensitive to the sequence-dependent linear and nonlinear elastic properties of dsDNA. PMID:23956222
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 Testing and Analysis of Space Shuttle Solid Rocket Motor Cylinders
NASA Technical Reports Server (NTRS)
Weidner, Thomas J.; Larsen, David V.; McCool, Alex (Technical Monitor)
2002-01-01
A series of full-scale buckling tests were performed on the space shuttle Reusable Solid Rocket Motor (RSRM) cylinders. The tests were performed to determine the buckling capability of the cylinders and to provide data for analytical comparison. A nonlinear ANSYS Finite Element Analysis (FEA) model was used to represent and evaluate the testing. Analytical results demonstrated excellent correlation to test results, predicting the failure load within 5%. The analytical value was on the conservative side, predicting a lower failure load than was applied to the test. The resulting study and analysis indicated the important parameters for FEA to accurately predict buckling failure. The resulting method was subsequently used to establish the pre-launch buckling capability of the space shuttle system.
Nonlinear Guided Waves in Continuously Welded Rails for Buckling Prediction
NASA Astrophysics Data System (ADS)
Phillips, Robert; Bartoli, Ivan; Coccia, Stefano; Lanza di Scalea, Francesco; Salamone, Salvatore; Nucera, Claudio; Fateh, Mahmood; Carr, Gary
2011-06-01
Most modern railways use Continuous Welded Rail (CWR). A major problem is the almost total absence of expansion joints that can create severe issues such as buckling in hot weather and breakage in cold weather. A related critical parameter is the rail Neutral Temperature (NT), or the temperature at which the net longitudinal force in the rail is zero. In June 2008 the University of California, San Diego (UCSD), under the sponsorship of a Federal Railroad Administration (FRA) Office of Research and Development (R&D) grant, began work to develop a technique for in-situ measurement of NT and detection of incipient buckling in CWR. The method under investigation is based on ultrasonic guided waves, and the ultimate goal is to build and test a prototype that can be used in motion. A large-scale full rail track (70 feet in length) has been constructed at UCSD's Powell Structural Laboratories, the largest laboratories in the country for structural testing, to validate the NT measurement and buckling detection technique under rail heating conditions well controlled in the laboratory. This paper reports on the status of this project, including proof-of-principle results of stress measurement and buckling detection on a steel I-beam, and initial test results from the large-scale rail testbed at the Powell Labs. These results pave the road for the future development of the rail NT/buckling detection prototype.
Non-Linear Vibration and Thermal Buckling of AN Orthotropic Annular Plate with a Centric Rigid Mass
NASA Astrophysics Data System (ADS)
LI, S.-R.; ZHOU, Y.-H.; SONG, X.
2002-03-01
A computational analysis of the non-linear vibration and thermal post-buckling of a heated orthotropic annular plate with a central rigid mass is examined for the cases of immovably hinged as well as clamped constraint conditions of the outer edge. First, based on von Karman's plate theory and Hamilton's principles, the governing equations, in terms of the displacements of the middle plane, of the problem are derived. Then, upon assuming that harmonic responses of the system exist, the non-linear partial differential equations are converted into the corresponding non-linear ordinary differential equations through elimination of the time variable by using the Kantorovich time-averaging method. Finally, by applying a shooting method, the fundamental responses of the non-linear vibration and thermal post-buckling of the plate are numerically obtained. For some prescribed values of the parameters, such as the material rigidity ratio, temperature rise and so on, the curves of the fundamental frequency versus specified amplitude and the thermal post-buckled equilibrium paths of the plate are numerically presented.
An Improved Analysis of the Thermal Buckling of Silicon Sheet
NASA Technical Reports Server (NTRS)
Dillon, O. W., Jr.; Deangelis, R.
1984-01-01
Buckling problems on the production of wide and thin silicon sheet are discussed. Buckling occurs in all of the processes which are investigated for their potential in mass producing wide silicon sheet for use in making solar cells. It is a fact that the processes which produce good ribbon 2 cm in width do not yield the same quality product at 10 cm in width. Buckling develops precisely because the sheets are wide and very very thin. The buckling of very thin cantilever plates due to temperature variations in the axial direction is considered. The temperature variation in the width direction was determined. Axial temperature variations which cause very thin plates to buckle in a torsional mode are demonstrated. It is assumed that the particular variation of the stress function in the width direction and thereafter the analysis is exact.
The eigenvalue problem associated with the nonlinear buckling of a shear bending column
NASA Astrophysics Data System (ADS)
Nishimura, Isao
2011-04-01
This paper discusses the eigenvalue problem of a nonlinear differential equation that governs the stability of a shear bending column under extremely large deformation. What is taken into consideration is the geometrical nonlinearity while the material is supposed to be linear. The reason of a superbly stable buckling behavior of a slender rubber bearing is physically explained by pointing out the analogy that is similar to the nonlinear wave propagation expressed in KdV equation. The nonlinear boundary condition and the nonlinear term of the differential equation cancel each other and make the associated eigenvalue rather constant. In other words, as far as the material is supposed to be linear, the column does not buckle no matter how large the deformation is. This theoretical prediction is experimentally verified and successfully applied to a base isolation system of a lightweight structure.
Artery buckling analysis using a four-fiber wall model
Liu, Qin; Wen, Qi; Mottahedi, Mohammad; Han, Hai-Chao
2014-01-01
Artery bent buckling has been suggested as a possible mechanism that leads to artery tortuosity, which is associated with aging, hypertension, atherosclerosis, and other pathological conditions. It is necessary to understand the relationship between microscopic wall structural changes and macroscopic artery buckling behavior. To this end, the objectives of this study were to develop arterial buckling equations using a microstructure-based 4-fiber reinforced wall model, and to simulate the effects of vessel wall microstructural changes on artery buckling. Our results showed that the critical pressure increased nonlinearly with the axial stretch ratio, and the 4-fiber model predicted higher critical buckling pressures than what the Fung model predicted. The buckling equation using the 4-fiber model captures the experimentally observed reduction of critical pressure induced by elastin degradation and collagen fiber orientation changes in the arterial wall. These results improve our understanding of arterial stability and its relationship to microscopic wall remodeling, and the model provides a useful tool for further studies. PMID:24972920
Buckling Analysis of Debonded Sandwich Panel Under Compression
NASA Technical Reports Server (NTRS)
Sleight, David W.; Wang, John T.
1995-01-01
A sandwich panel with initial through-the-width debonds is analyzed to study the buckling of its faceskin when subject to an in-plane compressive load. The debonded faceskin is modeled as a beam on a Winkler elastic foundation in which the springs of the elastic foundation represent the sandwich foam. The Rayleigh-Ritz and finite-difference methods are used to predict the critical buckling load for various debond lengths and stiffnesses of the sandwich foam. The accuracy of the methods is assessed with a plane-strain finite-element analysis. Results indicate that the elastic foundation approach underpredicts buckling loads for sandwich panels with isotropic foam cores.
Buckling analysis of cylindrical shells with cracks
Limam, A.; Jullien, J.F.; Ouayou, B.S.
1995-12-31
In many areas of aeronautical nuclear and civil engineering practice, large thin-walled structural panels are increasingly becoming characteristic architectural features. Indeed, nuclear reactor vessels and cryogenic tanks of a launcher, for instance, are made up of several thin-walled panels welded together. Instability and buckling phenomenon present over-riding constraints on the design process. In addition, the presence of joints which are very often the origin of surface fissures poses increasing dangers on the overall stability of these structures. This research deals with the analysis of the effects of cracks on the behavior of cylindrical shells subject to external pressure. The study was divided into two major parts. In the first part, experiments were carried out with shells without cracks, in order to obtain reference data. A numerical study of various models explains the experimental results and shows the combined effect of the geometric imperfections and boundary conditions on the critical load. The second part focused on several experimental tests and numerical simulations on shells with in- depth fissures as a function of their population, orientation, length and position with respect to the welds or joints. The agreement between numerical and experimental results confirms the new possibility to design with the aid of the finite element program under the condition that the calculations are carried out by means of an appropriate numerical method.
Statistical analysis of imperfection effect on cylindrical buckling response
NASA Astrophysics Data System (ADS)
Ismail, M. S.; Purbolaksono, J.; Muhammad, N.; Andriyana, A.; Liew, H. L.
2015-12-01
It is widely reported that no efficient guidelines for modelling imperfections in composite structures are available. In response, this work evaluates the imperfection factors of axially compressed Carbon Fibre Reinforced Polymer (CFRP) cylinder with different ply angles through finite element (FE) analysis. The sensitivity of imperfection factors were analysed using design of experiment: factorial design approach. From the analysis it identified three critical factors that sensitively reacted towards buckling load. Furthermore empirical equation is proposed according to each type of cylinder. Eventually, critical buckling loads estimated by empirical equation showed good agreements with FE analysis. The design of experiment methodology is useful in identifying parameters that lead to structures imperfection tolerance.
Buckling analysis of laminated thin shells in a hot environment
NASA Technical Reports Server (NTRS)
Gotsis, Pascal K.; Guptil, James D.
1993-01-01
Results are presented of parametric studies to assess the effects of various parameters on the buckling behavior of angle-ply, laminated thin shells in a hot environment. These results were obtained by using a three-dimensional finite element analysis. An angle-ply, laminated thin shell with fiber orientation of (theta/-theta)(sub 2) was subjected to compressive mechanical loads. The laminated thin shell had a cylindrical geometry. The laminate contained T300 graphite fibers embedded in an intermediate-modulus, high-strength (IMHS) matrix. The fiber volume fraction was 55 percent and the moisture content was 2 percent. The residual stresses induced into the laminate structure during the curing were taken into account. Parametric studies were performed to examine the effect on the critical buckling load of the following parameters: cylinder length and thickness, internal hydrostatic pressure, different ply thicknesses, different temperature profiles through the thickness of the structure, and different lay up configurations and fiber volume fractions. In conjunction with these parameters the ply orientation was varied from 0 deg to 90 deg. Seven ply angles were examined: 0 deg, 15 deg, 30 deg, 45 deg, 60 deg, 75 deg, and 90 deg. The results show that the ply angle theta and the laminate thickness had significant effects on the critical buckling load. The fiber volume fraction, the fiber orientations, and the internal hydrostatic pressure had important effects on the critical buckling load. The cylinder length had a moderate influence on the buckling load. The thin shell with (theta/-theta)(sub 2) or (theta/-theta)(sub s) angle-ply laminate had better buckling-load performance than the thin shell with (theta)(sub 4) angle-ply laminate. The temperature profiles through the laminate thickness and various laminates with the different ply thicknesses has insignificant effects on the buckling behavior of the thin shells.
Nonlinear and Buckling Behavior of Curved Panels Subjected to Combined Loads
NASA Technical Reports Server (NTRS)
Hilburger, Mark W.; Nemeth, Michael P.; Starnes, James H., Jr.
2001-01-01
The results of an analytical study of the nonlinear and buckling response characteristics of curved panels subjected to combined loads are presented. Aluminum and laminated composite panels are considered in the study and a flat and shallow curved panel configurations are considered as well. The panels are subjected to combined axial compression and transverse tension or compression loads or combined axial compression and inplane shear loads. Results illustrating the effects of various combined load states on the buckling response of the panels are presented. In addition, results illustrating the effects of laminate orthotropy and anisotropy and panel curvature on the panel response are presented. The results indicate that panel curvature can have a significant effect on the nonlinear and buckling behavior of the panels subjected to combined loads. Results are included that show that geometrically perfect panels do not exhibit bifurcation points for some combined loads. Results are also presented that show the effects of laminate orthotropy and anisotropy on the interaction of combined loads.
Buckling analysis of geodesically stiffened composite panels with discrete stiffeners
NASA Astrophysics Data System (ADS)
Gurdal, Zafer; Grall, Bruno
1994-09-01
A computationally efficient analysis is developed to predict the buckling loads of geodesically stiffened composite panels with discrete plate-like stiffeners under in-plane loads. The procedure accounts for the contribution of the in-plane extensional and out-of-plane bending stiffnesses of the stiffeners through the use of a Lagrange multipliers technique in an energy method solution. The analysis is capable of predicting the buckling loads of grid-stiffened panels for a variety of stiffener aspect ratios and stiffener laminate stacking sequences. It can also be used to design panels with variable density grid stiffeners across the panel width. Results of the proposed analysis showed that the buckling loads of geodesically stiffened panels are predicted more accurately, especially in the case of panels with shallow stiffeners, compared to an earlier analysis that assumes the stiffeners to be beam-like components. For plate-like stiffeners, laminate stacking sequence of the stiffeners is found to have a substantial effect on the critical load of a panel. It was demonstrated that the optimal stiffener is not always unidirectional, and tailoring the stiffener ply sequence can lead to improvement in panel stability. It was also shown that panels with a variable grid density can lead to designs with improved buckling performance compared to uniform density panels.
Gao, Li; Zhang, Yihui; Zhang, Hui; Doshay, Sage; Xie, Xu; Luo, Hongying; Shah, Deesha; Shi, Yan; Xu, Siyi; Fang, Hui; Fan, Jonathan A; Nordlander, Peter; Huang, Yonggang; Rogers, John A
2015-06-23
Large-scale, dense arrays of plasmonic nanodisks on low-modulus, high-elongation elastomeric substrates represent a class of tunable optical systems, with reversible ability to shift key optical resonances over a range of nearly 600 nm at near-infrared wavelengths. At the most extreme levels of mechanical deformation (strains >100%), nonlinear buckling processes transform initially planar arrays into three-dimensional configurations, in which the nanodisks rotate out of the plane to form linear arrays with "wavy" geometries. Analytical, finite-element, and finite-difference time-domain models capture not only the physics of these buckling processes, including all of the observed modes, but also the quantitative effects of these deformations on the plasmonic responses. The results have relevance to mechanically tunable optical systems, particularly to soft optical sensors that integrate on or in the human body. PMID:25906085
Numerical analysis of linear buckling of wind turbine blade with different trailing bonding models
NASA Astrophysics Data System (ADS)
Zhang, J. D.; Xu, Y.
2013-12-01
The work focus on the linear buckling analysis of wind turbine blade with different trailing bonding models. Based on finite element model, it has been demonstrated that there are some differences for buckling load factor between different models. Several different models are valid for buckling analysis.
NASA Astrophysics Data System (ADS)
Prakash, T.; Sundararajan, N.; Ganapathi, M.
2007-01-01
Here, the dynamic thermal buckling behavior of functionally graded spherical caps is studied considering geometric nonlinearity based on von Karman's assumptions. The formulation is based on first-order shear deformation theory and it includes the in-plane and rotary inertia effects. The material properties are graded in the thickness direction according to the power-law distribution in terms of volume fractions of the material constituents. The effective material properties are evaluated using homogenization method. The governing equations obtained using finite element approach are solved employing the Newmark's integration technique coupled with a modified Newton-Raphson iteration scheme. The pressure load corresponding to a sudden jump in the maximum average displacement in the time history of the shell structure is taken as the dynamic buckling load. The present model is validated against the available isotropic case. A detailed numerical study is carried out to highlight the influences of shell geometries, power law index of functional graded material and boundary conditions on the dynamic buckling load of shallow spherical shells.
High-Fidelity Buckling Analysis of Composite Cylinders Using the STAGS Finite Element Code
NASA Technical Reports Server (NTRS)
Hilburger, Mark W.
2014-01-01
Results from previous shell buckling studies are presented that illustrate some of the unique and powerful capabilities in the STAGS finite element analysis code that have made it an indispensable tool in structures research at NASA over the past few decades. In particular, prototypical results from the development and validation of high-fidelity buckling simulations are presented for several unstiffened thin-walled compression-loaded graphite-epoxy cylindrical shells along with a discussion on the specific methods and user-defined subroutines in STAGS that are used to carry out the high-fidelity simulations. These simulations accurately account for the effects of geometric shell-wall imperfections, shell-wall thickness variations, local shell-wall ply-gaps associated with the fabrication process, shell-end geometric imperfections, nonuniform applied end loads, and elastic boundary conditions. The analysis procedure uses a combination of nonlinear quasi-static and transient dynamic solution algorithms to predict the prebuckling and unstable collapse response characteristics of the cylinders. Finally, the use of high-fidelity models in the development of analysis-based shell-buckling knockdown (design) factors is demonstrated.
NASA Astrophysics Data System (ADS)
El-Sayed, Sami Ibrahim
Delamination is an important mode of failure in laminated and sandwich composites. This study describes a cohesive layer model which has been successfully employed to predict the initiation and track the growth of delamination. A significant feature of the present model is that it can be used for geometrically nonlinear problems as it is formulated in terms of appropriate stresses and strains. A finite element approach which could account for the contact between delaminated surfaces as well as the progressive failure of the cohesive layer was employed to study several test cases. As a preliminary, examples of a double cantilever and a compressed beam specimens were studied in detail to identify the role of the key parameters of the model, viz. the thickness of the cohesive layer and the strength and stiffness of the cohesive layer material. It is found that the model is fairly robust and is not sensitive to changes in parameters other than the critical strain energy release rates in the opening and shearing modes respectively. This was followed by an investigation of delamination growth in columns and rings made of laminated composite material as well as sandwich columns. A dynamic analysis incorporating appropriate damping with a sufficiently slow rate of application of load was implemented to closely simulate quasi-static loading. Experimental results are found to corroborate the accuracy of the model. In laminated composites, matrix cracking was found to have a significant effect in the advanced stages of loading history and this has been accounted for by the implementation of a micro-mechanical model installed in the material in conjunction with the cohesive layer model placed along the potential delamination. Better correlation with experimental results was thus achieved. It was observed in experiments that the interfacial crack in sandwich structures may not remain at the interface and tends to kink into the core. A kinking model which is based on identifying
Jiang, H.; Sun, Y.; Rogers, J. A.; Huang, Y.; Arizona State Univ.; Univ. of Illinois; Northwestern Univ.
2008-04-01
The precisely controlled buckling of stiff thin films (e.g., Si or GaAs nano ribbons) on the patterned surface of elastomeric substrate (e.g., poly(dimethylsiloxane) (PDMS)) with periodic inactivated and activated regions was designed by Sun et al. [Sun, Y., Choi, W.M., Jiang, H., Huang, Y.Y., Rogers, J.A., 2006. Controlled buckling of semiconductor nanoribbons for stretchable electronics. Nature Nanotechnology 1, 201-207] for important applications of stretchable electronics. We have developed a post-buckling model based on the energy method for the precisely controlled buckling to study the system stretchability. The results agree with Sun et al.'s (2006) experiments without any parameter fitting, and the system can reach 120% stretchability.
NASA Astrophysics Data System (ADS)
Byun, Wanil; Kim, Min Ki; Park, Kook Jin; Kim, Seung Jo; Chung, Minho; Cho, Jin Yeon; Park, Sung-Han
2011-12-01
The supercavitating vehicle is an underwater vehicle that is surrounded almost completely by a supercavity to reduce hydrodynamic drag substantially. Since the cruise speed of the vehicle is much higher than that of conventional submarines, the drag force is huge and a buckling may occur. The buckling phenomenon is analyzed in this study through static and dynamic approaches. Critical buckling load and pressure as well as buckling mode shapes are calculated using static buckling analysis and a stability map is obtained from dynamic buckling analysis. When the finite element method (FEM) is used for the buckling analysis, the solver requires a linear static solver and an eigenvalue solver. In this study, these two solvers are integrated and a consolidated buckling analysis module is constructed. Furthermore, Particle Swarm Optimization (PSO) algorithm is combined in the buckling analysis module to perform a design optimization computation of a simplified supercavitating vehicle. The simplified configuration includes cylindrical shell structure with three stiffeners. The target for the design optimization process is to minimize total weight while maintaining the given structure buckling-free.
Buckling of spherical capsules.
Knoche, Sebastian; Kierfeld, Jan
2011-10-01
We investigate buckling of soft elastic capsules under negative pressure or for reduced capsule volume. Based on nonlinear shell theory and the assumption of a hyperelastic capsule membrane, shape equations for axisymmetric and initially spherical capsules are derived and solved numerically. A rich bifurcation behavior is found, which is presented in terms of bifurcation diagrams. The energetically preferred stable configuration is deduced from a least-energy principle both for prescribed volume and prescribed pressure. We find that buckled shapes are energetically favorable already at smaller negative pressures and larger critical volumes than predicted by the classical buckling instability. By preventing self-intersection for strongly reduced volume, we obtain a complete picture of the buckling process and can follow the shape from the initial undeformed state through the buckling instability into the fully collapsed state. Interestingly, the sequences of bifurcations and stable capsule shapes differ for prescribed volume and prescribed pressure. In the buckled state, we find a relation between curvatures at the indentation rim and the bending modulus, which can be used to determine elastic moduli from experimental shape analysis. PMID:22181297
Post Buckling Progressive Failure Analysis of Composite Laminated Stiffened Panels
NASA Astrophysics Data System (ADS)
Anyfantis, Konstantinos N.; Tsouvalis, Nicholas G.
2012-06-01
The present work deals with the numerical prediction of the post buckling progressive and final failure response of stiffened composite panels based on structural nonlinear finite element methods. For this purpose, a progressive failure model (PFM) is developed and applied to predict the behaviour of an experimentally tested blade-stiffened panel found in the literature. Failure initiation and propagation is calculated, owing to the accumulation of the intralaminar failure modes induced in fibre reinforced composite materials. Hashin failure criteria have been employed in order to address the fiber and matrix failure modes in compression and tension. On the other hand, the Tsai-Wu failure criterion has been utilized for addressing shear failure. Failure detection is followed with the introduction of corresponding material degradation rules depending on the individual failure mechanisms. Failure initiation and failure propagation as well as the post buckling ultimate attained load have been numerically evaluated. Final failure behaviour of the simulated stiffened panel is due to sudden global failure, as concluded from comparisons between numerical and experimental results being in good agreement.
COMPPAP - COMPOSITE PLATE BUCKLING ANALYSIS PROGRAM (IBM PC VERSION)
NASA Technical Reports Server (NTRS)
Smith, J. P.
1994-01-01
The Composite Plate Buckling Analysis Program (COMPPAP) was written to help engineers determine buckling loads of orthotropic (or isotropic) irregularly shaped plates without requiring hand calculations from design curves or extensive finite element modeling. COMPPAP is a one element finite element program that utilizes high-order displacement functions. The high order of the displacement functions enables the user to produce results more accurate than traditional h-finite elements. This program uses these high-order displacement functions to perform a plane stress analysis of a general plate followed by a buckling calculation based on the stresses found in the plane stress solution. The current version assumes a flat plate (constant thickness) subject to a constant edge load (normal or shear) on one or more edges. COMPPAP uses the power method to find the eigenvalues of the buckling problem. The power method provides an efficient solution when only one eigenvalue is desired. Once the eigenvalue is found, the eigenvector, which corresponds to the plate buckling mode shape, results as a by-product. A positive feature of the power method is that the dominant eigenvalue is the first found, which is this case is the plate buckling load. The reported eigenvalue expresses a load factor to induce plate buckling. COMPPAP is written in ANSI FORTRAN 77. Two machine versions are available from COSMIC: a PC version (MSC-22428), which is for IBM PC 386 series and higher computers and compatibles running MS-DOS; and a UNIX version (MSC-22286). The distribution medium for both machine versions includes source code for both single and double precision versions of COMPPAP. The PC version includes source code which has been optimized for implementation within DOS memory constraints as well as sample executables for both the single and double precision versions of COMPPAP. The double precision versions of COMPPAP have been successfully implemented on an IBM PC 386 compatible running
Buckling Analysis of a Honeycomb-Core Composite Cylinder with Initial Geometric Imperfections
NASA Technical Reports Server (NTRS)
Cha, Gene; Schultz, Marc R.
2013-01-01
Thin-walled cylindrical shell structures often have buckling as the critical failure mode, and the buckling of such structures can be very sensitive to small geometric imperfections. The buckling analyses of an 8-ft-diameter, 10-ft-long honeycomb-core composite cylinder loaded in pure axial compression is discussed in this document. Two loading configurations are considered configuration 1 uses simple end conditions, and configuration 2 includes additional structure that may more closely approximate experimental loading conditions. Linear eigenvalue buckling analyses and nonlinear analyses with and without initial geometric imperfections were performed on both configurations. The initial imperfections were introduced in the shell by applying a radial load at the midlength of the cylinder to form a single inward dimple. The critical bifurcation buckling loads are predicted to be 924,190 lb and 924,020 lb for configurations 1 and 2, respectively. Nonlinear critical buckling loads of 918,750 lb and 954,900 lb were predicted for geometrically perfect configurations 1 and 2, respectively. Lower-bound critical buckling loads for configurations 1 and 2 with radial perturbations were found to be 33% and 36% lower, respectively, than the unperturbed critical loads. The inclusion of the load introduction cylinders in configuration 2 increased the maximum bending-boundary-layer rotation up to 11%.
A NASTRAN DMAP alter for linear buckling analysis under dynamic loading
NASA Technical Reports Server (NTRS)
Aiello, Robert A.; Grady, Joseph E.
1989-01-01
A modification to the NASTRAN solution sequence for transient analysis with direct time integration (COSMIC NASTRAN rigid format 9) was developed and incorporated into a DMAP alter. This DMAP alter calculates the buckling stability of a dynamically loaded structure, and is used to predict the onset of structural buckling under stress-wave loading conditions. The modified solution sequence incorporates the linear buckling analysis capability (rigid format 5) of NASTRAN into the existing Transient solution rigid format in such a way as to provide a time dependent eigensolution which is used to assess the buckling stability of the structure as it responds to the impulsive load. As a demonstration of the validity of this modified solution procedure, the dynamic buckling of a prismatic bar subjected to an impulsive longitudinal compression is analyzed and compared to the known theoretical solution. In addition, a dynamic buckling analysis is performed for the analytically less tractable problem of the localized dynamic buckling of an initially flawed composite laminate under transverse impact loading. The addition of this DMAP alter to the transient solution sequence in NASTRAN facilitates the computational prediction of both the time at which the onset of dynamic buckling occurs in an impulsively loaded structure, and the dynamic buckling mode shapes of that structure.
Thermo-mechanical buckling analysis of FGM plate using generalized plate theory
NASA Astrophysics Data System (ADS)
Sharma, Kanishk; Kumar, Dinesh; Gite, Anil
2016-05-01
This paper investigates the thermo-mechanical buckling behavior of simply-supported FGM plate under the framework of generalized plate theory (GPT), which includes classical plate theory (CPT), first order shear deformation theory (FSDT) and higher order shear deformation theory (HSDT) as special cases. The governing equations for FGM plate under thermal and mechanical loading conditions are derived from the principle of virtual displacements and Navier-type solution is assumed for simply supported boundary condition. The efficiency and applicability of presented methodology is illustrated by considering various examples of thermal and mechanical buckling of FGM plates. The closed form solutions in the form of critical thermal and mechanical buckling loads, predicted by CPT, FSDT and HSDT are compared for different side-to-thickness of FGM plate. Subsequently, the effect of material gradation profile on critical buckling parameters is examined by evaluating the buckling response for a range of power law indexes. The effect of geometrical parameters on mechanical buckling of FGM plate under uni-axial and bi-axial loading conditions are also illustrated by calculating the critical load for various values of slenderness ratios. Furthermore a comparative analysis of critical thermal buckling loads of FGM plate for different temperature profiles is also presented. It is identified that all plate theories predicted approximately same critical buckling loads and critical buckling temperatures for thin FGM plate, however for thick FGM plates, CPT overestimates the critical buckling parameters. Moreover the critical buckling loads and critical buckling temperatures of FGM plate are found to be significantly lower than the corresponding homogenous isotropic ceramic plate (n=0).
A NASTRAN DMAP alter for linear buckling analysis under dynamic loading
NASA Technical Reports Server (NTRS)
Aiello, Robert A.; Grady, Joseph E.
1988-01-01
A unique modification to the NASTRAN solution sequence for transient analysis with direct time integration (COSMIC NASTRAN rigid format 9) was developed and incorporated into a DMAP alter. This DMAP alter calculates the buckling stability of a dynamically loaded structure, and is used to predict the onset of structural buckling under stress wave loading conditions. The modified solution sequence incorporates the linear buckling analysis capability (rigid format 5) of NASTRAN into the existing Transient solution rigid format in such a way as to provide a time dependent eigensolution which is used to assess the buckling stability of the structure as it responds to the impulsive load. As a demonstration of the validity of this modified solution procedure, the dynamic buckling of a prismatic bar subjected to an impulsive longitudinal compression is analyzed and compared to the known theoretical solution. In addition, a dynamic buckling analysis is performed for the analytically less tractable problem of the localized dynamic buckling of an initially flawed composite laminate under transverse impact loading. The addition of this DMAP alter to the transient solution sequence in NASTRAN facilitates the prediction of both time and mode of buckling.
A Nonlinear Theory of Bending and Buckling of Thin Elastic Shallow Spherical Shells
NASA Technical Reports Server (NTRS)
Kaplan, A; Fung, Y C
1954-01-01
The problem of the finite displacement and buckling, of a shallow spherical dome is investigated both theoretically and experimentally. Experimental results seem to indicate that the classical criterion of buckling is applicable to very shallow spherical domes for which the theoretical calculation was made. A transition to energy criterion for higher domes is also indicated.
NASA Astrophysics Data System (ADS)
Gunda, Jagadish Babu; Venkateswara Rao, Gundabathula
2016-04-01
Post-buckling and large amplitude free vibration analysis of composite beams with axially immovable ends is investigated in the present study using a simple intuitive formulation. Geometric nonlinearity of Von-Karman type is considered in the analysis which accounts for mid-plane stretching action of the beam. Intuitive formulation uses only two parameters: the critical bifurcation point and the axial stretching force developed due to membrane stretching action of the beam. Hinged-hinged, clamped-clamped and clamped-hinged boundary conditions are considered. Numerical accuracy of the proposed analytical closed-form solutions obtained from the intuitive formulation are compared to available finite element solutions for symmetric and asymmetric layup schemes of laminated composite beam which indicates the confidence gained on the present formulation.
New Nonlinear Multigrid Analysis
NASA Technical Reports Server (NTRS)
Xie, Dexuan
1996-01-01
The nonlinear multigrid is an efficient algorithm for solving the system of nonlinear equations arising from the numerical discretization of nonlinear elliptic boundary problems. In this paper, we present a new nonlinear multigrid analysis as an extension of the linear multigrid theory presented by Bramble. In particular, we prove the convergence of the nonlinear V-cycle method for a class of mildly nonlinear second order elliptic boundary value problems which do not have full elliptic regularity.
NASA Astrophysics Data System (ADS)
Zhang, Hui; Gao, Li; Zhang, Yihui; Xie, Xu; Doshay, Sage; Fang, Hui; Fan, Jonathan A.; Nordlander, Peter; Huang, Yonggang; Rogers, John A.; Deesha, Shad; Xu, Siyi
2015-09-01
Large scale, dense arrays of plasmonic nanodisks (Au) on low modulus, high elongation elastomeric substrates (PDMS) represent a class of tunable optical system, with reversible ability to shift plasmon resonances, originating from array deformation, over a range of nearly 600nm in the visible region. At the most extreme levels of mechanical deformation (strains <100%), non-linear buckling processes transform initially planar arrays into three dimensional configurations, in which the nanodisks rotate out of the plane, giving rise to an increase of transition rate, to form linear arrays with `wavy' geometries. Analytical and finite element models capture not only the physics of these buckling processes, including all of distinct modes that occur, but also the quantitative effects of these deformations on the plasmonic responses. The results have relevance to mechanically tunable optical systems, with potential relevance to soft optical sensors that integrate on or in the human body.
NASA Technical Reports Server (NTRS)
Starnes, James H., Jr.; Hilburger, Mark W.
2003-01-01
The results of an experimental and analytical study of the effects of initial imperfections on the buckling response of unstiffened thin-walled compression-loaded graphite-epoxy cylindrical shells are presented. The analytical results include the effects of traditional and nontraditional initial imperfections and uncertainties in the values of selected shell parameters on the buckling loads of the shells. The nonlinear structural analysis results correlate very well with the experimental results. The high-fidelity nonlinear analysis procedure used to generate the analytical results can also be used to form the basis of a new shell design procedure that could reduce the traditional dependence on empirical results in the shell design process. KEYWORDS: high-fidelity nonlinear structural analysis, composite shells, shell stability, initial imperfections
Buckling analysis for structural sections and stiffened plates reinforced with laminated composites.
NASA Technical Reports Server (NTRS)
Viswanathan, A. V.; Soong, T.-C.; Miller, R. E., Jr.
1972-01-01
A classical buckling analysis is developed for stiffened, flat plates composed of a series of linked flat plate and beam elements. Plates are idealized as multilayered orthotropic elements; structural beads and lips are idealized as beams. The loaded edges of the stiffened plate are simply supported and the conditions at the unloaded edges can be prescribed arbitrarily. The plate and beam elements are matched along their common junctions for displacement continuity and force equilibrium in an exact manner. Offsets between elements are considered in the analysis. Buckling under uniaxial compressive load for plates, sections and stiffened plates is investigated. Buckling loads are found as the lowest of all possible general and local failure modes and the mode shape is used to determine whether buckling is a local or general instability. Numerical correlations with existing analysis and test data for plates, sections and stiffened plates including boron-reinforced structures are discussed. In general, correlations are reasonably good.
NASA Technical Reports Server (NTRS)
Ko, William L.; Jackson, Raymond H.
1993-01-01
Combined inplane compressive and shear buckling analysis was conducted on flat rectangular sandwich panels using the Raleigh-Ritz minimum energy method with a consideration of transverse shear effect of the sandwich core. The sandwich panels were fabricated with titanium honeycomb core and laminated metal matrix composite face sheets. The results show that slightly slender (along unidirectional compressive loading axis) rectangular sandwich panels have the most desirable stiffness-to-weight ratios for aerospace structural applications; the degradation of buckling strength of sandwich panels with rising temperature is faster in shear than in compression; and the fiber orientation of the face sheets for optimum combined-load buckling strength of sandwich panels is a strong function of both loading condition and panel aspect ratio. Under the same specific weight and panel aspect ratio, a sandwich panel with metal matrix composite face sheets has much higher buckling strength than one having monolithic face sheets.
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. PMID:25123434
Buckling and dynamic analysis of drill strings for core sampling
Ziada, H.H., Westinghouse Hanford
1996-05-15
This supporting document presents buckling and dynamic stability analyses of the drill strings used for core sampling. The results of the drill string analyses provide limiting operating axial loads and rotational speeds to prevent drill string failure, instability and drill bit overheating during core sampling. The recommended loads and speeds provide controls necessary for Tank Waste Remediation System (TWRS) programmatic field operations.
BUCKO- A BUCKLING ANALYSIS FOR RECTANGULAR PLATES WITH CENTRALLY LOCATED CUTOUTS
NASA Technical Reports Server (NTRS)
Nemeth, M. P.
1994-01-01
BUCKO is a computer program developed to predict the buckling load of a rectangular compression-loaded orthotropic plate with a centrally located cutout. The plate is assumed to be a balanced, symmetric laminate of uniform thickness. The cutout shape can be elliptical, circular, rectangular, or square. The BUCKO package includes sample data that demonstrates the essence of the program and its ease of usage. BUCKO uses an approximate one-dimensional formulation of the classical two-dimensional buckling problem following the Kantorovich method. The boundary conditions are considered to be simply supported unloaded edges and either clamped or simply supported loaded edges. The plate is loaded in uniaxial compression by either uniformly displacing or uniformly stressing two opposite edges of the plate. The BUCKO analysis consists of two parts: calculation of the inplane stress distribution prior to buckling, and calculation of the plate axial load and displacement at buckling. User input includes plate planform and cutout geometry, plate membrane and bending stiffnesses, finite difference parameters, boundary condition data, and loading data. Results generated by BUCKO are the prebuckling strain energy, inplane stress resultants, buckling mode shape, critical end shortening, and average axial and transverse strains at buckling. BUCKO is written in FORTRAN V for batch execution and has been implemented on a CDC CYBER 170 series computer operating under NOS with a central memory requirement of approximately 343K of 60 bit words. This program was developed in 1984 and was last updated in 1990.
Post-buckling behavior of a beam-column on a nonlinear elastic foundation with a gap
NASA Technical Reports Server (NTRS)
Kuznetsov, E. N.; Johns, T. G.
1980-01-01
The structural behavior of an elastic beam-column placed with a gap between two nonlinearity elastic layers each resting on a rigid foundation was examined. The beam-column was laterally supported at both ends and subjected to a uniform transverse load and axial compression. Its slenderness was such that the axial compressive force exceeds the amount that would be necessary to buckle it as a simple supported column. The elastic layers were represented by an elastic foundation with a strongly nonlinear specific reaction taken as a rapidly increasing function of the layer compression. The analytical model developed simulated the entire pattern of the deflection and stress state including layer and end support reactions, under gradually increasing axial force.
TRBUCKL - A NASTRAN DMAP ALTER FOR LINEAR BUCKLING ANALYSIS UNDER DYNAMIC LOADING
NASA Technical Reports Server (NTRS)
Aiello, R. A.
1994-01-01
Delaminations near the outer surface of a laminate are susceptible to local buckling and buckling-induced delamination propagation when the laminate is subjected to transverse impact loading. This results in a loss of stiffness and strength. TRBUCKL is an unique dynamic delamination buckling and delamination propagation analysis capability that can be incorporated into the structural analysis program, NASTRAN. This capability will aid engineers in the design of structures incorporating composite laminates. The capability consists of: (1) a modification of the direct time integration solution sequence which provides a new analysis algorithm that can be used to predict delamination buckling in a laminate subjected to dynamic loading; and (2) a new method of modeling the composite laminate using plate bending elements and multipoint constraints. The capability now exists to predict the time at which the onset of dynamic delamination buckling occurs, the dynamic buckling mode shape, and the dynamic delamination strain energy release rate. A procedure file for NASTRAN, TRBUCKL predicts both impact induced buckling in composite laminates with initial delaminations and the strain energy release rate due to extension of the delamination. In addition, the file is useful in calculating the dynamic delamination strain energy release rate for a composite laminate under impact loading. This procedure simplifies the simulation of progressive crack extension. TRBUCKL has been incorporated into COSMIC NASTRAN. TRBUCKL is a DMAP Alter for NASTRAN. It is intended for use only with the COSMIC NASTRAN Direct Transient Analysis (RF 9) solution sequence. The program is available as a listing only. TRBUCKL was developed in 1987.
NASA Technical Reports Server (NTRS)
McGowan, David M.
1999-01-01
The analytical formulation of curved-plate non-linear equilibrium equations including transverse-shear-deformation effects is presented. A unified set of non-linear strains that contains terms from both physical and tensorial strain measures is used. Linearized, perturbed equilibrium equations (stability equations) that describe the response of the plate just after buckling occurs are derived. These equations are then modified to allow the plate reference surface to be located a distance z(sub c) from the centroidal surface. The implementation of the new theory into the VICONOPT exact buckling and vibration analysis and optimum design computer program is described. The terms of the plate stiffness matrix using both classical plate theory (CPT) and first-order shear-deformation plate theory (SDPT) are presented. The effects of in-plane transverse and in-plane shear loads are included in the in-plane stability equations. Numerical results for several example problems with different loading states are presented. Comparisons of analyses using both physical and tensorial strain measures as well as CPT and SDPT are made. The computational effort required by the new analysis is compared to that of the analysis currently in the VICONOPT program. The effects of including terms related to in-plane transverse and in-plane shear loadings in the in-plane stability equations are also examined. Finally, results of a design-optimization study of two different cylindrical shells subject to uniform axial compression are presented.
NASA Technical Reports Server (NTRS)
Viswanathan, A. V.; Tamekuni, M.
1973-01-01
Analytical methods based on linear theory are presented for predicting the thermal stresses in and the buckling of heated structures with arbitrary uniform cross section. The structure is idealized as an assemblage of laminated plate-strip elements, curved and planar, and beam elements. Uniaxially stiffened plates and shells of arbitrary cross section are typical examples. For the buckling analysis the structure or selected elements may be subjected to mechanical loads, in additional to thermal loads, in any desired combination of inplane transverse load and axial compression load. The analysis is also applicable to stiffened structures under inplane loads varying through the cross section, as in stiffened shells under bending. The buckling analysis is general and covers all modes of instability. The analysis has been applied to a limited number of problems and the results are presented. These while showing the validity and the applicability of the method do not reflect its full capability.
Stochastic behavior of nanoscale dielectric wall buckling
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
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.
Nonlinear rotordynamics analysis
NASA Technical Reports Server (NTRS)
Day, W. B.
1985-01-01
The special nonlinearities of the Jeffcott equations in rotordynamics are examined. The immediate application of this analysis is directed toward understanding the excessive vibrations recorded in the LOX pump of the SSME during hot firing ground testing. Deadband, side force and rubbing are three possible sources of inducing nonlinearity in the Jeffcott equations. The present analysis initially reduces these problems to the same mathematical description. A special frequency, named the nonlinear natural frequency is defined and used to develop the solutions of the nonlinear Jeffcott equations as asympotic expansions. This nonlinear natural frequency which is the ratio of the cross-stiffness and the damping, plays a major role in determining response frequencies. Numerical solutions are included for comparison with the analysis. Also, nonlinear frequency-response tables are made for a typical range of values.
Buckling and postbuckling analysis of stiffened composite panels in axial compression
NASA Astrophysics Data System (ADS)
Park, Oung
The major objective of this study is to analyze buckling and delamination behavior of composite stiffened panels subjected to axial compression. First, a combined analytical and experimental study of a blade stiffened composite panel subjected to axial compression was conducted. The effects of the differences between a simple model used to design the panel and the actual experimental conditions were examined. It was found that in spite of many simplifying assumptions the design model did reasonably well in that the experimental failure load was only 10% higher than the design load. Several structural analysis programs, including PANDA2, STAGS, and ABAQUS, were used to obtain high fidelity analysis results. The buckling loads from STAGS agreed well with the experimental failure loads. However, substantial differences were found in the out-of-plane displacements of the panel. Efforts were made to identify the source of these differences. Implementing non-uniform load introduction with general contact definition in the STAGS finite element model improved correlation between the measured and predicted out-of-plane deformations. Next, a new method called Crack Tip Force Method (CTFM) is derived for computing point-wise energy release rate along the delamination front in delaminated plates. The CTFM is computationally simple as the G is computed using the forces transmitted at the crack-tip between the top and bottom sub-laminates and the sub-laminate properties. Finally, buckling and postbuckling of a blade-stiffened composite panel under axial compression with a partial skin-stiffener debond are investigated. Two different finite element models, where nodes of the panel skin and the stiffener flange are located on the mid-plane or at the interface between skin and flange, are used. Linear buckling analysis is conducted using both STAGS and ABAQUS. Postbuckling analysis is conducted with STAGS. Comparison between the present results and previous buckling analysis
Post-Buckling Analysis of Curved Honeycomb Sandwich Panels Containing Interfacial Disbonds
NASA Technical Reports Server (NTRS)
Pineda, Evan J.; Bednarcyk, Brett A.; Krivanek, Thomas K.
2016-01-01
A numerical study on the effect of facesheet-core disbonds on the post-buckling response of curved honeycomb sandwich panels is presented herein. This work was conducted as part of the development of a damage tolerance plan for the next-generation Space Launch System heavy lift launch vehicle payload fairing. As such, the study utilized full-scale fairing barrel segments as the structure of interest. The panels were composed of carbon fiber reinforced polymer facesheets and aluminum honeycomb core. The panels were analyzed numerically using the finite element method incorporating geometric nonlinearity. In a predetermined circular region, facesheet and core nodes were detached to simulate a disbond, between the outer mold line facesheet and honeycomb core, induced via low-speed impact. Surface-to-surface contact in the disbonded region was invoked to prevent interpenetration of the facesheet and core elements and obtain realistic stresses in the core. The diameter of this disbonded region was varied and the effect of the size of the disbond on the post-buckling response was observed. Significant changes in the slope of the edge load-deflection response were used to determine the onset of global buckling and corresponding buckling load. Finally, several studies were conducted to determine the sensitivity of the numerical predictions to refinement in the finite element mesh.
A digital computer study of the buckling of shallow spherical caps and truncated hemispheres
NASA Technical Reports Server (NTRS)
Stilwell, W. C.; Ball, R. E.
1972-01-01
A study of the buckling of thin shells was conducted using a digital computer program for the geometrically nonlinear analysis of arbitrarily loaded shells of revolution. The objective was an evaluation of the program's applicability to bifurcation buckling and imperfection sensitivity analysis. Clamped spherical caps under pressure loading and clamped truncated hemispheres under axial tension were investigated. Buckling loads were determined for axisymmetric and nearly axisymmetric loads and are compared with previously published analytical results based on geometric imperfections.
Post-Buckling and Ultimate Strength Analysis of Stiffened Composite Panel Base on Progressive Damage
NASA Astrophysics Data System (ADS)
Zhang, Guofan; Sun, Xiasheng; Sun, Zhonglei
Stiffened composite panel is the typical thin wall structure applied in aerospace industry, and its main failure mode is buckling subjected to compressive loading. In this paper, the development of an analysis approach using Finite Element Method on post-buckling behavior of stiffened composite structures under compression was presented. Then, the numerical results of stiffened panel are obtained by FE simulations. A thorough comparison were accomplished by comparing the load carrying capacity and key position strains of the specimen with test. The comparison indicates that the FEM results which adopted developed methodology could meet the demand of engineering application in predicting the post-buckling behavior of intact stiffened structures in aircraft design stage.
NASA Technical Reports Server (NTRS)
Ko, William L.
1996-01-01
Mechanical and thermal buckling behavior of monolithic and metal-matrix composite hat-stiffened panels were investigated. The panels have three types of face-sheet geometry: Flat face sheet, microdented face sheet, and microbulged face sheet. The metal-matrix composite panels have three types of face-sheet layups, each of which is combined with various types of hat composite layups. Finite-element method was used in the eigenvalue extractions for both mechanical and thermal buckling. The thermal buckling analysis required both eigenvalue and material property iterations. Graphical methods of the dual iterations are shown. The mechanical and thermal buckling strengths of the hat-stiffened panels with different face-sheet geometry are compared. It was found that by just microdenting or microbulging of the face sheet, the axial, shear, and thermal buckling strengths of both types of hat-stiffened panels could be enhanced considerably. This effect is more conspicuous for the monolithic panels. For the metal-matrix composite panels, the effect of fiber orientations on the panel buckling strengths was investigated in great detail, and various composite layup combinations offering, high panel buckling strengths are presented. The axial buckling strength of the metal-matrix panel was sensitive to the change of hat fiber orientation. However, the lateral, shear, and thermal buckling strengths were insensitive to the change of hat fiber orientation.
A Simple Buckling Analysis Method for Airframe Composite Stiffened Panel by Finite Strip Method
NASA Astrophysics Data System (ADS)
Tanoue, Yoshitsugu
Carbon fiber reinforced plastics (CFRP) have been used in structural components for newly developed aircraft and spacecraft. The main structures of an airframe, such as the fuselage and wings, are essentially composed of stiffened panels. Therefore, in the structural design of airframes, it is important to evaluate the buckling strength of the composite stiffened panels. Widely used finite element method (FEM) can analyzed any stiffened panel shape with various boundary conditions. However, in the early phase of airframe development, many studies are required in structural design prior to carrying out detail drawing. In this phase, performing structural analysis using only FEM may not be very efficient. This paper describes a simple buckling analysis method for composite stiffened panels, which is based on finite strip method. This method can deal with isotropic and anisotropic laminated plates and shells with several boundary conditions. The accuracy of this method was verified by comparing it with theoretical analysis and FEM analysis (NASTRAN). It has been observed that the buckling coefficients calculated via the present method are in agreement with results found by detail analysis methods. Consequently, this method is designed to be an effective calculation tool for the buckling analysis in the early phases of airframe design.
Buckling analysis of fully anisotropic plates containing cutouts and elastically restrained edges
NASA Technical Reports Server (NTRS)
Jones, Kevin M.; Klang, Eric C.
1992-01-01
An analysis is developed which combines the Ritz and collocation methods for the stability solution of an anisotropic plate with a cutout and elastically restrained edges. Results are presented which agree closely with experiment for isotropic and orthotropic materials. Results are also given for restrained anisotropic plates with circular holes loaded in compression and shear. Difference is noted in the critical buckling loads between displacement and stress loaded panels as hole size is increased. Clamping is also seen to affect the trends in buckling associated with hole size.
Limit Load and Buckling Analysis for Assessing Hanford Single-Shell Tank Dome Structural Integrity
Johnson, Kenneth I.; Deibler, John E.; Julyk, Larry J.; Karri, Naveen K.; Pilli, Siva Prasad
2012-12-07
The U.S. Department of Energy, Office of River Protection has commissioned a structural analysis of record (AOR) for the Hanford single shell tanks (SSTs) to assess their structural integrity. The analysis used finite element techniques to predict the tank response to the historical thermal and operating loads. The analysis also addressed the potential tank response to a postulated design basis earthquake. The combined response to static and seismic loads was then evaluated against the design requirements of American Concrete Institute (ACI) standard, ACI-349-06, for nuclear safety-related concrete structures. Further analysis was conducted to estimate the plastic limit load and the elastic-plastic buckling capacity of the tanks. The limit load and buckling analyses estimate the margin between the applied loads and the limiting load capacities of the tank structure. The potential for additional dome loads from waste retrieval equipment and the addition of large dome penetrations to accommodate retrieval equipment has generated additional interest in the limit load and buckling analyses. This paper summarizes the structural analysis methods that were used to evaluate the limit load and buckling of the single shell tanks.
Numerical analysis of pulse signal restoration by stochastic resonance in a buckled microcavity.
Sun, Heng; Liu, Hongjun; Sun, Qibing; Huang, Nan; Wang, Zhaolu; Han, Jing
2016-04-20
A novel scheme is proposed to restore weak pulse signals immersed in noise by stochastic resonance based on photothermal-effect-induced optical bistability in a buckled dome microcavity. The bistable properties of the dome microcavity are analyzed with different initial detuning wavelengths and effective cavity lengths, and bistable transmission can be obtained for input powers in submilliwatt range. A theoretical model is derived to interpret the nonlinear process of pulse signal recovery through double-well potential theory. The cross-correlation coefficient between output signals and pure input pulses is calculated to quantitatively analyze the influence of noise intensity on stochastic resonance. A cross-correlation gain of 7 is obtained, and the noise-hidden signal can be recovered effectively though the buckled dome microcavity with negligible distortion. The simulation results show the potential of using this structure to restore low-level or noise-hidden pulse signals in all-optical integrated systems. PMID:27140110
NASA Technical Reports Server (NTRS)
1984-01-01
Nonlinear structural analysis techniques for engine structures and components are addressed. The finite element method and boundary element method are discussed in terms of stress and structural analyses of shells, plates, and laminates.
Bending and buckling behavior analysis of foamed metal circular plate.
Fan, Jian Ling; Ma, Lian Sheng; Zhang, Lu; De Su, Hou
2016-01-01
This paper establishes a density gradient model along the thickness direction of a circular plate made of foamed material. Based on the first shear deformation plate theory, the result is deduced that the foamed metal circular plate with graded density along thickness direction yields axisymmetric bending problem under the action of uniformly distributed load, and the analytical solution is obtained by solving the governing equation directly. The analyses on two constraint conditions of edge radial clamping and simply supported show that the density gradient index and external load may affect the axisymmetric bending behavior of the plate. Then, based on the classical plate theory, the paper analyzes the behavior of axisymmetric buckling under radial pressure applied on the circular plate. Shooting method is used to obtain the critical load, and the effects of gradient nature of material properties and boundary conditions on the critical load of the plate are analyzed. PMID:27339281
A buckling analysis for rectangular orthotropic plates with centrally located cutouts
NASA Technical Reports Server (NTRS)
Nemeth, M. P.
1984-01-01
An analysis to obtain the buckling loads of a rectangular orthotropic plate with a centrally located cutout is described. Cutout shapes can be elliptical, circular, rectangular, or square. The boundary conditions considered in the analysis are simply supported unloaded edges and either clamped or simply supported loaded edges. The plate is loaded in uniaxial compression by either uniform edge displacement or uniform edge stress. A computer program that implements this analysis is described, and the program use is demonstrated by sample problems.
Rigorous buckling analysis of size-dependent functionally graded cylindrical nanoshells
NASA Astrophysics Data System (ADS)
Sun, Jiabin; Lim, C. W.; Zhou, Zhenhuan; Xu, Xinsheng; Sun, Wei
2016-06-01
This paper presents new analytical solutions for buckling of carbon nanotubes (CNTs) and functionally graded (FG) cylindrical nanoshells subjected to compressive and thermal loads. The model applies Eringen's nonlocal differential constitutive relation to describe the size-dependence of nanoshells. Based on Reddy's higher-order shear deformation theory, governing equations are established and solved by separating the variables. The analysis first re-examines the classical buckling of single-walled CNTs. Accurate solutions are established, and it is found that the buckling stress decreases drastically when the nonlocal parameter reaches a certain value. For CNTs with constant wall-thickness, the buckling stress eventually decreases with enhanced size effect. By comparing with CNTs molecular dynamic simulations, the obtained nonlocal parameters are much smaller than those proposed previously. Subsequently, FG cylindrical nanoshells are analyzed, and it is concluded that similar behavior that has been observed for CNTs is also valid for FG cylindrical nanoshells. The paper further discusses in detail the effects of different geometric parameters, material distribution, and temperature field.
Design guide for predicting nonlinear random response (including snap-through) of buckled plates
NASA Technical Reports Server (NTRS)
Ng, Chung Fai
1989-01-01
This design guide describes a method for predicting the random response of flat and curved plates which is based on theoretical analyses and experimental results. The plate curvature can be due to postbuckling, in-plane mechanical or thermal stresses. Based on a single mode formula, root mean square values of the strain response to broadband excitation are evaluated for different static buckled configurations using the equivalent linearization technique. The effects on the overall strain response due to instability motion of snap-through are included. Panel parameters include clamped and simply-supported boundaries, aspect ratio, thickness and length. Analytical results are compared with experimental results from tests with 12 in. x 15 in. aluminum plates under thermal loading in a progressive wave facility. Comparisons are also made with results from tests with a 2 in. x 15 in. x 0.032 in. aluminum beam under base mechanical excitation. The comparisons help to assess the accuracy of the theory and the conditions under which deviations from the theory due to effects of imperfection and higher modes are significant.
NASA Astrophysics Data System (ADS)
Borovkov, Alexei I.; Avdeev, Ilya V.; Artemyev, A.
1999-05-01
In present work, the stress, vibration and buckling finite element analysis of laminated beams is performed. Review of the equivalent single-layer (ESL) laminate theories is done. Finite element algorithms and procedures integrated into the original FEA program system and based on the classical laminated plate theory (CLPT), first-order shear deformation theory (FSDT), third-order theory of Reddy (TSDT-R) and third- order theory of Kant (TSDT-K) with the use of the Lanczos method for solving of the eigenproblem are developed. Several numerical tests and examples of bending, free vibration and buckling of multilayered and sandwich beams with various material, geometry properties and boundary conditions are solved. New effective higher-order hierarchical element for the accurate calculation of transverse shear stress is proposed. The comparative analysis of results obtained by the considered models and solutions of 2D problems of the heterogeneous anisotropic elasticity is fulfilled.
Effects of Imperfections on the Buckling Response of Compression-Loaded Composite Shells
NASA Technical Reports Server (NTRS)
Hilburger, Mark W.; Starnes, James H., Jr.
2000-01-01
The results of an experimental and numerical study of the effects of imperfections on the buckling response of unstiffened thin-walled composite cylindrical shells are presented. Results that identify the individual and combined effects of traditional initial geometric shell-wall imperfections and non-traditional shell-wall thickness variations, shell-end geometric imperfections and variations in loads applied to the ends of the shells on the shell buckling response are included. In addition, results illustrating the effects of manufacturing flaws in the form of gaps between adjacent pieces of graphite-epoxy tape in some of the laminate plies are presented in detail. The shells have been analyzed with a nonlinear finite-element analysis code that accurately accounts for these effects on the buckling and nonlinear responses of the shells. The numerical results indicate that traditional and nontraditional initial imperfections can cause a significant reduction in the buckling load of a compression-loaded composite shell. Furthermore, the results indicate that the imperfections couple in a nonlinear manner. The numerical results correlate well with the experimental results. The nonlinear analysis results are also compared to the results from a traditional linear bifurcation buckling analysis. The results suggest that the nonlinear analysis procedure can be used for determining accurate, high-fidelity design knockdown factors for shell buckling and collapse. The results can also be used to determine the effects of manufacturing tolerances on the buckling response of composite shells.
Free vibrations and buckling analysis of laminated plates by oscillatory radial basis functions
NASA Astrophysics Data System (ADS)
Neves, A. M. A.; Ferreira, A. J. M.
2015-12-01
In this paper the free vibrations and buckling analysis of laminated plates is performed using a global meshless method. A refined version of Kant's theorie which accounts for transverse normal stress and through-the-thickness deformation is used. The innovation is the use of oscillatory radial basis functions. Numerical examples are performed and results are presented and compared to available references. Such functions proved to be an alternative to the tradicional nonoscillatory radial basis functions.
NASA Technical Reports Server (NTRS)
Stoll, Frederick; Gurdal, Zafer; Starnes, James H., Jr.
1991-01-01
A method was developed for the geometrically nonlinear analysis of the static response of thin-walled stiffened composite structures loaded in uniaxial or biaxial compression. The method is applicable to arbitrary prismatic configurations composed of linked plate strips, such as stiffened panels and thin-walled columns. The longitudinal ends of the structure are assumed to be simply supported, and geometric shape imperfections can be modeled. The method can predict the nonlinear phenomena of postbuckling strength and imperfection sensitivity which are exhibited by some buckling-dominated structures. The method is computer-based and is semi-analytic in nature, making it computationally economical in comparison to finite element methods. The method uses a perturbation approach based on the use of a series of buckling mode shapes to represent displacement contributions associated with nonlinear response. Displacement contributions which are of second order in the model amplitudes are incorported in addition to the buckling mode shapes. The principle of virtual work is applied using a finite basis of buckling modes, and terms through the third order in the model amplitudes are retained. A set of cubic nonlinear algebraic equations are obtained, from which approximate equilibrium solutions are determined. Buckling mode shapes for the general class of structure are obtained using the VIPASA analysis code within the PASCO stiffened-panel design code. Thus, subject to some additional restrictions in loading and plate anisotropy, structures which can be modeled with respect to buckling behavior by VIPASA can be analyzed with respect to nonlinear response using the new method. Results obtained using the method are compared with both experimental and analytical results in the literature. The configurations investigated include several different unstiffened and blade-stiffening panel configurations, featuring both homogeneous, isotropic materials, and laminated composite
Thermal Buckling Analysis of Rectangular Panels Subjected to Humped Temperature Profile Heating
NASA Technical Reports Server (NTRS)
Ko, William I.
2004-01-01
This research investigates thermal buckling characteristics of rectangular panels subjected to different types of humped temperature profile heating. Minimum potential energy and finite-element methods are used to calculate the panel buckling temperatures. The two methods give fairly close thermal buckling solutions. 'Buckling temperature magnification factor of the first kind, eta' is established for the fixed panel edges to scale up the buckling solution of uniform temperature loading case to give the buckling solution of the humped temperature profile loading cases. Also, 'buckling temperature magnification factor of the second kind, xi' is established for the free panel edges to scale up the buckling solution of humped temperature profile loading cases with unheated boundary heat sinks to give the buckling solutions when the boundary heat sinks are heated up.
The thermal effect on buckling analysis of a DWCNT embedded on the Pasternak foundation
NASA Astrophysics Data System (ADS)
Ghorbanpour Arani, A.; Zarei, M. S.; Mohammadimehr, M.; Arefmanesh, A.; Mozdianfard, M. R.
2011-07-01
In this article, the thermal effect on the buckling analysis of a double-walled carbon nanotube (DWCNT) embedded in an elastic medium subjected to a uniform external pressure is investigated. Based on the nonlocal continuum cylindrical shell theory, the following effects are studied: small scale effect, van der Waals (vdW) forces between inner and outer tubes, surrounding elastic medium, and influence of temperature change in high-temperature environment. The interaction between matrix and the outer tube is modeled as a Pasternak foundation. The obtained results of numerical simulation indicate that for any specific circumferential wave number ( n), the nonlocal critical buckling pressure ( pcrit) is related directly to the axial half wave number ( m). Furthermore, the effect of temperature change on the critical buckling pressure is negligible, especially for stiff elastic medium; however, this is not the case if the elastic medium is soft. The strength of the DWCNT is directly related to the Winkler and shear moduli; hence, increase in the latter leads to enhanced pcrit.
An enriched 1D finite element for the buckling analysis of sandwich beam-columns
NASA Astrophysics Data System (ADS)
Sad Saoud, Kahina; Le Grognec, Philippe
2016-06-01
Sandwich constructions have been widely used during the last few decades in various practical applications, especially thanks to the attractive compromise between a lightweight and high mechanical properties. Nevertheless, despite the advances achieved to date, buckling still remains a major failure mode for sandwich materials which often fatally leads to collapse. Recently, one of the authors derived closed-form analytical solutions for the buckling analysis of sandwich beam-columns under compression or pure bending. These solutions are based on a specific hybrid formulation where the faces are represented by Euler-Bernoulli beams and the core layer is described as a 2D continuous medium. When considering more complex loadings or non-trivial boundary conditions, closed-form solutions are no more available and one must resort to numerical models. Instead of using a 2D computationally expensive model, the present paper aims at developing an original enriched beam finite element. It is based on the previous analytical formulation, insofar as the skin layers are modeled by Timoshenko beams whereas the displacement fields in the core layer are described by means of hyperbolic functions, in accordance with the modal displacement fields obtained analytically. By using this 1D finite element, linearized buckling analyses are performed for various loading cases, whose results are confronted to either analytical or numerical reference solutions, for validation purposes.
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
Buckling analysis and test correlation of hat stiffened panels for hypersonic vehicles
NASA Technical Reports Server (NTRS)
Percy, Wendy C.; Fields, Roger A.
1990-01-01
The paper discusses the design, analysis, and test of hat stiffened panels subjected to a variety of thermal and mechanical load conditions. The panels were designed using data from structural optimization computer codes and finite element analysis. Test methods included the grid shadow moire method and a single gage force stiffness method. The agreement between the test data and analysis provides confidence in the methods that are currently being used to design structures for hypersonic vehicles. The agreement also indicates that post buckled strength may potentially be used to reduce the vehicle weight.
NASA Technical Reports Server (NTRS)
Simitses, G. J.; Carlson, R. L.; Riff, R.
1985-01-01
The objective of the present research is to develop a general mathematical model and solution methodologies for analyzing the structural response of thin, metallic shell structures under large transient, cyclic, or static thermomechanical loads. Among the system responses associated with these loads and conditions are thermal buckling, creep buckling, and ratcheting. Thus geometric and material nonlinearities (of high order) can be anticipated and must be considered in developing the mathematical model. A complete, true ab-initio rate theory of kinematics and kinetics for continuum and curved thin structures, without any restriction on the magnitude of the strains or the deformations, was formulated. The time dependence and large strain behavior are incorporated through the introduction of the time rates of metric and curvature in two coordinate systems: fixed (spatial) and convected (material). The relations between the time derivative and the covariant derivative (gradient) were developed for curved space and motion, so the velocity components supply the connection between the equations of motion and the time rates of change of the metric and curvature tensors.
NASA Technical Reports Server (NTRS)
Farrokh, Babak; Segal, Kenneth N.; Akkerman, Michael; Glenn, Ronald L.; Rodini, Benjamin T.; Fan, Wei-Ming; Kellas, Sortiris; Pineda, Evan J.
2014-01-01
In this work, an all-bonded out-of-autoclave (OoA) curved longitudinal composite joint concept, intended for use in the next generation of composite heavy lift launch vehicles, was evaluated and verified through finite element (FE) analysis, fabrication, testing, and post-test inspection. The joint was used to connect two curved, segmented, honeycomb sandwich panels representative of a Space Launch System (SLS) fairing design. The overall size of the resultant panel was 1.37 m by 0.74 m (54 in by 29 in), of which the joint comprised a 10.2 cm (4 in) wide longitudinal strip at the center. NASTRAN and ABAQUS were used to perform linear and non-linear analyses of the buckling and strength performance of the jointed panel. Geometric non-uniformities (i.e., surface contour imperfections) were measured and incorporated into the FE model and analysis. In addition, a sensitivity study of the specimens end condition showed that bonding face-sheet doublers to the panel's end, coupled with some stress relief features at corner-edges, can significantly reduce the stress concentrations near the load application points. Ultimately, the jointed panel was subjected to a compressive load. Load application was interrupted at the onset of buckling (at 356 kN 80 kips). A post-test non-destructive evaluation (NDE) showed that, as designed, buckling occurred without introducing any damage into the panel or the joint. The jointed panel was further capable of tolerating an impact damage to the same buckling load with no evidence of damage propagation. The OoA cured all-composite joint shows promise as a low mass factory joint for segmented barrels.
Cap buckling as a potential mechanism of atherosclerotic plaque vulnerability.
Abdelali, Maria; Reiter, Steven; Mongrain, Rosaire; Bertrand, Michel; L'Allier, Philippe L; Kritikou, Ekaterini A; Tardif, Jean-Claude
2014-04-01
Plaque rupture in atherosclerosis is the primary cause of potentially deadly coronary events, yet about 40% of ruptures occur away from the plaque cap shoulders and cannot be fully explained with the current biomechanical theories. Here, cap buckling is considered as a potential destabilizing factor which increases the propensity of the atherosclerotic plaque to rupture and which may also explain plaque failure away from the cap shoulders. To investigate this phenomenon, quasistatic 2D finite element simulations are performed, considering the salient geometrical and nonlinear material properties of diverse atherosclerotic plaques over the range of physiological loads. The numerical results indicate that buckling may displace the location of the peak von Mises stresses in the deflected caps. Plaque buckling, together with its deleterious effects is further observed experimentally in plaque caps using a physical model of deformable mock coronary arteries with fibroatheroma. Moreover, an analytical approach combining quasistatic equilibrium equations with the Navier-Bresse formulas is used to demonstrate the buckling potential of a simplified arched slender cap under intraluminal pressure and supported by foundations. This analysis shows that plaque caps - calcified, fibrotic or cellular - may buckle in specific undulated shapes once submitted to critical loads. Finally, a preliminary analysis of intravascular ultrasonography recordings of patients with atherosclerotic coronary arteries corroborates the numerical, experimental and theoretical findings and shows that various plaque caps buckle in vivo. By displacing the sites of high stresses in the plaque cap, buckling may explain the atherosclerotic plaque cap rupture at various locations, including cap shoulders. PMID:24491969
Stress analysis and buckling of J-stiffened graphite-epoxy panel
NASA Technical Reports Server (NTRS)
Davis, R. C.
1980-01-01
A graphite epoxy shear panel with bonded on J stiffeners was investigated. The panel, loaded to buckling in a picture frame shear test is described. Two finite element models, each of which included the doubler material bonded to the panel skin under the stiffeners and at the panel edges, were used to make a stress analysis of the panel. The shear load distributions in the panel from two commonly used boundary conditions, applied shear load and applied displacement, were compared with the results from one of the finite element models that included the picture frame test fixture.
Current research on shear buckling and thermal loads with PASCO: Panel Analysis and Sizing Code
NASA Technical Reports Server (NTRS)
Stroud, W. J.; Greene, W. H.; Anderson, M. S.
1981-01-01
The PASCO computer program to obtain the detailed dimensions of optimum stiffened composite structural panels is described. Design requirements in terms of inequality constraints can be placed on buckling loads or vibration frequencies, lamina stresses and strains, and overall panel stiffness for each of many load conditions. General panel cross sections can be treated. An analysis procedure involving a smeared orthotropic solution was investigated. The conservatism in the VIPASA solution and the danger in a smeared orthotropic solution is explored. PASCO's capability to design for thermal loadings is also described. It is emphasized that design studies illustrate the importance of the multiple load condition capability when thermal loads are present.
NASA Technical Reports Server (NTRS)
Ko, William L.
1994-01-01
The combined load (mechanical or thermal load) buckling equations were established for orthotropic rectangular sandwich panels under four different edge conditions by using the Rayleigh-Ritz method of minimizing the total potential energy of a structural system. Two-dimensional buckling interaction curves and three-dimensional buckling interaction surfaces were constructed for high-temperature honeycomb-core sandwich panels supported under four different edge conditions. The interaction surfaces provide overall comparison of the panel buckling strengths and the domains of symmetrical and antisymmetrical buckling associated with the different edge conditions. In addition, thermal buckling curves of these sandwich panels are presented. The thermal buckling conditions for the cases with and without thermal moments were found to be identical for the small deformation theory.
Instability signature for detecting snap-through buckling of dome structures
NASA Astrophysics Data System (ADS)
Yan, Guirong; Duan, Qiuhua; Hua, Xugang
2016-04-01
Dome structures have been built as roofs for venues where many people convene. Failure of this type of structure may jeopardize the safety of hundreds or even thousands people. For this type of structure, snap-through buckling may occur in a local area and gradually expand to the entire structure, leading to a failure of the overall structure. Although numerous structural health monitoring techniques and damage detection approaches have been developed, no research on the detection of a snap-through buckling has been reported. The objective of this study is to find a signature that is sensitive to snap-through buckling in dome structures and can be used to detect snap-through buckling. Considering that a snap-through buckling results in a significant deformation in a local area, which can be reflected by the change in tilting angles of members in that local area, the change in tilting angles of members will be proposed to be a signature to detect snap-through buckling. To verify the proposed instability signature, a reticulated dome structure will be investigated. Both an eigenvalue buckling analysis and a nonlinear buckling analysis will be conducted. The significant changes in tilting angles of members in the buckled regions have demonstrated the efficacy of the proposed instability signature. This research will bridge the research gap between structural health monitoring and structural stability research.
Analysis of Potential for Titanium Liner Buckling after Proof in a Large Kevlar/Epoxy COPV
NASA Technical Reports Server (NTRS)
Phoenix, S. Leigh; Kezirian, Michael T.
2009-01-01
We analyze the potential for liner buckling in a 40-in Kevlar49/epoxy overwrapped spherical pressure vessel (COPV) due to long, local depressions or valleys in the titanium liner, which appeared after proof testing (autofrettage). We begin by presenting the geometric characteristics of approximately 20 mil (0.02 in.) deep depressions measured by laser profilometry in several vessels. While such depths were more typical, depths of more than 40 mils (0.02 in.) were seen near the equator in one particular vessel. Such depressions are largely the result of overlap of the edges of overwrap bands (with rectangular cross-section prepreg tows) from the first or second wrap patterns particularly where they start and end. We then discuss the physical mechanisms of formation of the depressions during the autofrettage process in terms of uneven void compaction in the overwrap around the tow overlap lines and the resulting 10-fold increase in through-thickness stiffness of the overwrap. We consider the effects of liner plastic yielding mechanisms in the liner on residual bending moments and interface pressures with the overwrap both at the peak proof pressure (approx.6500 psi) and when reducing the pressure to 0 psi. During depressurization the Bauschinger phenomenon becomes very important whereby extensive yielding in tension reduces the magnitude of the yield threshold in compression by 30 to 40%, compared to the virgin annealed state of the liner titanium. In the absence of a depression, the liner is elastically stable in compression even at liner overwrap interface pressures nominally 6 times the approx. 1000 psi interface pressure that exists at 0 psi. Using a model based on a plate-on-an-elastic-foundation, we develop an extensive analysis of the possible destabilizing effects of a frozen-in valley. The analysis treats the modifying effects of the residual bending moments and interface pressures remaining after the proof hold as well as the Bauschinger effect on the
Buckling 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.
Buckling instability in arteries.
Vandiver, Rebecca M
2015-04-21
Arteries can become tortuous in response to abnormal growth stimuli, genetic defects and aging. It is suggested that a buckling instability is a mechanism that might lead to artery tortuosity. Here, the buckling instability in arteries is studied by examining asymmetric modes of bifurcation of two-layer cylindrical structures that are residually stressed. These structures are loaded by an axial force, internal pressure and have nonlinear, anisotropic, hyperelastic responses to stresses. Strain-softening and reduced opening angle are shown to lower the critical internal pressure leading to buckling. In addition, the ratio of the media thickness to the adventitia thickness is shown to have a dramatic impact on arterial instability. PMID:25661070
NASA Astrophysics Data System (ADS)
Kim, Nam-Il; Fu, Chung C.; Kim, Moon-Young
2007-02-01
Based on the power series method, the static and dynamic stiffness matrices for the flexural-torsional buckling and free vibration analysis of thin-walled beam with non-symmetric cross-section subjected to linearly variable axial force are newly presented. Additionally, the static stiffness matrix for the lateral buckling analysis of non-symmetric beam is presented for the first time. For this, the elastic strain energy, the potential energy considering the second-order terms of finite rotations, and the kinetic energy for thin-walled beam with non-symmetric cross-section are introduced. Then equations of motion and force-deformation relations are derived from the energy principle. Explicit expressions for displacement parameters are derived based on power series expansions of displacement components. Finally, the static and dynamic element stiffness matrices are determined using force-deformation relationships. In order to verify the accuracy of this study, the numerical solutions are presented and compared with the finite element solutions using the Hermitian beam elements and ABAQUS's shell elements.
Combined compressive and shear buckling analysis of hypersonic aircraft structural sandwich panels
NASA Technical Reports Server (NTRS)
Ko, William L.; Jackson, Raymond H.
1991-01-01
The combined-load (compression and shear) buckling equations were established for orthotropic sandwich panels by using the Rayleigh-Ritz method to minimize the panel total potential energy. The resulting combined-load buckling equations were used to generate buckling interaction curves for super-plastically-formed/diffusion-bonded titanium truss-core sandwich panels and titanium honeycomb-core sandwich panels having the same specific weight. The relative combined-load buckling strengths of these two types of sandwich panels are compared with consideration of their sandwich orientations. For square and nearly square panels of both types, the combined load always induces symmetric buckling. As the panel aspect ratios increase, antisymmetric buckling will show up when the loading is shear-dominated combined loading. The square panel (either type) has the highest combined buckling strength, but the combined load buckling strength drops sharply as the panel aspect ratio increases. For square panels, the truss-core sandwich panel has higher compression-dominated combined load buckling strength. However, for shear dominated loading, the square honeycomb-core sandwich panel has higher shear-dominated combined load buckling strength.
NASA Technical Reports Server (NTRS)
Hilburger, Mark W.; Nemeth, Michael P.; Riddick, Jaret C.; Thornburgh, Robert P.
2004-01-01
A parametric study of the effects of test-fixture-induced initial prestress and elastic edge restraints on the prebuckling and buckling responses of a compression-loaded, quasi-isotropic curved panel is presented. The numerical results were obtained by using a geometrically nonlinear finite element analysis code with high-fidelity models. The results presented show that a wide range of prebuckling and buckling behavior can be obtained by varying parameters that represent circumferential loaded-edge restraint and rotational unloaded-edge restraint provided by a test fixture and that represent the mismatch in specimen and test-fixture radii of curvature. For a certain range of parameters, the panels exhibit substantial nonlinear prebuckling deformations that yield buckling loads nearly twice the corresponding buckling load predicted by a traditional linear bifurcation buckling analysis for shallow curved panels. In contrast, the results show another range of parameters exist for which the nonlinear prebuckling deformations either do not exist or are relatively benign, and the panels exhibit buckling loads that are nearly equal to the corresponding linear bifurcation buckling load. Overall, the results should also be of particular interest to scientists, engineers, and designers involved in simulating flight-hardware boundary conditions in structural verification and certification tests, involved in validating structural analysis tools, and interested in tailoring buckling performance.
Design, Analysis, and On-Sun Evaluation of Reflective Strips Under Controlled Buckling
NASA Technical Reports Server (NTRS)
Jaworske, D. A.; Sechkar, E. A.; Colozza, A. J.
2014-01-01
Solar concentrators are envisioned for use in a variety of space-based applications, including applications involving in situ resource utilization. Identifying solar concentrators that minimize mass and cost are of great interest, especially since launch cost is driven in part by the mass of the payload. Concentrators must also be able to survive the wide temperature excursions on the lunar surface. Identifying smart structures which compensate for changes in concentrator geometry brought about by temperature extremes are of interest. Some applications may benefit from the ability to change the concentrator's focal pattern at will. This paper addresses a method of designing a single reflective strip to produce a desired focal pattern through the use of controlled buckling. Small variations in the cross section over the length of the reflective strip influence the distribution of light in the focal region. A finite element method of analysis is utilized here which calculates the curve produced for a given strip cross section and axial load. Varying axial force and strip cross section over the length of the reflective strip provide a means of optimizing ray convergence in the focal region. Careful selection of a tapered cross section yields a reflective strip that approximates a parabola. An array of reflective strips under controlled buckling produces a light weight concentrator and adjustments in the compression of individual strips provide a means of compensating for temperature excursions or changing the focal pattern at will.
Design, Analysis, and On-Sun Evaluation of Reflective Strips Under Controlled Buckling
NASA Technical Reports Server (NTRS)
Jaworske, Donald A.; Sechkar, Edward A.; Colozza, Anthony J.
2014-01-01
Solar concentrators are envisioned for use in a variety of space-based applications, including applications involving in situ resource utilization. Identifying solar concentrators that minimize mass and cost are of great interest, especially since launch cost is driven in part by the mass of the payload. Concentrators must also be able to survive the wide temperature excursions on the lunar surface. Identifying smart structures which compensate for changes in concentrator geometry brought about by temperature extremes are of interest. Some applications may benefit from the ability to change the concentrators focal pattern at will. This paper addresses a method of designing a single reflective strip to produce a desired focal pattern through the use of controlled buckling. Small variations in the cross section over the length of the reflective strip influence the distribution of light in the focal region. A finite element method of analysis is utilized here which calculates the curve produced for a given strip cross section and axial load. Varying axial force and strip cross section over the length of the reflective strip provide a means of optimizing ray convergence in the focal region. Careful selection of a tapered cross section yields a reflective strip that approximates a parabola. An array of reflective strips under controlled buckling produces a light weight concentrator and adjustments in the compression of individual strips provide a means of compensating for temperature excursions or changing the focal pattern at will.
Mechanical and thermal buckling analysis of sandwich panels under different edge conditions
NASA Technical Reports Server (NTRS)
Ko, William L.
1993-01-01
By using the Rayleigh-Ritz method of minimizing the total potential energy of a structural system, combined load (mechanical or thermal load) buckling equations are established for orthotropic rectangular sandwich panels supported under four different edge conditions. Two-dimensional buckling interaction curves and three dimensional buckling interaction surfaces are constructed for high-temperature honeycomb-core sandwich panels supported under four different edge conditions. The interaction surfaces provide easy comparison of the panel buckling strengths and the domains of symmetrical and antisymmetrical buckling associated with the different edge conditions. Thermal buckling curves of the sandwich panels also are presented. The thermal buckling conditions for the cases with and without thermal moments were found to be identical for the small deformation theory. In sandwich panels, the effect of transverse shear is quite large, and by neglecting the transverse shear effect, the buckling loads could be overpredicted considerably. Clamping of the edges could greatly increase buckling strength more in compression than in shear.
NASA Technical Reports Server (NTRS)
Stein, M.; Housner, J. D.
1978-01-01
A numerical analysis developed for the buckling of rectangular orthotropic layered panels under combined shear and compression is described. This analysis uses a central finite difference procedure based on trigonometric functions instead of using the conventional finite differences which are based on polynomial functions. Inasmuch as the buckle mode shape is usually trigonometric in nature, the analysis using trigonometric finite differences can be made to exhibit a much faster convergence rate than that using conventional differences. Also, the trigonometric finite difference procedure leads to difference equations having the same form as conventional finite differences; thereby allowing available conventional finite difference formulations to be converted readily to trigonometric form. For two-dimensional problems, the procedure introduces two numerical parameters into the analysis. Engineering approaches for the selection of these parameters are presented and the analysis procedure is demonstrated by application to several isotropic and orthotropic panel buckling problems. Among these problems is the shear buckling of stiffened isotropic and filamentary composite panels in which the stiffener is broken. Results indicate that a break may degrade the effect of the stiffener to the extent that the panel will not carry much more load than if the stiffener were absent.
High-Fidelity Nonlinear Analysis of Compression-Loaded Composite Shells
NASA Technical Reports Server (NTRS)
Hilburger, Mark W.; Starnes, James H., Jr.
2001-01-01
The results of an experimental and analytical study of the effects of initial imperfections on the buckling and postbuckling response of unstiffened thin-walled compression-loaded graphite-epoxy cylindrical shells are presented. The shells considered in the study have four different shell-wall laminates and two different shell-radius-to-thickness ratios. The shell-wall laminates include two different orthotropic laminates and two different quasi-isotropic laminates. The shell-radius-to-thickness ratios include shell-radius-to-thickness ratios equal to 100 and 200. The results identify the effects of traditional and nontraditional initial imperfections on the nonlinear response characteristics and buckling loads of the shells. The traditional imperfections include the geometric shell-wall mid-surface imperfections that are commonly discussed in the literature on thin shell buckling. The nontraditional imperfections include shell-wall thickness variations, local shell-wall ply-gaps associated with the fabrication process, shell-end geometric imperfections, nonuniform applied end loads, and variations in the boundary conditions including the effects of elastic boundary conditions. A high-fidelity nonlinear shell analysis procedure that accurately accounts for the effects of these traditional and nontraditional imperfections on the nonlinear response characteristics and buckling loads of the shells is described. The analysis procedure includes a nonlinear static analysis that predicts the stable response characteristics of the shells, and a nonlinear transient analysis that predicts the unstable response characteristics. The results of a local shell-wall stress analysis used to estimate failure stresses are also described.
Dynamic buckling analysis of delaminated composite plates using semi-analytical finite strip method
NASA Astrophysics Data System (ADS)
Ovesy, H. R.; Totounferoush, A.; Ghannadpour, S. A. M.
2015-05-01
The delamination phenomena can become of paramount importance when the design of the composite plates is concerned. In the current study, the effect of through-the-width delamination on dynamic buckling behavior of a composite plate is studied by implementing semi-analytical finite strip method. In this method, the energy and work integrations are computed analytically due to the implementation of trigonometric functions. Moreover, the method can lead to converged results with comparatively small number of degrees of freedom. These features have made the method quite efficient. To account for delamination effects, displacement field is enriched by adding appropriate terms. Also, the penetration of the delamination surfaces is prevented by incorporating an appropriate contact scheme into the time response analysis. Some selected results are validated against those available in the literature.
Analyses of Buckling and Stable Tearing in Thin-Sheet Materials
NASA Technical Reports Server (NTRS)
Seshadri, B. R.; Newman, J. C., Jr.
1998-01-01
This paper was to verify the STAGS (general shell, geometric and material nonlinear) code and the critical crack tip opening angle (CTOA) fracture criterion for predicting stable tearing in cracked panels that fail with severe out of plane buckling. Materials considered ranged from brittle to ductile behavior. Test data used in this study are reported elsewhere. The STAGS code was used to model stable tearing using a critical CTOA value that was determined from a cracked panel that was 'restrained' from buckling. ne analysis methodology was then used to predict the influence of buckling on stable tearing and failure loads. Parameters like crack length to specimen width ratio, crack configuration, thickness, and material tensile properties had a significant influence on the buckling behavior of cracked thin sheet materials. Experimental and predicted results showed a varied buckling response for different crack length to sheet thickness ratios because different buckling modes were activated. Effects of material tensile properties and fracture toughness on buckling response were presented. The STAGS code and the CTOA fracture criterion were able to predict the influence of buckling on stable tearing behavior and failure loads on a variety of materials and crack configurations.
Artery buckling analysis using a two-layered wall model with collagen dispersion.
Mottahedi, Mohammad; Han, Hai-Chao
2016-07-01
Artery buckling has been proposed as a possible cause for artery tortuosity associated with various vascular diseases. Since microstructure of arterial wall changes with aging and diseases, it is essential to establish the relationship between microscopic wall structure and artery buckling behavior. The objective of this study was to developed arterial buckling equations to incorporate the two-layered wall structure with dispersed collagen fiber distribution. Seven porcine carotid arteries were tested for buckling to determine their critical buckling pressures at different axial stretch ratios. The mechanical properties of these intact arteries and their intima-media layer were determined via pressurized inflation test. Collagen alignment was measured from histological sections and modeled by a modified von-Mises distribution. Buckling equations were developed accordingly using microstructure-motivated strain energy function. Our results demonstrated that collagen fibers disperse around two mean orientations symmetrically to the circumferential direction (39.02°±3.04°) in the adventitia layer; while aligning closely in the circumferential direction (2.06°±3.88°) in the media layer. The microstructure based two-layered model with collagen fiber dispersion described the buckling behavior of arteries well with the model predicted critical pressures match well with the experimental measurement. Parametric studies showed that with increasing fiber dispersion parameter, the predicted critical buckling pressure increases. These results validate the microstructure-based model equations for artery buckling and set a base for further studies to predict the stability of arteries due to microstructural changes associated with vascular diseases and aging. PMID:27031686
Shell Buckling Design Criteria Based on Manufacturing Imperfection Signatures
NASA Technical Reports Server (NTRS)
Hilburger, Mark W.; Nemeth, Michael P.; Starnes, James H., Jr.
2004-01-01
An analysis-based approach .for developing shell-buckling design criteria for laminated-composite cylindrical shells that accurately accounts for the effects of initial geometric imperfections is presented. With this approach, measured initial geometric imperfection data from six graphite-epoxy shells are used to determine a manufacturing-process-specific imperfection signature for these shells. This imperfection signature is then used as input into nonlinear finite-element analyses. The imperfection signature represents a "first-approximation" mean imperfection shape that is suitable for developing preliminary-design data. Comparisons of test data and analytical results obtained by using several different imperfection shapes are presented for selected shells. Overall, the results indicate that the analysis-based approach presented for developing reliable preliminary-design criteria has the potential to provide improved, less conservative buckling-load estimates, and to reduce the weight and cost of developing buckling-resistant shell structures.
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.
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
Probabilistic progressive buckling of trusses
NASA Technical Reports Server (NTRS)
Pai, Shantaram S.; Chamis, Christos C.
1991-01-01
A three-bay, space, cantilever truss is probabilistically evaluated to describe progressive buckling and truss collapse in view of the numerous uncertainties associated with the structural, material, and load variables (primitive variables) that describe the truss. Initially, the truss is deterministically analyzed for member forces, and member(s) in which the axial force exceeds the Euler buckling load are identified. These member(s) are then discretized with several intermediate nodes and a probabilistic buckling analysis is performed on the truss to obtain its probabilistic buckling loads and respective mode shapes. Furthermore, sensitivities associated with the uncertainties in the primitive variables are investigated, margin of safety values for the truss are determined, and truss end node displacements are noted. These steps are repeated by sequentially removing the buckled member(s) until onset of truss collapse is reached. Results show that this procedure yields an optimum truss configuration for a given loading and for a specified reliability.
NASA Technical Reports Server (NTRS)
Housner, J. M.; Stein, M.
1975-01-01
A computer program is presented which was developed for the combined compression and shear of stiffened variable thickness orthotropic composite panels on discrete springs: boundary conditions are general and include elastic boundary restraints. Buckling solutions are obtained by using a newly developed trigonometric finite difference procedure which improves the solution convergence rate over conventional finite difference methods. The classical general shear buckling results which exist only for simply supported panels over a limited range of orthotropic properties, were extended to the complete range of these properties for simply supported panels and, in addition, to the complete range of orthotropic properties for clamped panels. The program was also applied to parametric studies which examine the effect of filament orientation upon the buckling of graphite-epoxy panels. These studies included an examination of the filament orientations which yield maximum shear or compressive buckling strength for panels having all four edges simply supported or clamped over a wide range of aspect ratios. Panels with such orientations had higher buckling loads than comparable, equal weight, thin skinned aluminum panels. Also included among the parameter studies were examinations of combined axial compression and shear buckling and examinations of panels with rotational elastic edge restraints.
Investigations on Buckling Behaviour of Laminated Curved Composite Stiffened Panels
NASA Astrophysics Data System (ADS)
Kumar, N. Jeevan; Babu, P. Ramesh; Pandu, Ratnakar
2014-04-01
In Industrial applications structural efficiency is primary concern, this brings about the need of strong and lightweight materials. Due to their high specific strength, fibre reinforced polymers find wide application in these areas. Panels made of composite materials are widely used in aerospace structures, automobile, civil, marine and biomedical industries because of their good mechanical properties, impact resistance, excellent damage tolerance and also low fabrication cost. In this Paper, buckling and post-buckling analysis was performed on composite stiffened panel to obtain the critical load and modes of failures, with different parameters like ply-orientation, different composite materials, and stiffeners and by changing the number of stiffeners was derived. To analyze the post buckling behaviour of composite stiffened panels the nonlinear finite element analysis is employed and substantial investigations are undertaken using finite element (FE) model. Effect of critical parameters on buckling behaviour is studied and parametric studies were conducted with analytical tool to understand the structural behaviour in the post buckling range.
Buckle driven delamination in thin hard film compliant substrate systems.
Cordill, Megan J.; Adams, David Price; Moody, Neville Reid; Corona, Edmundo; Kennedy, Marian S.; Bahr, David F.; Reedy, Earl David, Jr.
2010-06-01
rigid elastic solutions. To address this issue we developed a finite element analysis technique that employed a cohesive zone model to simulate interfacial crack growth. Specifying the traction-separation relationship, cohesive strength, and work of separation along with film thickness, film stress, and film and substrate properties, buckle width and height were determined as a function of interfacial toughness. The simulations indicate that an analysis based on rigid substrate solutions significantly underestimate toughness for prescribed buckle widths: a result consistent with an analysis by Yu and Hutchinson that pieced together a solution based on non-linear plate theory with a solution for the linear film on substrate problem. More importantly, the results defined a lower limiting bound to seemingly disparate buckle deflection data. The variance from linear elastic behavior, especially for the small buckles, indicates more than substrate compliance is controlling behavior. Comparison of the experimental results with cohesive zone simulations suggests that the two buckle behaviors are associated with different levels of substrate yielding. In this presentation we will use the results to show how substrate compliance and deformation affect delamination and buckling of films on compliant substrates and provide a means to predict device performance.
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
Non-isothermal buckling behavior of viscoplastic shell structures
NASA Technical Reports Server (NTRS)
Riff, Richard; Simitses, G. J.
1988-01-01
Described are the mathematical model and solution methodologies for analyzing the structural response of thin, metallic elasto-viscoplastic shell structures under large thermomechanical loads and their non-isothermal buckling behavior. Among the system responses associated with these loads and conditions are snap-through, buckling, thermal buckling, and creep buckling. This geometric and material nonlinearities (of high order) can be anticipated and are considered in the model and the numerical treatment.
Pre-Test Analysis Predictions for the Shell Buckling Knockdown Factor Checkout Tests - TA01 and TA02
NASA Technical Reports Server (NTRS)
Thornburgh, Robert P.; Hilburger, Mark W.
2011-01-01
This report summarizes the pre-test analysis predictions for the SBKF-P2-CYL-TA01 and SBKF-P2-CYL-TA02 shell buckling tests conducted at the Marshall Space Flight Center (MSFC) in support of the Shell Buckling Knockdown Factor (SBKF) Project, NASA Engineering and Safety Center (NESC) Assessment. The test article (TA) is an 8-foot-diameter aluminum-lithium (Al-Li) orthogrid cylindrical shell with similar design features as that of the proposed Ares-I and Ares-V barrel structures. In support of the testing effort, detailed structural analyses were conducted and the results were used to monitor the behavior of the TA during the testing. A summary of predicted results for each of the five load sequences is presented herein.
Analysis of bending and buckling of pre-twisted beams: A bioinspired study
NASA Astrophysics Data System (ADS)
Zhao, Zi-Long; Zhao, Hong-Ping; Chang, Zheng; Feng, Xi-Qiao
2014-08-01
Twisting chirality is widely observed in artificial and natural materials and structures at different length scales. In this paper, we theoretically investigate the effect of twisting chiral morphology on the mechanical properties of elastic beams by using the Timoshenko beam model. Particular attention is paid to the transverse bending and axial buckling of a pre-twisted rectangular beam. The analytical solution is first derived for the deflection of a clamped-free beam under a uniformly or periodically distributed transverse force. The critical buckling condition of the beam subjected to its self-weight and an axial compressive force is further solved. The results show that the twisting morphology can significantly improve the resistance of beams to both transverse bending and axial buckling. This study helps understand some phenomena associated with twisting chirality in nature and provides inspirations for the design of novel devices and structures.
Buckling Analysis of Anisotropic Curved Panels and Shells with Variable Curvature
NASA Technical Reports Server (NTRS)
Jaunky, Navin; Knight, Norman F., Jr.; Ambur, Damodar R.
1998-01-01
A buckling formulation for anisotropic curved panels with variable curvature is presented in this paper. The variable curvature panel is assumed to consists of two or more panels of constant but different curvatures. Bezier functions are used as Ritz functions Displacement (C(sup 0)), and slope (C(sup 1)) continuities between segments are imposed by manipulation of the Bezier control points. A first-order shear-deformation theory is used in the buckling formulation. Results obtained from the present formulation are compared with those from finite element simulations and are found to be in good agreement.
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
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.
A novel method for studying the buckling of nanotubes considering geometrical imperfections
NASA Astrophysics Data System (ADS)
Anoop Krishnan, N. M.; Ghosh, Debraj
2014-05-01
Buckling of nanotubes has been studied using many methods such as molecular dynamics (MD), molecular mechanics, and continuum-based shell theories. In MD, motion of the individual atoms is tracked under applied temperature and pressure, ensuring a reliable estimate of the material response. The response thus simulated varies for individual nanotubes and is only as accurate as the force field used to model the atomic interactions. On the other hand, there exists a rich literature on the understanding of continuum mechanics-based shell theories. Based on the observations on the behavior of nanotubes, there have been a number of shell theory-based approaches to study the buckling of nanotubes. Although some of these methods yield a reasonable estimate of the buckling stress, investigation and comparison of buckled mode shapes obtained from continuum analysis and MD are sparse. Previous studies show that the direct application of shell theories to study nanotube buckling often leads to erroneous results. The present study reveals that a major source of this error can be attributed to the departure of the shape of the nanotube from a perfect cylindrical shell. Analogous to the shell buckling in the macro-scale, in this work, the nanotube is modeled as a thin-shell with initial imperfection. Then, a nonlinear buckling analysis is carried out using the Riks method. It is observed that this proposed approach yields significantly improved estimate of the buckling stress and mode shapes. It is also shown that the present method can account for the variation of buckling stress as a function of the temperature considered. Hence, this can prove to be a robust method for a continuum analysis of nanosystems taking in the effect of variation of temperature as well.
Effects of Imperfections on the Buckling Response of Compression-Loaded Composite Shells
NASA Technical Reports Server (NTRS)
Hilburger, Mark W.; Starnes, James H., Jr.
2002-01-01
The results of an experimental and analytical study of the effects of initial imperfections on the buckling and postbuckling response of three unstiffened thin-walled compression-loaded graphite-epoxy cylindrical shells with different orthotropic and quasi-isotropic shell-wall laminates are presented. The results identify the effects of traditional and non-traditional initial imperfections on the non-linear response and buckling loads of the shells. The traditional imperfections include the geometric shell-wall mid-surface imperfect ions that are commonly discussed in the literature on thin shell buckling. The non-traditional imperfections include shell-wall thickness variations local shell-wall ply-gaps associated with the fabrication process, sheltered geometric imperfections, non-uniform applied end loads, and variations in the boundary conditions including the effects of elastic boundary conditions. A high-fidelity non-linear shell analysis procedure that accurately accounts for the effects of these traditional and non-traditional imperfections on the nonlinear response, and buckling loads of the shells is described. The analysis procedure includes a non-linear static analysis that predicts stable response characteristics of the shells and a non-linear transient analysis that predicts unstable response characteristics.
Thermal-structural panel buckling tests
NASA Technical Reports Server (NTRS)
Thompson, Randolph C.; Richards, W. Lance
1991-01-01
The buckling characteristics of a titanium matrix composite hat-stiffened panel were experimentally examined for various combinations of thermal and mechanical loads. Panel failure was prevented by maintaining the applied loads below real-time critical buckling predictions. The test techniques used to apply the loads, minimize boundary were shown to compare well with a finite-element buckling analysis for previous panels. Comparisons between test predictions and analysis for this panel are ongoing.
Mechanics of precisely controlled thin film buckling on Elastomeric substrate.
Sun, Y.; Jiang, H.; Rogers, J.; Huang, Y.; Arizone State Univ.; Beckman Inst.; University of Illinois Urbana-Champaign
2007-01-01
Stretchable electronics has many important and emerging applications. Sun et al. [Nature Nanotech. 1, 201 (2006)] recently demonstrated stretchable electronics based on precisely controlled buckle geometries in GaAs and Si nanoribbons on elastomeric substrates. A nonlinear buckling model is presented in this letter to study the mechanics of this type of thin film/substrate system. An analytical solution is obtained for the buckling geometry (wavelength and amplitude) and the maximum strain in buckled thin film. This solution agrees very well with the experiments, and shows explicitly how buckling can significantly reduce the thin film strain to achieve the system stretchability.
Experimental analysis of buckling in aircraft skin panels by fibre optic sensors
NASA Astrophysics Data System (ADS)
Güemes, J. A.; Menendez, J. M.; Frövel, M.; Fernandez, I.; Pintado, J. M.
2001-06-01
Three blade-stiffened CFRP panels with co-cured stiffener webs, manufactured by means of an elastomeric mould, have been tested under compressive load. Several Bragg grating sensors have been surface bonded on two of the stiffened panels and have been embedded into the stiffener webs of the third panel. The Bragg grating sensors measured the strain distribution in the stiffener web and in the skin panels. The bucking onset was clearly detected in every case, the post-buckling behaviour can be tracked, but the information is heavily dependent on the right choice of the sensor position and the buckling mode. To calibrate the system, and to evaluate the influence of different curing pressures, and the use of unidirectional or fabric prepreg material, tensile test specimens were made on flat panels. The strain measurements provided by the optical fibre sensors in tensile tests were compared with the strain measurements provided by conventional clamp extensometers.
NASA Astrophysics Data System (ADS)
Lai, Changliang; Wang, Junbiao; Liu, Chuang
2014-10-01
Six typical composite grid cylindrical shells are constructed by superimposing three basic types of ribs. Then buckling behavior and structural efficiency of these shells are analyzed under axial compression, pure bending, torsion and transverse bending by finite element (FE) models. The FE models are created by a parametrical FE modeling approach that defines FE models with original natural twisted geometry and orients cross-sections of beam elements exactly. And the approach is parameterized and coded by Patran Command Language (PCL). The demonstrations of FE modeling indicate the program enables efficient generation of FE models and facilitates parametric studies and design of grid shells. Using the program, the effects of helical angles on the buckling behavior of six typical grid cylindrical shells are determined. The results of these studies indicate that the triangle grid and rotated triangle grid cylindrical shell are more efficient than others under axial compression and pure bending, whereas under torsion and transverse bending, the hexagon grid cylindrical shell is most efficient. Additionally, buckling mode shapes are compared and provide an understanding of composite grid cylindrical shells that is useful in preliminary design of such structures.
Buckling of conical shell with local imperfections
NASA Technical Reports Server (NTRS)
Cooper, P. A.; Dexter, C. B.
1974-01-01
Small geometric imperfections in thin-walled shell structures can cause large reductions in buckling strength. Most imperfections found in structures are neither axisymmetric nor have the shape of buckling modes but rather occur locally. This report presents the results of a study of the effect of local imperfections on the critical buckling load of a specific axially compressed thin-walled conical shell. The buckling calculations were performed by using a two-dimensional shell analysis program referred to as the STAGS (Structural Analysis of General Shells) computer code, which has no axisymmetry restrictions. Results show that the buckling load found from a bifurcation buckling analysis is highly dependent on the circumferential arc length of the imperfection type studied. As the circumferential arc length of the imperfection is increased, a reduction of up to 50 percent of the critical load of the perfect shell can occur. The buckling load of the cone with an axisymmetric imperfections is nearly equal to the buckling load of imperfections which extended 60 deg or more around the circumference, but would give a highly conservative estimate of the buckling load of a shell with an imperfection of a more local nature.
Simplified dynamic buckling assessment of steel containments
Farrar, C.R.; Duffey, T.A.; Renick, D.H.
1993-02-01
A simplified, three-degree-of-freedom analytical procedure for performing a response spectrum buckling analysis of a thin containment shell is developed. Two numerical examples with R/t values which bound many existing steel containments are used to illustrate the procedure. The role of damping on incipient buckling acceleration level is evaluated for a regulatory seismic spectrum using the two numerical examples. The zero-period acceleration level that causes incipient buckling in either of the two containments increases 31% when damping is increased from 1% to 4% of critical. Comparisons with finite element results on incipient buckling levels are favorable.
Nonlinear Principal Components Analysis: Introduction and Application
ERIC Educational Resources Information Center
Linting, Marielle; Meulman, Jacqueline J.; Groenen, Patrick J. F.; van der Koojj, Anita J.
2007-01-01
The authors provide a didactic treatment of nonlinear (categorical) principal components analysis (PCA). This method is the nonlinear equivalent of standard PCA and reduces the observed variables to a number of uncorrelated principal components. The most important advantages of nonlinear over linear PCA are that it incorporates nominal and ordinal…
NASA Technical Reports Server (NTRS)
Anderson, Melvin S.; Kennedy, David
1993-01-01
The problem considered is the development of the necessary plate stiffnesses for use in the general purpose program VICONOPT for buckling and vibration of composite plate assemblies. The required stiffnesses include the effects of transverse shear deformation and are for sinusoidal response along the plate length as required in VICONOPT. The method is based on the exact solution of the plate differential equations for a composite laminate having fully populated A, B, and D stiffness matrices which leads to an ordinary differential equation of tenth order.
NASA Technical Reports Server (NTRS)
Jaunky, Navin; Knight, Norman F., Jr.; Ambur, Damodar R.
1995-01-01
A smeared stiffener theory for stiffened panels is presented that includes skin-stiffener interaction effects. The neutral surface profile of the skin-stiffener combination is developed analytically using the minimum potential energy principle and statics conditions. The skin-stiffener interaction is accounted for by computing the stiffness due to the stiffener and the skin in the skin-stiffener region about the neutral axis at the stiffener. Buckling load results for axially stiffened, orthogrid, and general grid-stiffened panels are obtained using the smeared stiffness combined with a Rayleigh-Ritz method and are compared with results from detailed finite element analyses.
Initial post-buckling of variable-stiffness curved panels
NASA Astrophysics Data System (ADS)
White, S. C.; Raju, G.; Weaver, P. M.
2014-11-01
Variable-stiffness shells are curved composite structures in which the fibre-reinforcement follow curvilinear paths in space. Having a wider design space than traditional composite shells, they have the potential to improve a wide variety of weight-critical structures. In this paper, a new method for computing the initial post-buckling response of variable-stiffness cylindrical panels is presented, based on the differential quadrature method. Integro-differential governing and boundary equations governing the problem, derived with Koiter's theory (Koiter, 1945), are solved using a mixed generalised differential quadrature (GDQ) and integral quadrature (GIQ) approach. The post-buckling behaviour is determined on the basis of a quadratic expansion of the displacement fields. Orthogonality of the mode-shapes in the expansion series is ensured by a novel use of the Moore-Penrose generalised matrix inverse for solving the GDQ-GIQ equations. The new formulation is validated against benchmark analytical post-buckling results for constant stiffness plates and shells, and compared with non-linear finite-element (FE) analysis for variable-stiffness shells. Stability estimates are found to be in good agreement with incremental FE results in the vicinity of the buckling load, requiring only a fraction of the number of variables used by the current method.
Buckling analysis of moderately thick rectangular plates using coupled displacement field method
NASA Astrophysics Data System (ADS)
Meera Saheb, K.; Aruna, K.
2015-12-01
A simple and efficient coupled displacement field method is developed to study the buckling load parameters of the moderately thick rectangular plates. This method has been successfully applied to study the same for the Timoshenko beams. A single term trigonometric admissible displacement field is assumed for one of the variables, say, the total rotations (in both X, Y directions). Making use of the coupling equations, the spatial variation for the remaining lateral displacement field is derived in terms of the total rotations. The coupled displacement field method makes the energy formulation to contains half the number of unknown independent coefficients, in the case of a rectangular plate, contrary to the conventional Rayleigh-Ritz method. The expressions for the non-dimensional buckling load parameters of the moderately thick rectangular plates with all the edges simply supported are derived. The numerical values of these parameters obtained using the coupled displacement field method match very well with open literature demonstrating the effectiveness of the coupled displacement field method.
NASA Astrophysics Data System (ADS)
Rahmani, O.; Jandaghian, A. A.
2015-06-01
In this paper, a general third-order beam theory that accounts for nanostructure-dependent size effects and two-constituent material variation through the nanobeam thickness, i.e., functionally graded material (FGM) beam is presented. The material properties of FG nanobeams are assumed to vary through the thickness according to the power law. A detailed derivation of the equations of motion based on Eringen nonlocal theory using Hamilton's principle is presented, and a closed-form solution is derived for buckling behavior of the new model with various boundary conditions. The nonlocal elasticity theory includes a material length scale parameter that can capture the size effect in a functionally graded material. The proposed model is efficient in predicting the shear effect in FG nanobeams by applying third-order shear deformation theory. The proposed approach is validated by comparing the obtained results with benchmark results available in the literature. In the following, a parametric study is conducted to investigate the influences of the length scale parameter, gradient index, and length-to-thickness ratio on the buckling of FG nanobeams and the improvement on nonlocal third-order shear deformation theory comparing with the classical (local) beam model has been shown. It is found out that length scale parameter is crucial in studying the stability behavior of the nanobeams.
NASA Technical Reports Server (NTRS)
Shuart, M. J.
1985-01-01
The short-wavelength buckling (or the microbuckling) and the interlaminar and inplane shear failures of multi-directional composite laminates loaded in uniaxial compression are investigated. A laminate model is presented that idealizes each lamina. The fibers in the lamina are modeled as a plate, and the matrix in the lamina is modeled as an elastic foundation. The out-of-plane w displacement for each plate is expressed as a trigonometric series in the half-wavelength of the mode shape for laminate short-wavelength buckling. Nonlinear strain-displacement relations are used. The model is applied to symmetric laminates having linear material behavior. The laminates are loaded in uniform end shortening and are simply supported. A linear analysis is used to determine the laminate stress, strain, and mode shape when short-wavelength buckling occurs. The equations for the laminate compressive stress at short-wavelength buckling are dominated by matrix contributions.
Nonlinear principal component analysis of climate data
Boyle, J.; Sengupta, S.
1995-06-01
This paper presents the details of the nonlinear principal component analysis of climate data. Topic discussed include: connection with principal component analysis; network architecture; analysis of the standard routine (PRINC); and results.
Buckling of Multiwall Carbon Nanotubes under Axial Compression
NASA Astrophysics Data System (ADS)
Akita, Seiji; Nishio, Mitsumasa; Nakayama, Yoshikazu
2006-06-01
We have investigated the axial buckling of multiwall nanotubes under the axial compression using nanomanipulation experiments and molecular dynamics (MD) simulations. Experimentally, Young’s moduli of nanotubes with different inner hollow diameters for the same outer diameters are consistent with the Eulers buckling model based on the continuum analysis. The MD simulations for the buckling behavior of triple- and double-walled nanotubes are also consistent with the continuum analysis. This good agreement indicates that Euler’s buckling model is applicable to the analysis of the axial buckling behavior of the multiwall nanotubes.
Nonlinear Analysis and Preliminary Testing Results of a Hybrid Wing Body Center Section Test Article
NASA Technical Reports Server (NTRS)
Przekop, Adam; Jegley, Dawn C.; Rouse, Marshall; Lovejoy, Andrew E.; Wu, Hsi-Yung T.
2015-01-01
A large test article was recently designed, analyzed, fabricated, and successfully tested up to the representative design ultimate loads to demonstrate that stiffened composite panels with through-the-thickness reinforcement are a viable option for the next generation large transport category aircraft, including non-conventional configurations such as the hybrid wing body. This paper focuses on finite element analysis and test data correlation of the hybrid wing body center section test article under mechanical, pressure and combined load conditions. Good agreement between predictive nonlinear finite element analysis and test data is found. Results indicate that a geometrically nonlinear analysis is needed to accurately capture the behavior of the non-circular pressurized and highly-stressed structure when the design approach permits local buckling.
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.
Probabilistic Dynamic Buckling of Smart Composite Shells
NASA Technical Reports Server (NTRS)
Chamis, Christos C.; Abumeri, Galib H.
2007-01-01
A computational simulation method is presented to evaluate the deterministic and nondeterministic dynamic buckling of smart composite shells. The combined use of intraply hybrid composite mechanics, finite element computer codes, and probabilistic analysis enable the effective assessment of the dynamic buckling load of smart composite shells. A universal plot is generated to estimate the dynamic buckling load of composite shells at various load rates and probabilities. The shell structure is also evaluated with smart fibers embedded in the plies right next to the outer plies. The results show that, on the average, the use of smart fibers improved the shell buckling resistance by about 10% at different probabilities and delayed the buckling occurrence time. The probabilistic sensitivities results indicate that uncertainties in the fiber volume ratio and ply thickness have major effects on the buckling load while uncertainties in the electric field strength and smart material volume fraction have moderate effects. For the specific shell considered in this evaluation, the use of smart composite material is not recommended because the shell buckling resistance can be improved by simply re-arranging the orientation of the outer plies, as shown in the dynamic buckling analysis results presented in this report.
Probabilistic Dynamic Buckling of Smart Composite Shells
NASA Technical Reports Server (NTRS)
Abumeri, Galib H.; Chamis, Christos C.
2003-01-01
A computational simulation method is presented to evaluate the deterministic and nondeterministic dynamic buckling of smart composite shells. The combined use of composite mechanics, finite element computer codes, and probabilistic analysis enable the effective assessment of the dynamic buckling load of smart composite shells. A universal plot is generated to estimate the dynamic buckling load of composite shells at various load rates and probabilities. The shell structure is also evaluated with smart fibers embedded in the plies right below the outer plies. The results show that, on the average, the use of smart fibers improved the shell buckling resistance by about 10 percent at different probabilities and delayed the buckling occurrence time. The probabilistic sensitivities results indicate that uncertainties in the fiber volume ratio and ply thickness have major effects on the buckling load while uncertainties in the electric field strength and smart material volume fraction have moderate effects. For the specific shell considered in this evaluation, the use of smart composite material is not recommended because the shell buckling resistance can be improved by simply re-arranging the orientation of the outer plies, as shown in the dynamic buckling analysis results presented in this report.
Nonlinear Finite Element Analysis of Shells with Large Aspect Ratio
NASA Technical Reports Server (NTRS)
Chang, T. Y.; Sawamiphakdi, K.
1984-01-01
A higher order degenerated shell element with nine nodes was selected for large deformation and post-buckling analysis of thick or thin shells. Elastic-plastic material properties are also included. The post-buckling analysis algorithm is given. Using a square plate, it was demonstrated that the none-node element does not have shear locking effect even if its aspect ratio was increased to the order 10 to the 8th power. Two sample problems are given to illustrate the analysis capability of the shell element.
NASA Technical Reports Server (NTRS)
Lovejoy, Andrew E.; Hilburger, Mark W.
2013-01-01
This document outlines a Modeling and Analysis Plan (MAP) to be followed by the SBKF analysts. It includes instructions on modeling and analysis formulation and execution, model verification and validation, identifying sources of error and uncertainty, and documentation. The goal of this MAP is to provide a standardized procedure that ensures uniformity and quality of the results produced by the project and corresponding documentation.
Design sensitivity analysis of nonlinear structural response
NASA Technical Reports Server (NTRS)
Cardoso, J. B.; Arora, J. S.
1987-01-01
A unified theory is described of design sensitivity analysis of linear and nonlinear structures for shape, nonshape and material selection problems. The concepts of reference volume and adjoint structure are used to develop the unified viewpoint. A general formula for design sensitivity analysis is derived. Simple analytical linear and nonlinear examples are used to interpret various terms of the formula and demonstrate its use.
Nonlinear Analysis of the Space Shuttle Superlightweight External Fuel Tank
NASA Technical Reports Server (NTRS)
Nemeth, Michael P.; Britt, Vicki O.; Collins, Timothy J.; Starnes, James H., Jr.
1996-01-01
Results of buckling and nonlinear analyses of the Space Shuttle external tank superlightweight liquid-oxygen (LO2) tank are presented. Modeling details and results are presented for two prelaunch loading conditions and for two full-scale structural tests that were conducted on the original external tank. The results illustrate three distinctly different types of nonlinear response for thin-walled shells subjected to combined mechanical and thermal loads. The nonlinear response phenomena consist of bifurcation-type buckling, short-wavelength nonlinear bending, and nonlinear collapse associated with a limit point. For each case, the results show that accurate predictions of non- linear behavior generally require a large-scale, high-fidelity finite-element model. Results are also presented that show that a fluid-filled launch-vehicle shell can be highly sensitive to initial geometric imperfections. In addition, results presented for two full-scale structural tests of the original standard-weight external tank suggest that the finite-element modeling approach used in the present study is sufficient for representing the nonlinear behavior of the superlightweight LO2 tank.
Geometrically Nonlinear Static Analysis of 3D Trusses Using the Arc-Length Method
NASA Technical Reports Server (NTRS)
Hrinda, Glenn A.
2006-01-01
Rigorous analysis of geometrically nonlinear structures demands creating mathematical models that accurately include loading and support conditions and, more importantly, model the stiffness and response of the structure. Nonlinear geometric structures often contain critical points with snap-through behavior during the response to large loads. Studying the post buckling behavior during a portion of a structure's unstable load history may be necessary. Primary structures made from ductile materials will stretch enough prior to failure for loads to redistribute producing sudden and often catastrophic collapses that are difficult to predict. The responses and redistribution of the internal loads during collapses and possible sharp snap-back of structures have frequently caused numerical difficulties in analysis procedures. The presence of critical stability points and unstable equilibrium paths are major difficulties that numerical solutions must pass to fully capture the nonlinear response. Some hurdles still exist in finding nonlinear responses of structures under large geometric changes. Predicting snap-through and snap-back of certain structures has been difficult and time consuming. Also difficult is finding how much load a structure may still carry safely. Highly geometrically nonlinear responses of structures exhibiting complex snap-back behavior are presented and analyzed with a finite element approach. The arc-length method will be reviewed and shown to predict the proper response and follow the nonlinear equilibrium path through limit points.
Buckling and vibration of a rotating beam†
NASA Astrophysics Data System (ADS)
Nachman, A.
1986-09-01
The equations for the vibration of a rotating beam, such as a helicopter blade, are exhibited. The beam is elastic (in general non-linearly so), the description is geometrically exact, the axis of rotation does not necessarily pass through the beam's clamped end (precession) and cross-sectional shearing is accounted for by using a director theory. Particular attention is paid to the impossibility of vibration (or buckling) confined to a plane making an angle β to the axis of rotation unless β=π/2 (orπ/2 or 0) or rotatory inertia is neglected. For purposed of illustration the analysis is specialized to describe Euler-Bernoulli and Timoshenko beams.
Buckling instability of self-assembled colloidal columns.
Swan, James W; Vasquez, Paula A; Furst, Eric M
2014-09-26
Suspended, slender self-assembled domains of magnetically responsive colloids are observed to buckle in microgravity. Upon cessation of the magnetic field that drives their assembly, these columns expand axially and buckle laterally. This phenomenon resembles the buckling of long beams due to thermal expansion; however, linear stability analysis predicts that the colloidal columns are inherently susceptible to buckling because they are freely suspended in a Newtonian fluid. The dominant buckling wavelength increases linearly with column thickness and is quantitatively described using an elastohydrodynamic model and the suspension thermodynamic equation of state. PMID:25302919
Buckling Instability of Self-Assembled Colloidal Columns
NASA Astrophysics Data System (ADS)
Swan, James W.; Vasquez, Paula A.; Furst, Eric M.
2014-09-01
Suspended, slender self-assembled domains of magnetically responsive colloids are observed to buckle in microgravity. Upon cessation of the magnetic field that drives their assembly, these columns expand axially and buckle laterally. This phenomenon resembles the buckling of long beams due to thermal expansion; however, linear stability analysis predicts that the colloidal columns are inherently susceptible to buckling because they are freely suspended in a Newtonian fluid. The dominant buckling wavelength increases linearly with column thickness and is quantitatively described using an elastohydrodynamic model and the suspension thermodynamic equation of state.
Computer aided nonlinear electrical networks analysis
NASA Technical Reports Server (NTRS)
Slapnicar, P.
1977-01-01
Techniques used in simulating an electrical circuit with nonlinear elements for use in computer-aided circuit analysis programs are described. Elements of the circuit include capacitors, resistors, inductors, transistors, diodes, and voltage and current sources (constant or time varying). Simulation features are discussed for dc, ac, and/or transient circuit analysis. Calculations are based on the model approach of formulating the circuit equations. A particular solution of transient analysis for nonlinear storage elements is described.
Nonlinear Analysis of Surface EMG Time Series
NASA Astrophysics Data System (ADS)
Zurcher, Ulrich; Kaufman, Miron; Sung, Paul
2004-04-01
Applications of nonlinear analysis of surface electromyography time series of patients with and without low back pain are presented. Limitations of the standard methods based on the power spectrum are discussed.
Macro stress mapping on thin film buckling
Goudeau, P.; Villain, P.; Renault, P.-O.; Tamura, N.; Celestre, R.S.; Padmore, H.A.
2002-11-06
Thin films deposited by Physical Vapour Deposition techniques on substrates generally exhibit large residual stresses which may be responsible of thin film buckling in the case of compressive stresses. Since the 80's, a lot of theoretical work has been done to develop mechanical models but only a few experimental work has been done on this subject to support these theoretical approaches and nothing concerning local stress measurement mainly because of the small dimension of the buckling (few 10th mm). This paper deals with the application of micro beam X-ray diffraction available on synchrotron radiation sources for stress mapping analysis of gold thin film buckling.
Static Nonlinear Analysis In Concrete Structures
Hemmati, Ali
2008-07-08
Push-over analysis is a simple and applied approach which can be used for estimation of demand responses influenced by earthquake stimulations. The analysis is non-linear static analysis of the structure affected under increasing lateral loads and specifying the displacement--load diagram or structure capacity curve, draw the curve the base shear values and lateral deflection on the roof level of the building will be used. However, for estimation of the real behavior of the structure against earthquake, the non-linear dynamic analysis approaches and various accelerographs should be applied. Of course it should be noted that this approach especially in relation with tall buildings is complex and time consuming. In the article, the different patterns of lateral loading in push-over analysis have been compared with non-linear dynamic analysis approach so that the results represented accordingly. The researches indicated the uniformly--distributed loading is closer to real status.
Buckling of graded coatings: A continuum model
NASA Astrophysics Data System (ADS)
Chiu, Tz-Cheng
2000-12-01
Requirements for the protection of hot section components in many high temperature applications such as earth-to-orbit winged planes and advanced turbine systems have led to the application of thermal barrier coatings (TBCs) that utilize ceramic coatings on metal substrates. An alternative concept to homogeneous ceramic coatings is the functionally graded materials (FGM) in which the composition of the coating is intentionally graded to improve the bonding strength and to reduce the magnitude of the residual and thermal stresses. A widely observed failure mode in such layered systems is known to be interface cracking that leads to spallation fracture. In most cases, the final stage of the failure process for a thin coating appears to be due to buckling instability under thermally or mechanically induced compressive stress. The objective of this study is to develop a solution to the buckling instability problem by using continuum elasticity rather than a structural mechanics approach. The emphasis in the solution will be on the investigation of the effect of material inhomogeneity in graded coatings on the instability load, the postbuckling behavior, and fracture mechanics parameters such as the stress intensity factors and strain energy release rate. In this analysis, a nonlinear continuum theory is employed to examine the interface crack problem. The analytical solution of the instability problem permits the study of the effect of material inhomogeneity upon the inception of buckling and establishes benchmark results for the numerical solutions of related problems. To study the postbuckling behavior and to calculate the stress intensity factors and strain energy release rate a geometrically nonlinear finite element procedure with enriched crack-tip element is developed. Both plane strain and axisymmetric interface crack problems in TBCs with either homogeneous or graded coating are then considered by using the finite element procedure. It is assumed that the
Geometrically nonlinear analysis of adhesively bonded joints
NASA Technical Reports Server (NTRS)
Dattaguru, B.; Everett, R. A., Jr.; Whitcomb, J. D.; Johnson, W. S.
1982-01-01
A geometrically nonlinear finite element analysis of cohesive failure in typical joints is presented. Cracked-lap-shear joints were chosen for analysis. Results obtained from linear and nonlinear analysis show that nonlinear effects, due to large rotations, significantly affect the calculated mode 1, crack opening, and mode 2, inplane shear, strain-energy-release rates. The ratio of the mode 1 to mode 2 strain-energy-relase rates (G1/G2) was found to be strongly affected by he adhesive modulus and the adherend thickness. The ratios between 0.2 and 0.8 can be obtained by varying adherend thickness and using either a single or double cracked-lap-shear specimen configuration. Debond growth rate data, together with the analysis, indicate that mode 1 strain-energy-release rate governs debond growth. Results from the present analysis agree well with experimentally measured joint opening displacements.
Seismic analysis of piping with nonlinear supports
Barta, D.A.; Huang, S.N.; Severud, L.K.
1980-01-01
The modeling and results of nonlinear time-history seismic analyses for three sizes of pipelines restrained by mechanical snubbes are presented. Numerous parametric analyses were conducted to obtain sensitivity information which identifies relative importance of the model and analysis ingredients. Special considerations for modeling the pipe clamps and the mechanical snubbers based on experimental characterization data are discussed. Comparisions are also given of seismic responses, loads and pipe stresses predicted by standard response spectra methods and the nonlinear time-history methods.
Nonlinear transient analysis via energy minimization
NASA Technical Reports Server (NTRS)
Kamat, M. P.; Knight, N. F., Jr.
1978-01-01
The formulation basis for nonlinear transient analysis of finite element models of structures using energy minimization is provided. Geometric and material nonlinearities are included. The development is restricted to simple one and two dimensional finite elements which are regarded as being the basic elements for modeling full aircraft-like structures under crash conditions. The results indicate the effectiveness of the technique as a viable tool for this purpose.
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.
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.
Nonlinear Analysis Of Rotor Dynamics
NASA Technical Reports Server (NTRS)
Day, William B.; Zalik, Richard
1988-01-01
Study explores analytical consequences of nonlinear Jeffcott equations of rotor dynamics. Section 1: Summary of previous studies. Section 2: Jeffcott Equations. Section 3: Proves two theorems that provide inequalities on coefficients of differential equations and magnitude of forcing function in absence of side force. Section 4: Numerical investigation of multiple-forcing-function problem by introducing both side force and mass imbalance. Section 5: Examples of numberical solutions of complex generalized Jeffcott equation with two forcing functions of different frequencies f1 and f2. Section 6: Boundedness and stability of solutions.Section 7: Concludes report reviewing analytical results and significance.
Stable Tearing and Buckling Responses of Unstiffened Aluminum Shells with Long Cracks
NASA Technical Reports Server (NTRS)
Starnes, James H., Jr.; Rose, Cheryl A.
1999-01-01
The results of an analytical and experimental study of the nonlinear response of thin, unstiffened, aluminum cylindrical shells with a long longitudinal crack are presented. The shells are analyzed with a nonlinear shell analysis code that accurately accounts for global and local structural response phenomena. Results are presented for internal pressure and for axial compression loads. The effect of initial crack length on the initiation of stable crack growth and unstable crack growth in typical shells subjected to internal pressure loads is predicted using geometrically nonlinear elastic-plastic finite element analyses and the crack-tip-opening angle (CTOA) fracture criterion. The results of these analyses and of the experiments indicate that the pressure required to initiate stable crack growth and unstable crack growth in a shell subjected to internal pressure loads decreases as the initial crack length increases. The effects of crack length on the prebuckling, buckling and postbuckling responses of typical shells subjected to axial compression loads are also described. For this loading condition, the crack length was not allowed to increase as the load was increased. The results of the analyses and of the experiments indicate that the initial buckling load and collapse load for a shell subjected to axial compression loads decrease as the initial crack length increases. Initial buckling causes general instability or collapse of a shell for shorter initial crack lengths. Initial buckling is a stable local response mode for longer initial crack lengths. This stable local buckling response is followed by a stable postbuckling response, which is followed by general or overall instability of the shell.
Stable Tearing and Buckling Responses of Unstiffened Aluminum Shells with Long Cracks
NASA Technical Reports Server (NTRS)
Starnes, James H., Jr.; Rose, Cheryl A.
1998-01-01
The results of an analytical and experimental study of the nonlinear response of thin, unstiffened, aluminum cylindrical shells with a long longitudinal crack are presented. The shells are analyzed with a nonlinear shell analysis code that accurately accounts for global and local structural response phenomena. Results are presented for internal pressure and for axial compression loads. The effect of initial crack length on the initiation of stable crack growth and unstable crack growth in typical shells subjected to internal pressure loads is predicted using geometrically nonlinear elastic-plastic finite element analyses and the crack-tip-opening angle (CTOA) fracture criterion. The results of these analyses and of the experiments indicate that the pressure required to initiate stable crack growth and unstable crack growth in a shell subjected to internal pressure loads decreases as the initial crack length increases. The effects of crack length on the prebuckling, buckling and postbuckling responses of typical shells subjected to axial compression loads are also described. For this loading condition, the crack length was not allowed to increase as the load was increased. The results of the analyses and of the experiments indicate that the initial buckling load and collapse load for a shell subjected to axial compression loads decrease as the initial crack length increases. Initial buckling causes general instability or collapse of a shell for shorter initial crack lengths. Initial buckling is a stable local response mode for longer initial crack lengths. This stable local buckling response is followed by a stable postbuckling response, which is followed by general or overall instability of the shell.
Statistical energy analysis of nonlinear vibrating systems.
Spelman, G M; Langley, R S
2015-09-28
Nonlinearities in practical systems can arise in contacts between components, possibly from friction or impacts. However, it is also known that quadratic and cubic nonlinearity can occur in the stiffness of structural elements undergoing large amplitude vibration, without the need for local contacts. Nonlinearity due purely to large amplitude vibration can then result in significant energy being found in frequency bands other than those being driven by external forces. To analyse this phenomenon, a method is developed here in which the response of the structure in the frequency domain is divided into frequency bands, and the energy flow between the frequency bands is calculated. The frequency bands are assigned an energy variable to describe the mean response and the nonlinear coupling between bands is described in terms of weighted summations of the convolutions of linear modal transfer functions. This represents a nonlinear extension to an established linear theory known as statistical energy analysis (SEA). The nonlinear extension to SEA theory is presented for the case of a plate structure with quadratic and cubic nonlinearity. PMID:26303923
NASA Astrophysics Data System (ADS)
Achong, A.
1999-05-01
This paper presents a non-linear analysis of the dome-shaped notes on the steelpan under compressive and thermal stresses. Equations are derived for the static and dynamic response of symmetrically distorted notes. Analytical results are obtained for modal frequencies, non-linear coupling coefficients and the buckling parameter. Experimental results demonstrate the vibration characteristics and their dependence on temperature. Experimental results were also obtained for the effects of stress relaxation which follows the shaping and tuning process of these notes by hammer peening. The results of the analysis are applicable to other shell-like structures not necessarily designed for musical purposes.
Simplified method for nonlinear structural analysis
NASA Technical Reports Server (NTRS)
Kaufman, A.
1983-01-01
A simplified inelastic analysis computer program was developed for predicting the stress-strain history of a thermomechanically cycled structure from an elastic solution. The program uses an iterative and incremental procedure to estimate the plastic strains from the material stress-strain properties and a simulated plasticity hardening model. The simplified method was exercised on a number of problems involving uniaxial and multiaxial loading, isothermal and nonisothermal conditions, and different materials and plasticity models. Good agreement was found between these analytical results and nonlinear finite element solutions for these problems. The simplified analysis program used less than 1 percent of the CPU time required for a nonlinear finite element analysis.
Functionalization of Buckled Graphene
NASA Astrophysics Data System (ADS)
Nelson, Timothy C.
Buckled graphene produced by the halogen based etching of 6H-SiC provides a new route for the functionalization of the graphene surface. This surface provides an important new stepping off point in the development of molecular electronics and sensors. While the graphene surface is relatively inert, the fluorinated defect sites inherent in the buckled graphene surface yield an excellent location for chemical reactions such as nucleophilic substitution. This thesis shows the utility of the fluorinated defect sites through the well characterized diazonium reaction. Buckled graphene films were prepared on silicon carbide substrates using inductively coupled plasma and reactive ion etching, and annealed at 1000° C to coalesce the BG. The films were reacted with benzene, nitrobenzene, acetonitrile, or a nitrophenyl diazonium salt solution. The diazonium salt was chosen due to its known reaction with graphene produced by other methods. Consequently, reaction of the diazonium with buckled graphene would provide a basis for comparing the reactivity of the surface with these other forums of graphene. The interactions of buckled graphene with the other species were investigated as they represent either constituent parts of the diazonium salt or the solvent. The reacted surfaces were analyzed by X-ray photoelectron spectroscopy, which reveals changes in the surface chemical state due to the functionalization of the buckled graphene by each species. Each reaction yielded significant pi-pi bonding, while the diazonium salt reaction produced additional covalently bonded phenyl groups on the buckled graphene surface. The covalent reaction site was shown to be the surface fluorinated defect site. This observation illustrates the utility of the buckled graphene surface in the functionalization of graphene. Moreover, it provides additional confirmation of the nature of the buckled graphene surface.
Nonlinear analysis of random gust response
NASA Astrophysics Data System (ADS)
Lee, Yan-Nian
In the present research, the nonlinear unsteady aerodynamics is incorporated in the application of Matched Filter Theory to determine the aerodynamic response to random gust. The analysis is focused on the gust response at low Mach numbers. Two airplane configurations, the F-18 HARV and F-16XL, have been tested in forced oscillation to provide the necessary data. The atmospheric turbulence is assumed to be characterized by the von Kármán gust power spectral density function. The nonlinear aerodynamic model is set up through Fourier functional analysis; while the linear aerodynamic model is calculated with the unsteady Quasi-Vortex-Lattice method. Both nonlinear and linear aerodynamic models are used to provide the airplane aerodynamics for comparison. The static results show that nonlinear unsteady aerodynamics produce at least 50% ~ 60% higher maximum lift responses than the linear unsteady aerodynamics. The pitching moment coefficients are more negative for the F-18 HARV and more positive for the F-16XL with the nonlinear aerodynamic models than the linear ones under the prescribed random gust In plunging motion, the dynamic results show that the use of nonlinear unsteady aerodynamics will result in 48.7% ~ 90.1% higher possible maximum gust load factors than with linear unsteady aerodynamics.
NASA Astrophysics Data System (ADS)
Xie, Dan; Xu, Min; Dai, Honghua; Dowell, Earl H.
2015-02-01
The proper orthogonal decomposition (POD) method for analysis of nonlinear panel flutter subjected to supersonic flow is presented. Optimal POD modes are extracted from a chaotic Galerkin mode responses. The aeroelastic equations of motion are constructed using von Karman plate theory, first-order piston theory and quasi-steady thermal stress theory. A simply-supported plate with thermal loads from a uniformly distributed temperature is considered. Many types of panel behaviors, including stable flat, dynamically stable buckled, limit cycle oscillation, nonharmonic periodic motion, quasi-periodic motion and chaotic motion are observed. Our primary focus is on chaos and the route to chaos. It is found that a sudden transition from the buckled state to chaos occurs. Time history, phase portrait, Poincaré map, bifurcation diagram and Lyapunov exponent are employed to study chaos. The POD chaotic results obtained are compared with the traditional Galerkin solutions. It is shown that the POD method can obtain accurate chaotic solutions, using fewer modes and less computational effort than the Galerkin mode approach; additionally, the POD method converges faster in the analysis of chaotic transients. Effects of length-to-width ratios and thermal loads are presented. It is found that a smaller width for fixed length will produce more stable flutter response, while the thermal loads degrade the flutter boundary and result in a more complex evolution of dynamic motions. The numerical simulations show that the robustness of the POD modes depends on the dynamic pressure but not on temperature.
Nonlinear Fourier analysis with cnoidal waves
Osborne, A.R.
1996-12-31
Fourier analysis is one of the most useful tools to the ocean engineer. The approach allows one to analyze wave data and thereby to describe a dynamical motion in terms of a linear superposition of ordinary sine waves. Furthermore, the Fourier technique allows one to compute the response function of a fixed or floating structure: each sine wave in the wave or force spectrum yields a sine wave in the response spectrum. The counting of fatigue cycles is another area where the predictable oscillations of sine waves yield procedures for the estimation of the fatigue life of structures. The ocean environment, however, is a source of a number of nonlinear effects which must also be included in structure design. Nonlinearities in ocean waves deform the sinusoidal shapes into other kinds of waves such as the Stokes wave, cnoidal wave or solitary wave. A key question is: Does there exist a generalization of linear Fourier analysis which uses nonlinear basis functions rather than the familiar sine waves? Herein addresses the dynamics of nonlinear wave motion in shallow water where the basis functions are cnoidal waves and discuss nonlinear Fourier analysis in terms of a linear superposition of cnoidal waves plus their mutual nonlinear interactions. He gives a number of simple examples of nonlinear Fourier wave motion and then analyzes an actual surface-wave time series obtained on an offshore platform in the Adriatic Sea. Finally, he briefly discusses application of the cnoidal wave spectral approach to the computation of the frequency response function of a floating vessel. The results given herein will prove useful in future engineering studies for the design of fixed, floating and complaint offshore structures.
Nonlinear Dynamical Analysis of Fibrillation
NASA Astrophysics Data System (ADS)
Kerin, John A.; Sporrer, Justin M.; Egolf, David A.
2013-03-01
The development of spatiotemporal chaotic behavior in heart tissue, termed fibrillation, is a devastating, life-threatening condition. The chaotic behavior of electrochemical signals, in the form of spiral waves, causes the muscles of the heart to contract in an incoherent manner, hindering the heart's ability to pump blood. We have applied the mathematical tools of nonlinear dynamics to large-scale simulations of a model of fibrillating heart tissue to uncover the dynamical modes driving this chaos. By studying the evolution of Lyapunov vectors and exponents over short times, we have found that the fibrillating tissue is sensitive to electrical perturbations only in narrow regions immediately in front of the leading edges of spiral waves, especially when these waves collide, break apart, or hit the edges of the tissue sample. Using this knowledge, we have applied small stimuli to areas of varying sensitivity. By studying the evolution of the effects of these perturbations, we have made progress toward controlling the electrochemical patterns associated with heart fibrillation. This work was supported by the U.S. National Science Foundation (DMR-0094178) and Research Corporation.
NASA Technical Reports Server (NTRS)
Dose, A
1941-01-01
The present report describes a device for ascertaining the bending and buckling effect in stress measurements on shell structures accessible from one side only. Beginning with a discussion of the relationship between flexural strain and certain parameters, the respective errors of the test method for great or variable skin curvature within the test range are analyzed and illustrated by specimen example.
NASA Technical Reports Server (NTRS)
1991-01-01
After an 800-foot-tall offshore oil recovery platform collapsed, the engineers at Engineering Dynamics, Inc., Kenner, LA, needed to learn the cause of the collapse, and analyze the proposed repairs. They used STAGSC-1, a NASA structural analysis program with geometric and nonlinear buckling analysis. The program allowed engineers to determine the deflected and buckling shapes of the structural elements. They could then view the proposed repairs under the pressure that caused the original collapse.
A method for nonlinear exponential regression analysis
NASA Technical Reports Server (NTRS)
Junkin, B. G.
1971-01-01
A computer-oriented technique is presented for performing a nonlinear exponential regression analysis on decay-type experimental data. The technique involves the least squares procedure wherein the nonlinear problem is linearized by expansion in a Taylor series. A linear curve fitting procedure for determining the initial nominal estimates for the unknown exponential model parameters is included as an integral part of the technique. A correction matrix was derived and then applied to the nominal estimate to produce an improved set of model parameters. The solution cycle is repeated until some predetermined criterion is satisfied.
Theory of buckling and post-buckling behavior of elastic structures
NASA Technical Reports Server (NTRS)
Budiansky, B.
1974-01-01
The present paper provides a unified, general presentation of the basic theory of the buckling and post-buckling behavior of elastic structures in a form suitable for application to a wide variety of special problems. The notation of functional analysis is used for this purpose. Before the general analysis, simple conceptual models are used to elucidate the basic concepts of bifurcation buckling, snap buckling, imperfection sensitivity, load-shortening relations, and stability. The energy approach, the virtual-work approach, and mode interaction are discussed. The derivations and results are applicable to continua and finite-dimensional systems. The virtual-work and energy approaches are given separate treatments, but their equivalence is made explicit. The basic concepts of stability occupy a secondary position in the present approach.
NASA Astrophysics Data System (ADS)
Cherniaev, Aleksandr; Komarov, Valeriy
2014-09-01
Composite drive shafts are extensively used in automotive and aeronautical applications due to lightweight combined with exceptional strength and stiffness. Complexity of the drive shaft design problem associated with the need to determine rational values for multiple parameters characterizing composite material (fiber orientation angles, stacking sequence and ply thicknesses), as well as with the fact that multiple conflicting design constraints should be considered simultaneously. In this paper we approach this problem considering carbon/epoxy drive shaft design as a multistep optimization process. It includes the following steps: 1) determination of fiber orientation angles and laminate stacking sequence based on analysis of loading conditions and analytical expressions predicting buckling load and minimal natural frequency of idealized drive shaft; 2) finding rational ply thicknesses using formal optimization procedure utilizing response surface approximations and gradient-based optimization algorithm; and 3) verification analysis of the optimized configuration with the use of nonlinear buckling analysis to ensure satisfaction of stability constraint.
NASA Astrophysics Data System (ADS)
Cherniaev, Aleksandr; Komarov, Valeriy
2015-10-01
Composite drive shafts are extensively used in automotive and aeronautical applications due to lightweight combined with exceptional strength and stiffness. Complexity of the drive shaft design problem associated with the need to determine rational values for multiple parameters characterizing composite material (fiber orientation angles, stacking sequence and ply thicknesses), as well as with the fact that multiple conflicting design constraints should be considered simultaneously. In this paper we approach this problem considering carbon/epoxy drive shaft design as a multistep optimization process. It includes the following steps: 1) determination of fiber orientation angles and laminate stacking sequence based on analysis of loading conditions and analytical expressions predicting buckling load and minimal natural frequency of idealized drive shaft; 2) finding rational ply thicknesses using formal optimization procedure utilizing response surface approximations and gradient-based optimization algorithm; and 3) verification analysis of the optimized configuration with the use of nonlinear buckling analysis to ensure satisfaction of stability constraint.
NASA Technical Reports Server (NTRS)
Pineda, Evan J.; Myers, David E.; Kosareo, Daniel N.; Kellas, Sotiris
2014-01-01
Four honeycomb sandwich panels, representing 1/16th arc segments of a 10 m diameter barrel section of the heavy lift launch vehicle, were manufactured under the NASA Composites for Exploration program and the NASA Constellation Ares V program. Two configurations were chosen for the panels: 6-ply facesheets with 1.125 in. honeycomb core and 8-ply facesheets with 1.000 in. honeycomb core. Additionally, two separate carbon fiber/epoxy material systems were chosen for the facesheets: inautoclave IM7/977-3 and out-of-autoclave T40-800B/5320-1. Smaller 3- by 5-ft panels were cut from the 1/16th barrel sections. These panels were tested under compressive loading at the NASA Langley Research Center. Furthermore, linear eigenvalue and geometrically nonlinear finite element analyses were performed to predict the compressive response of the 3- by 5-ft panels. This manuscript summarizes the experimental and analytical modeling efforts pertaining to the panel composed of 8-ply, T40-800B/5320-1 facesheets (referred to as Panel C). To improve the robustness of the geometrically nonlinear finite element model, measured surface imperfections were included in the geometry of the model. Both the linear and nonlinear, two-dimensional (2-D) and three-dimensional (3-D), models yield good qualitative and quantitative predictions. Additionally, it was predicted correctly that the panel would fail in buckling prior to failing in strength.
NASA Technical Reports Server (NTRS)
Pineda, Evan Jorge; Myers, David E.; Kosareo, Daniel N.; Zalewski, Bart F.; Kellas, Sotiris; Dixon, Genevieve D.; Krivanek, Thomas M.; Gyekenyesi, Thomas G.
2014-01-01
Four honeycomb sandwich panels, representing 1/16th arc segments of a 10-m diameter barrel section of the Heavy Lift Launch Vehicle, were manufactured and tested under the NASA Composites for Exploration and the NASA Constellation Ares V programs. Two configurations were chosen for the panels: 6-ply facesheets with 1.125 in. honeycomb core and 8-ply facesheets with 1.0 in. honeycomb core. Additionally, two separate carbon fiber/epoxy material systems were chosen for the facesheets: in-autoclave IM7/977-3 and out-of-autoclave T40-800b/5320-1. Smaller 3 ft. by 5 ft. panels were cut from the 1/16th barrel sections and tested under compressive loading. Furthermore, linear eigenvalue and geometrically nonlinear finite element analyses were performed to predict the compressive response of each 3 ft. by 5 ft. panel. To improve the robustness of the geometrically nonlinear finite element model, measured surface imperfections were included in the geometry of the model. Both the linear and nonlinear models yielded good qualitative and quantitative predictions. Additionally, it was correctly predicted that the panel would fail in buckling prior to failing in strength. Furthermore, several imperfection studies were performed to investigate the influence of geometric imperfections, fiber angle misalignments, and three-dimensional effects on the compressive response of the panel.
NASA 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.
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
On a compressed elastic-plastic column optimized for post-buckling behaviour
NASA Astrophysics Data System (ADS)
Bielski, Jan; Bochenek, Bogdan
2008-12-01
A model of a column is proposed in order to analyse the post-buckling behaviour of a structural element in the elastic-plastic deformation range. The ideal two point I-section applied here simplifies the deformation analysis, that is, the problem of development of plastic zones in a section is eliminated, but still gives the possibility for qualitative analysis and optimization of the post-critical equilibrium paths. The coefficients of linear or parabolic variability of thickness of the flanges and their distance (web width) are accepted as model parameters and hence could be used for design variables in the optimization procedure. Moreover, the stiffness of an additional elastic support of the free end of the beam is also included as a parameter or design variable. A material model is employed with non-linear asymptotic isotropic hardening without the Bauschinger effect. Change of the tangent modulus is continuous and smooth during the transition from the elastic to plastic deformation range. The main goal of the analysis is to determine the values of the design variables for which the post-critical equilibrium paths are stable at least in the specified range of a generalized displacement. The constraints for the constant volume of the flanges and web material are applied. The inequality constraints are imposed on the flange thickness and web width. Various formulations of the optimization problem are proposed for all types of non-linear behaviour, including elastic or plastic buckling and elastic or elastic-plastic post-buckling deformation.
NASA Astrophysics Data System (ADS)
Andrews, Blake M.; Song, Junho; Fahnestock, Larry A.
2009-09-01
Buckling-restrained braces (BRBs) have recently become popular in the United States for use as primary members of seismic lateral-force-resisting systems. A BRB is a steel brace that does not buckle in compression but instead yields in both tension and compression. Although design guidelines for BRB applications have been developed, systematic procedures for assessing performance and quantifying reliability are still needed. This paper presents an analytical framework for assessing buckling-restrained braced frame (BRBF) reliability when subjected to seismic loads. This framework efficiently quantifies the risk of BRB failure due to low-cycle fatigue fracture of the BRB core. The procedure includes a series of components that: (1) quantify BRB demand in terms of BRB core deformation histories generated through stochastic dynamic analyses; (2) quantify the limit-state of a BRB in terms of its remaining cumulative plastic ductility capacity based on an experimental database; and (3) evaluate the probability of BRB failure, given the quantified demand and capacity, through structural reliability analyses. Parametric studies were conducted to investigate the effects of the seismic load, and characteristics of the BRB and BRBF on the probability of brace failure. In addition, fragility curves (i.e., conditional probabilities of brace failure given ground shaking intensity parameters) were created by the proposed framework. While the framework presented in this paper is applied to the assessment of BRBFs, the modular nature of the framework components allows for application to other structural components and systems.
Nonlinear laminate analysis for metal matrix fiber composites
NASA Technical Reports Server (NTRS)
Chamis, C. C.; Sinclair, J. H.
1981-01-01
A nonlinear laminate analysis is described for predicting the mechanical behavior (stress-strain relationships) of angle-ply laminates in which the matrix is strained nonlinearly by both the residual stress and the mechanical load and in which additional nonlinearities are induced due to progressive fiber fractures and ply relative rotations. The nonlinear laminate analysis is based on linear composite mechanics and a piece-wise linear laminate analysis to handle the nonlinear responses. Results obtained by using this nonlinear analysis on boron-fiber/aluminum-matrix angle-ply laminates agree well with experimental data. The results shown illustrate the in situ ply stress-strain behavior and synergistic strength enhancement.
Nonlinear laminate analysis for metal matrix fiber composites
NASA Technical Reports Server (NTRS)
Chamis, C. C.; Sinclair, J. H.
1981-01-01
A nonlinear laminate analysis is described for predicting the mechanical behavior (stress-strain relationships) of angleplied laminates in which the matrix is strained nonlinearly by both the residual stress and the mechanical load and in which additional nonlinearities are induced due to progressive fiber fractures and ply relative rotations. The nonlinear laminate analysis (NLA) is based on linear composite mechanics and a piece wise linear laminate analysis to handle the nonlinear responses. Results obtained by using this nonlinear analysis on boron fiber/aluminum matrix angleplied laminates agree well with experimental data. The results shown illustrate the in situ ply stress-strain behavior and synergistic strength enhancement.
Nonlinear time-series analysis revisited
NASA Astrophysics Data System (ADS)
Bradley, Elizabeth; Kantz, Holger
2015-09-01
In 1980 and 1981, two pioneering papers laid the foundation for what became known as nonlinear time-series analysis: the analysis of observed data—typically univariate—via dynamical systems theory. Based on the concept of state-space reconstruction, this set of methods allows us to compute characteristic quantities such as Lyapunov exponents and fractal dimensions, to predict the future course of the time series, and even to reconstruct the equations of motion in some cases. In practice, however, there are a number of issues that restrict the power of this approach: whether the signal accurately and thoroughly samples the dynamics, for instance, and whether it contains noise. Moreover, the numerical algorithms that we use to instantiate these ideas are not perfect; they involve approximations, scale parameters, and finite-precision arithmetic, among other things. Even so, nonlinear time-series analysis has been used to great advantage on thousands of real and synthetic data sets from a wide variety of systems ranging from roulette wheels to lasers to the human heart. Even in cases where the data do not meet the mathematical or algorithmic requirements to assure full topological conjugacy, the results of nonlinear time-series analysis can be helpful in understanding, characterizing, and predicting dynamical systems.
Nonlinear time-series analysis revisited.
Bradley, Elizabeth; Kantz, Holger
2015-09-01
In 1980 and 1981, two pioneering papers laid the foundation for what became known as nonlinear time-series analysis: the analysis of observed data-typically univariate-via dynamical systems theory. Based on the concept of state-space reconstruction, this set of methods allows us to compute characteristic quantities such as Lyapunov exponents and fractal dimensions, to predict the future course of the time series, and even to reconstruct the equations of motion in some cases. In practice, however, there are a number of issues that restrict the power of this approach: whether the signal accurately and thoroughly samples the dynamics, for instance, and whether it contains noise. Moreover, the numerical algorithms that we use to instantiate these ideas are not perfect; they involve approximations, scale parameters, and finite-precision arithmetic, among other things. Even so, nonlinear time-series analysis has been used to great advantage on thousands of real and synthetic data sets from a wide variety of systems ranging from roulette wheels to lasers to the human heart. Even in cases where the data do not meet the mathematical or algorithmic requirements to assure full topological conjugacy, the results of nonlinear time-series analysis can be helpful in understanding, characterizing, and predicting dynamical systems. PMID:26428563
Probabilistic analysis of a materially nonlinear structure
NASA Technical Reports Server (NTRS)
Millwater, H. R.; Wu, Y.-T.; Fossum, A. F.
1990-01-01
A probabilistic finite element program is used to perform probabilistic analysis of a materially nonlinear structure. The program used in this study is NESSUS (Numerical Evaluation of Stochastic Structure Under Stress), under development at Southwest Research Institute. The cumulative distribution function (CDF) of the radial stress of a thick-walled cylinder under internal pressure is computed and compared with the analytical solution. In addition, sensitivity factors showing the relative importance of the input random variables are calculated. Significant plasticity is present in this problem and has a pronounced effect on the probabilistic results. The random input variables are the material yield stress and internal pressure with Weibull and normal distributions, respectively. The results verify the ability of NESSUS to compute the CDF and sensitivity factors of a materially nonlinear structure. In addition, the ability of the Advanced Mean Value (AMV) procedure to assess the probabilistic behavior of structures which exhibit a highly nonlinear response is shown. Thus, the AMV procedure can be applied with confidence to other structures which exhibit nonlinear behavior.
Analysis of nonlinear structures via mode synthesis
NASA Technical Reports Server (NTRS)
Gieseke, R. K.
1975-01-01
An effective procedure for NASTRAN was developed that permits any number of substructures of any size to be synthesized for the purpose of developing normal modes of vibration of the complete structural system. The technique is extended to permit modal transient analysis of the subdivided system. This latter procedure permits the use of NASTRAN's ability to include nonlinear forces in the problem. The five-phase process is accomplished using standard NASTRAN rigid formats with problem-independent alter packages and DMAP sequences.
Dynamic Snap-Through of Thermally Buckled Structures by a Reduced Order Method
NASA Technical Reports Server (NTRS)
Przekop, Adam; Rizzi, Stephen A.
2007-01-01
The goal of this investigation is to further develop nonlinear modal numerical simulation methods for application to geometrically nonlinear response of structures exposed to combined high intensity random pressure fluctuations and thermal loadings. The study is conducted on a flat aluminum beam, which permits a comparison of results obtained by a reduced-order analysis with those obtained from a numerically intensive simulation in physical degrees-of-freedom. A uniformly distributed thermal loading is first applied to investigate the dynamic instability associated with thermal buckling. A uniformly distributed random loading is added to investigate the combined thermal-acoustic response. In the latter case, three types of response characteristics are considered, namely: (i) small amplitude vibration around one of the two stable buckling equilibrium positions, (ii) intermittent snap-through response between the two equilibrium positions, and (iii) persistent snap-through response between the two equilibrium positions. For the reduced-order analysis, four categories of modal basis functions are identified including those having symmetric transverse, anti-symmetric transverse, symmetric in-plane, and anti-symmetric in-plane displacements. The effect of basis selection on the quality of results is investigated for the dynamic thermal buckling and combined thermal-acoustic response. It is found that despite symmetric geometry, loading, and boundary conditions, the anti-symmetric transverse and symmetric in-plane modes must be included in the basis as they participate in the snap-through behavior.
NASA Technical Reports Server (NTRS)
Myers, David E.; Pineda, Evan J.; Zalewski, Bart F.; Kosareo, Daniel N.; Kellas, Sotiris
2013-01-01
Four honeycomb sandwich panels, representing 1/16th arc segments of a 10-m diameter barrel section of the heavy lift launch vehicle, were manufactured under the NASA Composites for Exploration program and the NASA Space Launch Systems program. Two configurations were chosen for the panels: 6-ply facesheets with 1.125 in. honeycomb core and 8-ply facesheets with 1.000 in. honeycomb core. Additionally, two separate carbon fiber/epoxy material systems were chosen for the facesheets: inautoclave IM7/977-3 and out-of-autoclave T40-800b/5320-1. Smaller 3.00- by 5.00-ft panels were cut from the 1/16th barrel sections. These panels were tested under compressive loading at the NASA Langley Research Center. Furthermore, linear eigenvalue and geometrically nonlinear finite element analysis was performed to predict the compressive response of the 3.00- by 5.00-ft panels. This manuscript summarizes the experimental and analytical modeling efforts pertaining to the panel composed of 8-ply, IM7/977-3 facesheets (referred to Panel A). To improve the robustness of the geometrically nonlinear finite element model, measured surface imperfections were included in the geometry of the model. Both the linear and nonlinear models yield good qualitative and quantitative predictions. Additionally, it was predicted correctly that the panel would fail in buckling prior to failing in strength. Furthermore, several imperfection studies were performed to investigate the influence of geometric imperfections, fiber misalignments, and three-dimensional (3 D) effects on the compressive response of the panel.
A Biomechanical Model of Artery Buckling
Han, Hai-Chao
2010-01-01
The stability of arteries under blood pressure load is essential to the maintenance of normal arterial function and the loss of stability can lead to tortuosity and kinking that are associated with significant clinical complications. However, mechanical analysis of arterial bent buckling is lacking. To address this issue, this paper presents a biomechanical model of arterial buckling. Using a linear elastic cylindrical arterial model, the mechanical equations for arterial buckling were developed and the critical buckling pressure was found to be a function of the wall stiffness (Young’s modulus), arterial radius, length, wall thickness, and the axial strain. Both the model equations and experimental results demonstrated that the critical pressure is related to the axial strain. Arteries may buckle and become tortuous due to reduced (sub-physiological) axial strain, hypertensive pressure, and a weakened wall. These results are in accordance with, and provide a possible explanation to the clinical observations that these changes are the risk factors for arterial tortuosity and kinking. The current model is also applicable to veins and ureters. PMID:17689541
Nonlinear analysis of EEG for epileptic seizures
Hively, L.M.; Clapp, N.E.; Daw, C.S.; Lawkins, W.F.; Eisenstadt, M.L.
1995-04-01
We apply chaotic time series analysis (CTSA) to human electroencephalogram (EEG) data. Three epoches were examined: epileptic seizure, non-seizure, and transition from non-seizure to seizure. The CTSA tools were applied to four forms of these data: raw EEG data (e-data), artifact data (f-data) via application of a quadratic zero-phase filter of the raw data, artifact-filtered data (g- data) and that was the residual after subtracting f-data from e-data, and a low-pass-filtered version (h-data) of g-data. Two different seizures were analyzed for the same patient. Several nonlinear measures uniquely indicate an epileptic seizure in both cases, including an abrupt decrease in the time per wave cycle in f-data, an abrupt increase in the Kolmogorov entropy and in the correlation dimension for e-h data, and an abrupt increase in the correlation dimension for e-h data. The transition from normal to seizure state also is characterized by distinctly different trends in the nonlinear measures for each seizure and may be potential seizure predictors for this patient. Surrogate analysis of e-data shows that statistically significant nonlinear structure is present during the non-seizure, transition , and seizure epoches.
Generic element processor (application to nonlinear analysis)
NASA Technical Reports Server (NTRS)
Stanley, Gary
1989-01-01
The focus here is on one aspect of the Computational Structural Mechanics (CSM) Testbed: finite element technology. The approach involves a Generic Element Processor: a command-driven, database-oriented software shell that facilitates introduction of new elements into the testbed. This shell features an element-independent corotational capability that upgrades linear elements to geometrically nonlinear analysis, and corrects the rigid-body errors that plague many contemporary plate and shell elements. Specific elements that have been implemented in the Testbed via this mechanism include the Assumed Natural-Coordinate Strain (ANS) shell elements, developed with Professor K. C. Park (University of Colorado, Boulder), a new class of curved hybrid shell elements, developed by Dr. David Kang of LPARL (formerly a student of Professor T. Pian), other shell and solid hybrid elements developed by NASA personnel, and recently a repackaged version of the workhorse shell element used in the traditional STAGS nonlinear shell analysis code. The presentation covers: (1) user and developer interfaces to the generic element processor, (2) an explanation of the built-in corotational option, (3) a description of some of the shell-elements currently implemented, and (4) application to sample nonlinear shell postbuckling problems.
NASA Astrophysics Data System (ADS)
Wiggins, Andrew D.
Bow seals are critical components on advanced marine vehicles that rely on aerostatic support to reduce drag. They consist of a series of open-ended fabric cylinders ("fingers") that contact the free surface and, when inflated, form a compliant pressure barrier. Bow seals are unique in that, unlike a majority of structures in civil and mechanical engineering, bow seals operate in a buckled state. The response characteristics of these structures are of practical interest due to unacceptable wear rates on seal components and difficulties in predicting seal performance. Despite this, the hydroelastic response of the seal system, particularly basic information on seal vibration modes and the mechanisms responsible for seal wear, remains largely unknown. Similarly, estimates of the hydrodynamic loads on the seal system are inaccurate and based on heuristic scaling of data from small-scale experiments, where similitude is challenging to maintain. Thus, a large-scale test system is necessary to obtain accurate estimates of bow seal response. The work is comprised of three parts. Part one presents detailed observations of bow seal response acquired using a large-scale test platform developed as part of the present study. These high-resolution observations, the first of their kind, show bow seal response to be characterized by complex post-buckling behavior. Part two proposes an analytical framework for interpreting the wide range of behavior observed at large scale. Using this framework, key parameters driving seal conformation and stability are identified. It is found that, due to their buckled state, bow seals are highly susceptible to a mode switching instability, which may be a potential mechanism responsible for the damaging vibrations. In part three, a benchtop experiment is used to demonstrate that the scalings identified in this study hold across a wide range of bending rigidities. This work has implications for improving drag and wear characteristics in future bow
Scleral Buckling with Chandelier Illumination
Seider, Michael I.; Nomides, Riikka E. K.; Hahn, Paul; Mruthyunjaya, Prithvi; Mahmoud, Tamer H.
2016-01-01
Scleral buckling is a highly successful technique for the repair of rhegmatogenous retinal detachment that requires intra-operative examination of the retina and treatment of retinal breaks via indirect ophthalmoscopy. Data suggest that scleral buckling likely results in improved outcomes for many patients but is declining in popularity, perhaps because of significant advances in vitrectomy instrumentation and visualization systems. Emerging data suggest that chandelier-assisted scleral buckling is safe and has many potential advantages over traditional buckling techniques. By combining traditional scleral buckling with contemporary vitreoretinal visualization techniques, chandelier-assistance may increase the popularity of scleral buckling to treat primary rhegmatogenous retinal detachment for surgeons of the next generation, maintaining buckling as an option for appropriate patients in the future. PMID:27621789
NASA Technical Reports Server (NTRS)
Hilburger, Mark W.; Starnes, James H., Jr.
2004-01-01
The results of an experimental and numerical study of the effects of initial imperfections on the buckling response and failure of unstiffened thin-walled compression-loaded graphite-epoxy cylindrical shells are presented. The shells considered in the study have six different orthotropic or quasi-isotropic shell-wall laminates and two different shell-radius-to-thickness ratios. The numerical results include the effects of geometric shell-wall mid-surface imperfections, shell-wall thickness variations, local shell-wall ply-gaps associated with the fabrication process, shell-end geometric imperfections, nonuniform end loads, and the effects of elastic boundary conditions. Selected cylinder parameter uncertainties were also considered. Results that illustrate the effects of imperfections and uncertainties on the nonlinear response characteristics, buckling loads and failure the shells are presented. In addition, a common failure analysis is used to predict material failures in the shells.
Effect of boundary conditions on piezoelectric buckled beams for vibrational noise harvesting
NASA Astrophysics Data System (ADS)
Cottone, F.; Mattarelli, M.; Vocca, H.; Gammaitoni, L.
2015-11-01
Nonlinear bistable systems have proven to be advantageous for energy harvesting of random and real ambient vibrations. One simple way of implementing a bistable transducer is setting a piezoelectric beam in a post-buckled configuration by axial compression. Besides, hinged or clamped-clamped type of boundary conditions correspond to two different post-buckled shape functions. Here we study, through theoretical analysis and numerical simulations, the efficiency of a hinged and clamped-clamped piezoelectric bridge under band-limited random noise with progressive axial load. Clamped configuration results to harvest 26% more power than hinged around an optimal axial load of 0.05%, while, in the intra-well trapped situation, above 0.1%, the two configurations present no substantial difference. Nevertheless, simulations confirm the advantage of exploiting inter-well oscillations in bistable regime.
Parry, G.; Coupeau, C.; Colin, J.; Cimetiere, A.; Grilhe, J
2004-08-02
The transition from a straight-sided wrinkle to a periodic distribution of bubbles has been experimentally studied by atomic force microscopy for a stressed thin film relying on a substrate. A non-linear numerical analysis has been carried out and the different steps of the wrinkle evolution have been characterized. Different parameters of the buckling structure such as the shape parameter of the blisters and the stress relaxation have been determined and compared to the experimental data. The comparison of elastic strain energies has highlighted the possible coexistence of structures with different wavelengths.
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.
Buckling of hybrid nanocomposites with embedded graphene and carbon nanotubes
NASA Astrophysics Data System (ADS)
Chandra, Y.; Saavedra Flores, E. I.; Scarpa, F.; Adhikari, S.
2016-09-01
With the aid of atomistic multiscale modelling and analytical approaches, buckling strength has been determined for carbon nanofibres/epoxy composite systems. Various nanofibres configurations considered are single walled carbon nano tube (SWCNT) and single layer graphene sheet (SLGS) and SLGS/SWCNT hybrid systems. Computationally, both eigen-value and non-linear large deformation-based methods have been employed to calculate the buckling strength. The non-linear computational model generated here takes into account of complex features such as debonding between polymer and filler (delamination under compression), nonlinearity in the polymer, strain-based damage criteria for the matrix, contact between fillers and interlocking of distorted filler surfaces with polymer. The effect of bridging nanofibres with an interlinking compound on the buckling strength of nano-composites has also been presented here. Computed enhancement in buckling strength of the polymer system due to nano reinforcement is found to be in the range of experimental and molecular dynamics based results available in open literature. The findings of this work indicate that carbon based nanofillers enhance the buckling strength of host polymers through various local failure mechanisms.
NASA Technical Reports Server (NTRS)
Svalbonas, V.
1973-01-01
The User's manual for the shell theory automated for rotational structures (STARS) 2B and 2V (buckling, vibrations) is presented. Several features of the program are: (1) arbitrary branching of the shell meridians, (2) arbitrary boundary conditions, (3) minimum input requirements to describe a complex, practical shell of revolution structure, and (4) accurate analysis capability using a minimum number of degrees of freedom.
Buckling Capacity Curves for Steel Spherical Shells Loaded by the External Pressure
NASA Astrophysics Data System (ADS)
Błażejewski, Paweł; Marcinowski, Jakub
2015-03-01
Assessment of buckling resistance of pressurised spherical cap is not an easy task. There exist two different approaches which allow to achieve this goal. The first approach involves performing advanced numerical analyses in which material and geometrical nonlinearities would be taken into account as well as considering the worst imperfections of the defined amplitude. This kind of analysis is customarily called GMNIA and is carried out by means of the computer software based on FEM. The other, comparatively easier approach, relies on the utilisation of earlier prepared procedures which enable determination of the critical resistance pRcr, the plastic resistance pRpl and buckling parameters a, b, h, l 0 needed to the definition of the standard buckling resistance curve. The determination of the buckling capacity curve for the particular class of spherical caps is the principal goal of this work. The method of determination of the critical pressure and the plastic resistance were described by the authors in [1] whereas the worst imperfection mode for the considered class of spherical shells was found in [2]. The determination of buckling parameters defining the buckling capacity curve for the whole class of shells is more complicated task. For this reason the authors focused their attention on spherical steel caps with the radius to thickness ratio of R/t = 500, the semi angle j = 30o and the boundary condition BC2 (the clamped supporting edge). Taking into account all imperfection forms considered in [2] and different amplitudes expressed by the multiple of the shell thickness, sets of buckling parameters defining the capacity curve were determined. These parameters were determined by the methods proposed by Rotter in [3] and [4] where the method of determination of the exponent h by means of additional parameter k was presented. As a result of the performed analyses the standard capacity curves for all considered imperfection modes and amplitudes 0.5t, 1.0t, 1.5t
Turbine blade nonlinear structural and life analysis
NASA Technical Reports Server (NTRS)
Mcknight, R. L.; Laflen, J. H.; Halford, G. R.; Kaufman, A.
1982-01-01
The utility of advanced structural analysis and life prediction techniques was evaluated for the life assessment of a commercial air-cooled turbine blade with a history of tip cracking. Three dimensional, nonlinear finite element structural analyses were performed for the blade tip region. The computed strain-temperature history of the critical location was imposed on a uniaxial strain controlled test specimen to evaluate the validity of the structural analysis method. Experimental results indicated higher peak stresses and greater stress relaxation than the analytical predictions. Life predictions using the Strainrange Partitioning and Frequency Modified approaches predicted 1200 to 4420 cycles and 2700 cycles to crack initiation, respectively, compared to an observed life of 3000 cycles.
Buckling behavior and structural efficiency of open-section stiffened composite compression panels
NASA Technical Reports Server (NTRS)
Williams, J. G.; Stein, M.
1976-01-01
Several experiments with J- and blade-stiffened graphite/epoxy panels were conducted to obtain insight into how well experimental data could be correlated with analysis for the buckling behavior of open-section stiffened composite compression panels. Although some nonlinear behavior was observed during the experiments, adequate correlation with analysis was obtained to justify the use of linear, thin-plate buckling analysis in a minimum-weight design synthesis program for J- and blade-configurations. Results from two design studies using this program are presented. In the first study the minimum weights of Jand blade-configurations for two different material systems (graphite/epoxy and aluminum) are determined subject to buckling and strength constraints for a wide range of the compressive load index. In the second study the minimum weights required for graphite/epoxy blade-stiffened panels to satisfy additional stiffness constraints typical of medium-size commercial aircraft wing structures are determined. Both minimum-weight studies indicate that graphite/epoxy open-section stiffened panels can be designed so that weight savings of 30 to 50% are possible compared with the most efficient aluminum designs.
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
Numerical Simulation Of Buckling In Waffle Plants
NASA Technical Reports Server (NTRS)
Yin, Dah N.; Tran, Vu M.
1990-01-01
Accurate results obtained when fillet radii considered. Two reports describe numerical and experimental study of application of PASCO and WAFFLE computer programs to analysis of buckling in integrally machined, biaxially stiffened panel. PASCO (Panal Analysis and Sizing Code) is finite-element stress-and-strain code written for analysis and sizing of uniaxially stiffened panels. WAFFLE program provides comprehensive stress analysis of waffle panel, used to determine bending moments at interfaces.
Nonlinear and Failure Analysis of Composite Structures
NASA Technical Reports Server (NTRS)
Noor, Ahmed K.; Starnes, James H. (Technical Monitor)
2002-01-01
The overall goal of this research is to assess the effect of discontinuities and uncertainties on the nonlinear response and failure of stiffened composite panels subjected to combined mechanical and thermal loads. The key elements of the study are: (a) study of the effects of stiffener geometry and of transverse stresses on the response, damage initiation and propagation in stiffened composite panels; (b) use of hierarchical sensitivity coefficients to identify the major parameters that affect the response and damage in each of the different levels in the hierarchy (micromechanical, layer, panel, subcomponent and component levels); and, (c) application of fuzzy set techniques to identify the range and variation of possible responses. The computational models developed are used in conjunction with experiments to understand the physical phenomena associated with the nonlinear response and failure of stiffened composite panels. A toolkit is developed for use in conjunction with deterministic analysis programs to help the designer in assessing the effect of uncertainties in the different computational model parameters on the variability of the response quantities.
Nonlinear Analysis of the Space Shuttle Super-Lightweight External Fuel Tank
NASA Technical Reports Server (NTRS)
Nemeth, Michael P.; Britt, Vicki O.; Collins, Timothy J.; Starnes, James H., Jr.
1996-01-01
The results of buckling and nonlinear analyses of the Space Shuttle External Tank super-lightweight liquid oxygen (LOX) tank are presented. Modeling details and results are presented for two prelaunch loading conditions and for two full-scale structural tests conducted on the original external tank. These results illustrate three distinctly different types of nonlinear responses for thin-walled shells subjected to combined mechanical and thermal loads. These nonlinear response phenomena consist of bifurcation-type buckling, short-wavelength nonlinear bending, and nonlinear collapse associated with a limit point. For each case, the results show that accurate predictions of nonlinear behavior generally require a large scale high-fidelity finite element model. Results are also presented that show that a fluid filled launch vehicle shell can be highly sensitive to initial geometric imperfections. In addition, results presented for two full scale structural tests of the original standard weight external tank suggest that the finite element modeling approach used in the present study is sufficient for representing the nonlinear behavior of the super lightweight LOX tank.
NASA Astrophysics Data System (ADS)
Patil, Mayuri Suresh
Plates or members containing plate elements have been used in the offshore, aerospace and construction industry. Cutouts are often located to lighten the weight of the structure, but these cutouts reduce the ultimate strength of the plate. A number of studies have taken place for determining the buckling strength of a perforated plated but few discuss the effect of material strain hardening on the buckling strength of a perforated plate. Buckling strength is often considered as an important criterial to determine the serviceable limit of the perforated plate in the offshore structure. The aim of the present study is to investigate the effect of material strain hardening on the strength characteristic of a perforated plate under uniaxial loading. This load at some point could lead to a possibility of instability. A square plate with perforation is considered here. The plate is considered to be simply supported at all four edges and has been kept straight. The perforation is located at the center of the plate. A number of ANSYS static nonlinear analysis are undertaken with different strain hardening material properties for AL7075. The Ramberg-Osgood method is used to determine the stress-strain curve for different strain hardening values. The plate thickness and the cutout size of the perforation are varied to determine the effect on the strength. The study covers the behavior of the system in the elastic buckling and the elastic-plastic region.
Fujita, Katsuhisa; Nakamura, Kazuhiro; Ito, Tomohiro; Iwamoto, Yoichi
1996-12-01
In the Great Hanshin Earthquake which occurred in January 1995, extremely serious damages to the elevated expressways were found. Some of those piers are made of steel and many of them buckled and revealed plastic deformations. One of them revealed the circumferentially uniform outward bulge at the middle portion in the axial direction, though the buckling of a long circular cylinder will occur at it`s bottom end accompanied by more complicated deformation patterns typical to the bending buckling. In this study, simple reduced scale models of the pier were fabricated and the dynamic and static buckling tests were performed. The effect of the girder weight or vertical excitation on the buckling phenomena were investigated. In addition to the tests, static buckling analysis using FEM was also performed in order to clarify the causes for this specified buckling phenomena.
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.
Elastic torsional buckling of thin-walled composite cylinders
NASA Technical Reports Server (NTRS)
Marlowe, D. E.; Sushinsky, G. F.; Dexter, H. B.
1974-01-01
The elastic torsional buckling strength has been determined experimentally for thin-walled cylinders fabricated with glass/epoxy, boron/epoxy, and graphite/epoxy composite materials and composite-reinforced aluminum and titanium. Cylinders have been tested with several unidirectional-ply orientations and several cross-ply layups. Specimens were designed with diameter-to-thickness ratios of approximately 150 and 300 and in two lengths of 10 in. and 20 in. The results of these tests were compared with the buckling strengths predicted by the torsional buckling analysis of Chao.
On lateral buckling of end-loaded cantilevers, including the effect of warping stiffness
NASA Astrophysics Data System (ADS)
Reissner, E.; Reissner, J. E.; Wan, F. Y. M.
1987-06-01
We investigate the numerical consequences of the presence of certain non-linear terms in the expressions for the components of transverse shearing strain which occur in the derivation of one-dimensional equations for small finite deflections of straight beams from three-dimensional finite elasticity through use of the principle of minimum potential energy. While particular emphasis is placed on the effect of warping stiffness, the paper also includes results of interest in connection with the classical Michell-Prandtl-analysis of lateral buckling of endloaded cantilevers. Comprehensive numerical results are obtained for the entire range of the relevant dimensionless parameters, using power series, asymptotic expansion and modern numerical methods procedures.
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.
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 testing of composite columns
NASA Astrophysics Data System (ADS)
Barbero, Ever; Tomblin, John
1992-11-01
Euler buckling test results are presented for large composite columns relevant to the mass production of composite structural members by pultrusion. The experimental procedure employed yields highly reproducible and accurate results. All percentage differences between theory and experiment are below 6.2 percent; the theoretically predicted long-column buckling load is accurate even in the case of the most complex composite materials.
Buckling and Damage Resistance of Transversely-Loaded Composite Shells
NASA Technical Reports Server (NTRS)
Wardle, Brian L.
1998-01-01
Experimental and numerical work was conducted to better understand composite shell response to transverse loadings which simulate damage-causing impact events. The quasi-static, centered, transverse loading response of laminated graphite/epoxy shells in a [+/-45(sub n)/O(sub n)](sub s) layup having geometric characteristics of a commercial fuselage are studied. The singly-curved composite shell structures are hinged along the straight circumferential edges and are either free or simply supported along the curved axial edges. Key components of the shell response are response instabilities due to limit-point and/or bifurcation buckling. Experimentally, deflection-controlled shell response is characterized via load-deflection data, deformation-shape evolutions, and the resulting damage state. Finite element models are used to study the kinematically nonlinear shell response, including bifurcation, limit-points, and postbuckling. A novel technique is developed for evaluating bifurcation from nonlinear prebuckling states utilizing asymmetric spatial discretization to introduce numerical perturbations. Advantages of the asymmetric meshing technique (AMT) over traditional techniques include efficiency, robustness, ease of application, and solution of the actual (not modified) problems. The AMT is validated by comparison to traditional numerical analysis of a benchmark problem and verified by comparison to experimental data. Applying the technique, bifurcation in a benchmark shell-buckling problem is correctly identified. Excellent agreement between the numerical and experimental results are obtained for a number of composite shells although predictive capability decreases for stiffer (thicker) specimens which is attributed to compliance of the test fixture. Restraining the axial edge (simple support) has the effect of creating a more complex response which involves unstable bifurcation, limit-point buckling, and dynamic collapse. Such shells were noted to bifurcate into
Early detection of local buckling in structural members
NASA Astrophysics Data System (ADS)
Ali, Bashir; Sundaresan, Mannur J.; Schulz, Mark J.; Hughes, Derke
2005-05-01
Most structural health monitoring analyses to date have focused on the determination of damage in the form of crack growth in metallic materials or delamination or other types of damage growth in composite materials. However, in many applications, local instability in the form of buckling can be the precursor to more extensive damage and unstable failure of the structure. If buckling could be detected in the very early stages, there is a possibility of taking preventive measures to stabilize and save the structure. Relatively few investigations have addressed this type of damage initiation in structures. Recently, during the structural health monitoring of a wind turbine blade, local buckling was identified as the cause of premature failure. A stress wave propagation technique was used in this test to detect the precursor to the buckling failure in the form of early changes in the local curvature of the blade. These conditions have also been replicated in the laboratory and results are reported in this paper. A composite column was subjected to axial compression to induce various levels of buckling deformation. Two different techniques were used to detect the precursors to buckling in this column. The first identifier is the change in the vibration shapes and natural frequencies of the column. The second is the change in the characteristics of diagnostic Lamb waves during the buckling deformation. Experiments indicate that very small changes in curvature during the initial stages of buckling are detectable using the structural health monitoring techniques. The experimental vibration characteristics of the column with slight initial curvatures compared qualitatively with finite element results. The finite element analysis is used to identify the frequencies that are most sensitive to buckling deformation, and to select suitable locations for the placement of sensors that can detect even small changes in the local curvature.
Nonlinear adaptive wavelet analysis of electrocardiogram signals
NASA Astrophysics Data System (ADS)
Yang, H.; Bukkapatnam, S. T.; Komanduri, R.
2007-08-01
Wavelet representation can provide an effective time-frequency analysis for nonstationary signals, such as the electrocardiogram (EKG) signals, which contain both steady and transient parts. In recent years, wavelet representation has been emerging as a powerful time-frequency tool for the analysis and measurement of EKG signals. The EKG signals contain recurring, near-periodic patterns of P , QRS , T , and U waveforms, each of which can have multiple manifestations. Identification and extraction of a compact set of features from these patterns is critical for effective detection and diagnosis of various disorders. This paper presents an approach to extract a fiducial pattern of EKG based on the consideration of the underlying nonlinear dynamics. The pattern, in a nutshell, is a combination of eigenfunctions of the ensembles created from a Poincare section of EKG dynamics. The adaptation of wavelet functions to the fiducial pattern thus extracted yields two orders of magnitude (some 95%) more compact representation (measured in terms of Shannon signal entropy). Such a compact representation can facilitate in the extraction of features that are less sensitive to extraneous noise and other variations. The adaptive wavelet can also lead to more efficient algorithms for beat detection and QRS cancellation as well as for the extraction of multiple classical EKG signal events, such as widths of QRS complexes and QT intervals.
Methods of stability analysis in nonlinear mechanics
Warnock, R.L.; Ruth, R.D.; Gabella, W.; Ecklund, K.
1989-01-01
We review our recent work on methods to study stability in nonlinear mechanics, especially for the problems of particle accelerators, and compare our ideals to those of other authors. We emphasize methods that (1) show promise as practical design tools, (2) are effective when the nonlinearity is large, and (3) have a strong theoretical basis. 24 refs., 2 figs., 2 tabs.
Buckling and failure characteristics of graphite-polyimide shear panels
NASA Technical Reports Server (NTRS)
Shuart, M. J.; Hagaman, J. A.
1983-01-01
The buckling and failure characteristics of unstiffened, blade stiffened, and hat stiffened graphite-polyimide shear panels are described. The picture frame shear test is used to obtain shear stress-strain data at room temperature and at 316 deg C. The experimental results are compared with a linear buckling analysis, and the specimen failure modes are described. The effect of the 316 deg C test temperature on panel behavior are discussed.
Nonlinear analysis of helix traveling wave tubes
Freund, H.P.; Zaidman, E.G.; Vanderplaats, N.R.; Kodis, M.A.
1994-12-31
A nonlinear formulation of the interaction in a helix traveling wave tube (TWT) is presented. The formulation is intended to treat a wide class of helix TWTs including both emission-gated and multi-tone operation. The essential feature of each of these configurations is that multiple waves must be included in the formulation. As a result, a fully time-dependent analysis is required. The numerical procedure for this in a helix TWT is complicated by the fact that the radial profile of the field varies with frequency. This contrasts, for example, with the case of a smooth bore waveguide in which the radial profile for each TE{sub ln} or TM{sub ln} mode is invariant in frequency. Because of this, a complete self-consistent particle-in-cell (PIC) formulation must be three-dimensional. In order to circumvent the computational expense of a 3D PIC formulation, the authors adopt an approach in which the electromagnetic field is represented as a superposition of azimuthally symmetric modes in a vacuum sheath helix. The specific electron distributions are chosen to model either a continuous beam for the multi-tone TWT and a pulsed beam for the emission-gated TWT. Numerical results of the simulation for examples of interest to an emission-gated TWT experiment at NRL will be presented.
Nonlinear Analysis of Pulsating White Dwarf Lightcurves
NASA Astrophysics Data System (ADS)
Provencal, J. L.; Montgomery, M. H.; Shipman, H.; WET TEam
2015-06-01
Convection remains one of the largest sources of theoretical uncertainty in our understanding of stellar physics. For example, Bergeron (1995) show that basic parameters such as flux, line profiles, energy distribution, color indices, and equivalent widths are extremely sensitive to the assumed convective parameterization. This is compelling, since we use our knowledge of these basic parameters to calibrate white dwarf cooling sequences, provide detailed estimates for the ages of individual white dwarfs, and determine the age of the Galactic disk. The Whole Earth Telescope (WET) is engaged in a long term project to empirically calibrate the physical properties of convection in pulsating white dwarfs by combining asteroseismology and analysis of nonlinear light curves. Nonsinusoidal distortions, in the form of narrow peaks and wider valleys, are observed in many pulsating white dwarf light curves. These are a reflection of the local depth of the convection zone, a value which varies during a pulsation cycle. Applying asteroseismology and convective light curve fitting to a wide sample of pulsating white dwarfs provides an empirical map of how the convective response time (the convection zone “depth”) varies as a function of effective temperature, and this can be compared with theoretical models, both MLT and hydrodynamic. This project has resulted in a large database of white dwarf lightcurves and pulsation frequencies. We present current results for DA and DB pulsators, and provide a few examples of interesting pulsation behavior seen along the way.
Nonlinear damage detection in composite structures using bispectral analysis
NASA Astrophysics Data System (ADS)
Ciampa, Francesco; Pickering, Simon; Scarselli, Gennaro; Meo, Michele
2014-03-01
Literature offers a quantitative number of diagnostic methods that can continuously provide detailed information of the material defects and damages in aerospace and civil engineering applications. Indeed, low velocity impact damages can considerably degrade the integrity of structural components and, if not detected, they can result in catastrophic failure conditions. This paper presents a nonlinear Structural Health Monitoring (SHM) method, based on ultrasonic guided waves (GW), for the detection of the nonlinear signature in a damaged composite structure. The proposed technique, based on a bispectral analysis of ultrasonic input waveforms, allows for the evaluation of the nonlinear response due to the presence of cracks and delaminations. Indeed, such a methodology was used to characterize the nonlinear behaviour of the structure, by exploiting the frequency mixing of the original waveform acquired from a sparse array of sensors. The robustness of bispectral analysis was experimentally demonstrated on a damaged carbon fibre reinforce plastic (CFRP) composite panel, and the nonlinear source was retrieved with a high level of accuracy. Unlike other linear and nonlinear ultrasonic methods for damage detection, this methodology does not require any baseline with the undamaged structure for the evaluation of the nonlinear source, nor a priori knowledge of the mechanical properties of the specimen. Moreover, bispectral analysis can be considered as a nonlinear elastic wave spectroscopy (NEWS) technique for materials showing either classical or non-classical nonlinear behaviour.
Nonlinear analysis of structures. [within framework of finite element method
NASA Technical Reports Server (NTRS)
Armen, H., Jr.; Levine, H.; Pifko, A.; Levy, A.
1974-01-01
The development of nonlinear analysis techniques within the framework of the finite-element method is reported. Although the emphasis is concerned with those nonlinearities associated with material behavior, a general treatment of geometric nonlinearity, alone or in combination with plasticity is included, and applications presented for a class of problems categorized as axisymmetric shells of revolution. The scope of the nonlinear analysis capabilities includes: (1) a membrane stress analysis, (2) bending and membrane stress analysis, (3) analysis of thick and thin axisymmetric bodies of revolution, (4) a general three dimensional analysis, and (5) analysis of laminated composites. Applications of the methods are made to a number of sample structures. Correlation with available analytic or experimental data range from good to excellent.
Enhancement of Buckling Load with the Use of Active Materials
NASA Technical Reports Server (NTRS)
Yuan, F. G.
2002-01-01
In this paper, active buckling control of a beam using piezoelectric materials is investigated. Under small deformation, mathematical models are developed to describe the behavior of the beams subjected to an axial compressive load with geometric imperfections and load eccentricities under piezoelectric force. Two types of supports, simply supported and clamped, of the beam with a partially bonded piezoelectric actuator are used to illustrate the concept. For the beam with load eccentricities and initial geometric imperfections, the load- carrying capacity can be significantly enhanced by counteracting moments from the piezoelectric actuator. For the single piezoelectric actuator, using static feedback closed-loop control, the first buckling load can be eliminated. In the case of initially straight beams, analytical solutions of the enhanced first critical buckling load due to the increase of bending stiffness by piezoelectric actuators are derived based on linearized buckling analysis.
Sutureless scleral buckle in the management of rhegmatogenous retinal detachment
Shanmugam, P Mahesh; Singh, Tajinder Pal; Ramanjulu, Rajesh; Rodrigues, Gladys; Reddy, Srinivasulu
2015-01-01
Purpose: To evaluate the anatomical and functional outcomes of sutureless scleral buckling for the repair of rhegmatogenous retinal detachment (RD). Design: Retrospective interventional case series. Materials and Methods: Retrospective analysis of 50 eyes of 49 patients with rhegmatogenous RD, who underwent sutureless scleral buckling from January 2009 to March 2013. Results: Primary retinal re-attachment rate of 86% was achieved with single surgery, but final anatomical success was 94% with additional interventions in the form of intravitreal gas, buckle revision, and/or pars plana vitrectomy. Best corrected logarithm of minimum angle of resolution visual acuity improved from 1.44 ± 1.01 preoperatively to 0.50 ± 0.40 at a mean follow-up of 6.7 months. Conclusion: Sutureless scleral buckling achieves excellent anatomical and functional success in majority of the patients with rhegmatogenous RD. PMID:26576521
Ductility demands on buckling-restrained braced frames under earthquake loading
NASA Astrophysics Data System (ADS)
Fahnestock, Larry A.; Sause, Richard; Ricles, James M.; Lu, Le-Wu
2003-12-01
Accurate estimates of ductility demands on buckling-restrained braced frames (BRBFs) are crucial to performance-based design of BRBFs. An analytical study on the seismic behavior of BRBFs has been conducted at the ATLSS Center, Lehigh University to prepare for an upcoming experimental program. The analysis program DRAIN-2DX was used to model a one-bay, four-story prototype BRBF including material and geometric nonlinearities. The buckling-restrained brace (BRB) model incorporates both isotropic and kinematic hardening. Nonlinear static pushover and time-history analyses were performed on the prototype BRBF. Performance objectives for the BRBs were defined and used to evaluate the time-history analysis results. Particular emphasis was placed on global ductility demands and ductility demands on the BRBs. These demands were compared with anticipated ductility capacities. The analysis results, along with results from similar previous studies, are used to evaluate the BRBF design provisions that have been recommended for codification in the United States. The results show that BRB maximum ductility demands can be as high as 20 to 25. These demands significantly exceed those anticipated by the BRBF recommended provisions. Results from the static pushover and time-history analyses are used to demonstrate why the ductility demands exceed those anticipated by the recommended provisions. The BRB qualification testing protocol contained in the BRBF recommended provisions is shown to be inadequate because it requires only a maximum ductility demand of at most 7.5. Modifications to the testing protocol are recommended.
Nonlinearity Analysis and Parameters Optimization for an Inductive Angle Sensor
Ye, Lin; Yang, Ming; Xu, Liang; Zhuang, Xiaoqi; Dong, Zhaopeng; Li, Shiyang
2014-01-01
Using the finite element method (FEM) and particle swarm optimization (PSO), a nonlinearity analysis based on parameter optimization is proposed to design an inductive angle sensor. Due to the structure complexity of the sensor, understanding the influences of structure parameters on the nonlinearity errors is a critical step in designing an effective sensor. Key parameters are selected for the design based on the parameters' effects on the nonlinearity errors. The finite element method and particle swarm optimization are combined for the sensor design to get the minimal nonlinearity error. In the simulation, the nonlinearity error of the optimized sensor is 0.053% in the angle range from −60° to 60°. A prototype sensor is manufactured and measured experimentally, and the experimental nonlinearity error is 0.081% in the angle range from −60° to 60°. PMID:24590353
Analytical and experimental vibration and buckling characteristics of a pretensioned stayed column
NASA Technical Reports Server (NTRS)
Belvin, W. K.
1982-01-01
Modal vibration tests to determine lateral modes of vibration of a stayed column and static axial compression tests to determine the column's buckling and postbuckling behavior have been performed. Effects of stay tension levels and vibration-load interaction are presented. Two finite element models are used to analyze the column, a three-dimensional frame using NASTRAN and an equivalent two-dimensional frame using an exact dynamic stiffness matrix. Both analyses correlated well with the linear vibration and buckling experimental data. Results indicate premature buckling of the column due to vibration-load interaction and nonlinear oscillations due to stay slackening. Postbuckling behavior of the column is unusual because of stay slackening and results in a postbuckling restoring force of less than the bifurcation buckling load. Guidelines for design of pretensioned structures are presented which consider buckling, postbuckling and vibration behavior.
NASA Technical Reports Server (NTRS)
Haftka, Raphael T.; Cohen, Gerald A.; Mroz, Zenon
1990-01-01
A uniform variational approach to sensitivity analysis of vibration frequencies and bifurcation loads of nonlinear structures is developed. Two methods of calculating the sensitivities of bifurcation buckling loads and vibration frequencies of nonlinear structures, with respect to stiffness and initial strain parameters, are presented. A direct method requires calculation of derivatives of the prebuckling state with respect to these parameters. An adjoint method bypasses the need for these derivatives by using instead the strain field associated with the second-order postbuckling state. An operator notation is used and the derivation is based on the principle of virtual work. The derivative computations are easily implemented in structural analysis programs. This is demonstrated by examples using a general purpose, finite element program and a shell-of-revolution program.
NASA Technical Reports Server (NTRS)
Williams, F. W.; Anderson, M. S.; Kennedy, D.; Butler, R.; Aston, G.
1990-01-01
A computer program which is designed for efficient, accurate buckling and vibration analysis and optimum design of composite panels is described. The capabilities of the program are given along with detailed user instructions. It is written in FORTRAN 77 and is operational on VAX, IBM, and CDC computers and should be readily adapted to others. Several illustrations of the various aspects of the input are given along the example problems illustrating the use and application of the program.
NASA Technical Reports Server (NTRS)
Hoff, N J; Fuchs, S J; Cirillo, Adam J
1944-01-01
This paper is the second part of a series of reports on the inward bulge type buckling of monocoque cylinders. It presents the results of an experimental investigation of buckling in combined bending and compression. In the investigation it was found that the theory developed in part I of the present series predicts the buckling load in combined bending and compression with the same degree of accuracy as the older theory does in pure bending. In the realm covered by the experiments no systematic variation of the parameter N was observed. The analysis of the test results afforded a check on the theories of buckling of a curved panel. The agreement between experiment and theory was reasonably good. In addition, the effect of the end conditions upon the stress distribution under loads and upon initial stresses was investigated.
Buckling of Cracked Laminated Composite Cylindrical Shells Subjected to Combined Loading
NASA Astrophysics Data System (ADS)
Allahbakhsh, Hamidreza; Shariati, Mahmoud
2013-10-01
A series of finite element analysis on the cracked composite cylindrical shells under combined loading is carried out to study the effect of loading condition, crack size and orientation on the buckling behavior of laminated composite cylindrical shells. The interaction buckling curves of cracked laminated composite cylinders subject to different combinations of axial compression, bending, internal pressure and external pressure are obtained, using the finite element method. Results show that the internal pressure increases the critical buckling load of the CFRP cylindrical shells and bending and external pressure decrease it. Numerical analysis show that axial crack has the most detrimental effect on the buckling load of a cylindrical shell and results show that for lower values of the axial compressive load and higher values of the external pressure, the buckling is usually in the global mode and for higher values of axial compressive load and lower levels of external pressure the buckling mode is mostly in the local mode.
Identifying nonlinear biomechanical models by multicriteria analysis
NASA Astrophysics Data System (ADS)
Srdjevic, Zorica; Cveticanin, Livija
2012-02-01
In this study, the methodology developed by Srdjevic and Cveticanin (International Journal of Industrial Ergonomics 34 (2004) 307-318) for the nonbiased (objective) parameter identification of the linear biomechanical model exposed to vertical vibrations is extended to the identification of n-degree of freedom (DOF) nonlinear biomechanical models. The dynamic performance of the n-DOF nonlinear model is described in terms of response functions in the frequency domain, such as the driving-point mechanical impedance and seat-to-head transmissibility function. For randomly generated parameters of the model, nonlinear equations of motion are solved using the Runge-Kutta method. The appropriate data transformation from the time-to-frequency domain is performed by a discrete Fourier transformation. Squared deviations of the response functions from the target values are used as the model performance evaluation criteria, thus shifting the problem into the multicriteria framework. The objective weights of criteria are obtained by applying the Shannon entropy concept. The suggested methodology is programmed in Pascal and tested on a 4-DOF nonlinear lumped parameter biomechanical model. The identification process over the 2000 generated sets of parameters lasts less than 20 s. The model response obtained with the imbedded identified parameters correlates well with the target values, therefore, justifying the use of the underlying concept and the mathematical instruments and numerical tools applied. It should be noted that the identified nonlinear model has an improved accuracy of the biomechanical response compared to the accuracy of a linear model.
Tensile buckling of advanced turboprops
NASA Technical Reports Server (NTRS)
Chamis, C. C.; Aiello, R. A.
1982-01-01
Theoretical studies were conducted to determine analytically the tensile buckling of advanced propeller blades (turboprops) in centrifugal fields, as well as the effects of tensile buckling on other types of structural behavior, such as resonant frequencies and flutter. Theoretical studies were also conducted to establish the advantages of using high performance composite turboprops as compared to titanium. Results show that the vibration frequencies are not affected appreciably prior to 80 percent of the tensile speed. Some frequencies approach zero as the tensile buckling speed is approached. Composites provide a substantial advantage over titanium on a buckling speed to weight basis. Vibration modes change as the rotor speed is increased and substantial geometric coupling is present.
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.
Buckling and structural efficiency of sandwich-blade stiffened composite compression panels
NASA Technical Reports Server (NTRS)
Stein, M.; Williams, J. G.
1978-01-01
The minimum mass structural efficiency curve was determined for sandwich blade stiffened composite compression panels subjected to buckling and strength constraints. High structural efficiencies are attainable for this type of construction. A method of analysis is presented for the buckling of panels of this configuration which shows that buckling of such panels is strongly dependent on the through-the-thickness transverse shearing of the stiffener. Experimental results are presented and compared with theory.
A nonlinear analysis of the EHF booster
Colton, E.P.; Shi, D.
1987-01-01
We have analyzed particle motion at 1.2 GeV with assumption of nonlinearities arising from non-linear space charge forces and from the lattice sextupoles which are tuned to cancel the machine chromaticity. In the first case the motion is as expected and there are no problems as long as the x and y betatron tunes are separated by an integer or more. In the second case the motion is stable so long as the betatron amplitudes do not exceed values corresponding to beam normalized emittance of 100 mm-mr; when this occurs the effects of fifth-order betatron resonances are observed. 3 refs.
A Bayesian Approach for Multigroup Nonlinear Factor Analysis.
ERIC Educational Resources Information Center
Song, Xin-Yuan; Lee, Sik-Yum
2002-01-01
Developed a Bayesian approach for a general multigroup nonlinear factor analysis model that simultaneously obtains joint Bayesian estimates of the factor scores and the structural parameters subjected to some constraints across different groups. (SLD)
Buckling of Branched Cytoskeletal Filaments
NASA Astrophysics Data System (ADS)
Quint, D. A.; Schwarz, J. M.
2011-03-01
In vitro experiments of growing dendritic actin networks demonstrate reversible stress-softening at high loads, above some critical load. The transition to the stress-softening regime has been attributed to the elastic buckling of individual actin filaments. To estimate the critical load above which softening should occur, we extend the elastic theory of buckling of individual filaments embedded in a network to include the buckling of branched filaments, a signature trait of growing dendritic actin networks. Under certain assumptions, there will be approximately a seven-fold increase in the classical critical bucking load, when compared to the unbranched filament, which is entirely due to the presence of a branch. Moreover, we go beyond the classical buckling regime to investigate the effect of entropic fluctuations. The result of compressing the filament in this case leads to an increase in these fluctuations and eventually the harmonic approximation breaks down signifying the onset of the buckling transition. We compute corrections to the classical critical buckling load near this breakdown.
Single-strain-gage force/stiffness buckling prediction techniques on a hat-stiffened panel
NASA Technical Reports Server (NTRS)
Hudson, Larry D.; Thompson, Randolph C.
1991-01-01
Predicting the buckling characteristics of a test panel is necessary to ensure panel integrity during a test program. A single-strain-gage buckling prediction method was developed on a hat-stiffened, monolithic titanium buckling panel. The method is an adaptation of the original force/stiffness method which requires back-to-back gages. The single-gage method was developed because the test panel did not have back-to-back gages. The method was used to predict buckling loads and temperatures under various heating and loading conditions. The results correlated well with a finite element buckling analysis. The single-gage force/stiffness method was a valid real-time and post-test buckling prediction technique.
Nonlinear Robustness Analysis Tools for Flight Control Law Validation & Verification
NASA Astrophysics Data System (ADS)
Chakraborty, Abhijit
Loss of control in flight is among the highest aviation accident categories for both the number of accidents and the number of fatalities. The flight controls community is seeking an improved validation tools for safety critical flight control systems. Current validation tools rely heavily on linear analysis, which ignore the inherent nonlinear nature of the aircraft dynamics and flight control system. Specifically, current practices in validating the flight control system involve gridding the flight envelope and checking various criteria based on linear analysis to ensure safety of the flight control system. The analysis and certification methods currently applied assume the aircrafts' dynamics is linear. In reality, the behavior of the aircraft is always nonlinear due to its aerodynamic characteristics and physical limitations imposed by the actuators. This thesis develops nonlinear analysis tools capable of certifying flight control laws for nonlinear aircraft dynamics. The proposed analysis tools can handle both the aerodynamic nonlinearities and the physical limitations imposed by the actuators in the aircrafts' dynamics. This proposed validation technique will extend and enrich the predictive capability of existing flight control law validation methods to analyze nonlinearities. The objective of this thesis is to provide the flight control community with an advanced set of analysis tools to reduce aviation fatalities and accidents rate.
Employment of CB models for non-linear dynamic analysis
NASA Technical Reports Server (NTRS)
Klein, M. R. M.; Deloo, P.; Fournier-Sicre, A.
1990-01-01
The non-linear dynamic analysis of large structures is always very time, effort and CPU consuming. Whenever possible the reduction of the size of the mathematical model involved is of main importance to speed up the computational procedures. Such reduction can be performed for the part of the structure which perform linearly. Most of the time, the classical Guyan reduction process is used. For non-linear dynamic process where the non-linearity is present at interfaces between different structures, Craig-Bampton models can provide a very rich information, and allow easy selection of the relevant modes with respect to the phenomenon driving the non-linearity. The paper presents the employment of Craig-Bampton models combined with Newmark direct integration for solving non-linear friction problems appearing at the interface between the Hubble Space Telescope and its solar arrays during in-orbit maneuvers. Theory, implementation in the FEM code ASKA, and practical results are shown.
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.
NASA Technical Reports Server (NTRS)
Ko, William L.; Jackson, Raymond H.
1991-01-01
Combined compressive and shear buckling analysis was conducted on flat rectangular sandwich panels with the consideration of transverse shear effects of the core. The sandwich panel is fabricated with titanium honeycomb core and laminated metal matrix composite face sheets. The results show that the square panel has the highest combined load buckling strength, and that the buckling strength decreases sharply with the increases of both temperature and panel aspect ratio. The effect of layup (fiber orientation) on the buckling strength of the panels was studied in detail. The metal matrix composite sandwich panel was much more efficient than the sandwich panel with nonreinforced face sheets and had the same specific weight.
NASA Technical Reports Server (NTRS)
Li, Yi-Wei; Elishakoff, Isaac; Starnes, James H., Jr.; Bushnell, David
1998-01-01
This study is an extension of a previous investigation of the combined effect of axisymmetric thickness variation and axisymmetric initial geometric imperfection on buckling of isotropic shells under uniform axial compression. Here the anisotropic cylindrical shells are investigated by means of Koiter's energy criterion. An asymptotic formula is derived which can be used to determine the critical buckling load for composite shells with combined initial geometric imperfection and thickness variation. Results are compared with those obtained by the software packages BOSOR4 and PANDA2.
Theoretical and software considerations for nonlinear dynamic analysis
NASA Technical Reports Server (NTRS)
Schmidt, R. J.; Dodds, R. H., Jr.
1983-01-01
In the finite element method for structural analysis, it is generally necessary to discretize the structural model into a very large number of elements to accurately evaluate displacements, strains, and stresses. As the complexity of the model increases, the number of degrees of freedom can easily exceed the capacity of present-day software system. Improvements of structural analysis software including more efficient use of existing hardware and improved structural modeling techniques are discussed. One modeling technique that is used successfully in static linear and nonlinear analysis is multilevel substructuring. This research extends the use of multilevel substructure modeling to include dynamic analysis and defines the requirements for a general purpose software system capable of efficient nonlinear dynamic analysis. The multilevel substructuring technique is presented, the analytical formulations and computational procedures for dynamic analysis and nonlinear mechanics are reviewed, and an approach to the design and implementation of a general purpose structural software system is presented.
Ground motion estimation and nonlinear seismic analysis
McCallen, D.B.; Hutchings, L.J.
1995-08-14
Site specific predictions of the dynamic response of structures to extreme earthquake ground motions are a critical component of seismic design for important structures. With the rapid development of computationally based methodologies and powerful computers over the past few years, engineers and scientists now have the capability to perform numerical simulations of many of the physical processes associated with the generation of earthquake ground motions and dynamic structural response. This paper describes application of a physics based, deterministic, computational approach for estimation of earthquake ground motions which relies on site measurements of frequently occurring small (i.e. M < 3 ) earthquakes. Case studies are presented which illustrate application of this methodology for two different sites, and nonlinear analyses of a typical six story steel frame office building are performed to illustrate the potential sensitivity of nonlinear response to site conditions and proximity to the causative fault.
Nonlinear dynamic analysis for elastic robotic arms
NASA Astrophysics Data System (ADS)
Korayem, M. H.; Rahimi, H. N.
2011-06-01
The aim of the paper is to analyze the nonlinear dynamics of robotic arms with elastic links and joints. The main contribution of the paper is the comparative assessment of assumed modes and finite element methods as more convenient approaches for computing the nonlinear dynamic of robotic systems. Numerical simulations comprising both methods are carried out and results are discussed. Hence, advantages and disadvantages of each method are illustrated. Then, adding the joint flexibility to the system is dealt with and the obtained model is demonstrated. Finally, a brief description of the optimal motion generation is presented and the simulation is carried out to investigate the role of robot dynamic modeling in the control of robots.
Nonlinear analysis of the gradient drift instability
NASA Astrophysics Data System (ADS)
González, Rafael; Vega, Matías de la
An analytical study of the gradient drift instability in the equatorial electrojet of wavelengths in the order of one kilometer is presented. Different mechanisms, linear, non-local and turbulent, are found in the literature to explain the predominance of the 1 km wavelength in the electrojet. In the present work a simplified model is proposed in which the nonlinear evolution of three coupled modes is followed. By considering that one of the modes attains the stationary state, the evolution of the other two is obtained, and it is found that they follow equations of the Lotka-Volterra type. A stable stationary nonlinear solution for these equations is also found, and the conditions under which periodic solutions are possible are analyzed.