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At least 181 records · Page 10

Enhancement of Buckling Load with the Use of Active Materials

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.

Yuan, F. G.↗

Buckling Behavior of Long Anisotropic Plates Subjected to Elastically Restrained Thermal Expansion and Contraction

An approach for synthesizing buckling results for thin balanced and unbalanced symmetric laminates that are subjected to uniform heating or cooling and elastically restrained against thermal expansion or contraction is presented. This approach uses a nondimensional analysis for infinitely long, flexural anisotropic plates that are subjected to combined mechanical loads. In addition, stiffness-weighted laminate thermal-expansion parameters and compliance coefficients are derived that are used to determine critical temperatures in terms of physically intuitive mechanical-buckling coefficients. Many results are presented for some common laminates that are intended to facilitate a structural designer s transition to the use of the generic buckling design curves. Several curves that illustrate the fundamental parameters used in the analysis are presented, for nine contemporary material systems, that provide physical insight into the buckling response in addition to providing useful design data. Examples are presented that demonstrate the use of the generic design curves.

Nemeth, Michael P.↗

Buckling and Failure of Compression-loaded Composite Cylindrical Shells with Reinforced Cutouts

Results from a numerical and experimental study that illustrate the effects of selected cutout reinforcement configurations on the buckling and failure response of compression-loaded composite cylindrical shells with a cutout are presented. The effects of reinforcement size, thickness, and orthotropy on the overall response of compression-loaded shells are described. In general, reinforcement around a cutout in a compression-loaded shell can retard or eliminate the local buckling response and material failure near the cutout and increase the buckling load of the shell. However, some results show that certain reinforcement configurations can cause a significant increase in the local interlaminar failures that can accumulate near the free edges of a cutout during a local buckling event.

Hilburger, Mark W.↗

Buckling of Carbon Nanotube-Reinforced Polymer Laminated Composite Materials Subjected to Axial Compression and Shear Loadings

A multi-scale method to predict the stiffness and stability properties of carbon nanotube-reinforced laminates has been developed. This method is used in the prediction of the buckling behavior of laminated carbon nanotube-polyethylene composites formed by stacking layers of carbon nanotube-reinforced polymer with the nanotube alignment axes of each layer oriented in different directions. Linking of intrinsic, nanoscale-material definitions to finite scale-structural properties is achieved via a hierarchical approach in which the elastic properties of the reinforced layers are predicted by an equivalent continuum modeling technique. Solutions for infinitely long symmetrically laminated nanotube-reinforced laminates with simply-supported or clamped edges subjected to axial compression and shear loadings are presented. The study focuses on the influence of nanotube volume fraction, length, orientation, and functionalization on finite-scale laminate response. Results indicate that for the selected laminate configurations considered in this study, angle-ply laminates composed of aligned, non-functionalized carbon nanotube-reinforced lamina exhibit the greatest buckling resistance with 1% nanotube volume fraction of 450 nm uniformly-distributed carbon nanotubes. In addition, hybrid laminates were considered by varying either the volume fraction or nanotube length through-the-thickness of a quasi-isotropic laminate. The ratio of buckling load-to-nanotube weight percent for the hybrid laminates considered indicate the potential for increasing the buckling efficiency of nanotube-reinforced laminates by optimizing nanotube size and proportion with respect to laminate configuration.

Riddick, J. C.↗

Buckling and Failure of Compression-Loaded Composite Laminated Shells With Cutouts

Results from a numerical and experimental study that illustrate the effects of laminate orthotropy on the buckling and failure response of compression-loaded composite cylindrical shells with a cutout are presented. The effects of orthotropy on the overall response of compression-loaded shells is described. In general, preliminary numerical results appear to accurately predict the buckling and failure characteristics of the shell considered herein. In particular, some of the shells exhibit stable post-local-buckling behavior accompanied by interlaminar material failures near the free edges of the cutout. In contrast another shell with a different laminate stacking sequence appears to exhibit catastrophic interlaminar material failure at the onset of local buckling near the cutout and this behavior correlates well with corresponding experimental results.

Hilburger, Mark W.↗

Analysis of Potential for Titanium Liner Buckling after Proof in a Large Kevlar/Epoxy COPV

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 compressive yield threshold. The key result is that depression depths of up to 40 mils can be tolerated, but above 40 mils, the Bauschinger effect drives destabilization, and buckling becomes increasingly likely depending on the details of depression formation during autofrettage. It is almost certain that destabilization and buckling will occur for depression depths beyond 55 mils. The main equations and formulas for treating the various phases of depression development and potential buckling, are only briefly outlined in the paper, but are available from the authors.

Phoenix, S. Leigh↗

The Effects of Geometric and Loading Imperfections on the Response and Lower-Bound Buckling Load of a Compression-Loaded Cylindrical Shell

Results from a numerical study of the buckling response of a thin-walled compressionloaded isotropic circular cylindrical shell with initial geometric and loading imperfections are used to determine a lower bound buckling load estimate suitable for preliminary design. The lower bound prediction techniques presented herein include an imperfection caused by a lateral perturbation load, an imperfection in the shape of a single stress-free dimple (similar to the lateral pertubation imperfection), and a distributed load imperfection that induces a nonuniform load in the shell. The ABAQUS finite element code is used for the analyses. Responses of the cylinders for selected imperfection amplitudes and imperfection types are considered, and the effect of each imperfection is compared to the response of a geometrically perfect cylinder. The results indicate that compression-loaded shells subjected to a lateral perturbation load or a single dimple imperfection, and a nonuniform load imperfection, exhibit similar buckling behavior and lower bound trends and the predicted lower bounds are much less conservative than the corresponding design recommendation NASA SP-8007 for the design of buckling-critical shells. In addition, the lateral perturbation technique and the distributed load imperfection produce response characteristics that are physically meaningful and can be validated via laboratory testing.

Kriegesmann, Benedikt↗

Effects of Shell-Buckling Knockdown Factors in Large Cylindrical Shells

Shell-buckling knockdown factors (SBKF) have been used in large cylindrical shell structures to account for uncertainty in buckling loads. As the diameter of the cylinder increases, achieving the manufacturing tolerances becomes increasingly more difficult. Knockdown factors account for manufacturing imperfections in the shell geometry by decreasing the allowable buckling load of the cylinder. In this paper, large-diameter (33 ft) cylinders are investigated by using various SBKF's. An investigation that is based on finite-element analysis (FEA) is used to develop design sensitivity relationships. Different manufacturing imperfections are modeled into a perfect cylinder to investigate the effects of these imperfections on buckling. The analysis results may be applicable to large- diameter rockets, cylindrical tower structures, bulk storage tanks, and silos.

Hrinda, Glenn A.↗

Test and Analysis of a Buckling-Critical Large-Scale Sandwich Composite Cylinder

Structural stability is an important design consideration for launch-vehicle shell structures and it is well known that the buckling response of such shell structures can be very sensitive to small geometric imperfections. As part of an effort to develop new buckling design guidelines for sandwich composite cylindrical shells, an 8-ft-diameter honeycomb-core sandwich composite cylinder was tested under pure axial compression to failure. The results from this test are compared with finite-element-analysis predictions and overall agreement was very good. In particular, the predicted buckling load was within 1% of the test and the character of the response matched well. However, it was found that the agreement could be improved by including composite material nonlinearity in the analysis, and that the predicted buckling initiation site was sensitive to the addition of small bending loads to the primary axial load in analyses.

Schultz, Marc R.↗

Scaling Methodology for Buckling of Sandwich Composite Cylindrical Structures

The study of the buckling behavior of large shell structures through full-size tests can be complex and expensive. Therefore, scaled structures are often preferred to investigate the buckling behavior efficiently. However, it can be difficult to design scaled structures that are representative of the full-scale structures. Herein, an analytical scaling methodology for compression-loaded sandwich composite cylinders based on the nondimensionalization of the buckling equations is presented. The methodology is used to develop scaled configurations that show a similar buckling response. Both the baseline and the scaled configurations are verified by finite-element analysis. Limitations of the methodology are discussed and are a result of neglecting the flexural anisotropy and the transverse shear compliance.

Balbin, Ines Uriol↗

Integration of Fatigue R-Curve Effects into VCCT for Durability Predictions, Part 1: Buckled Composite Single-Stringer Stiffened Panels

Composite structures have become popular in modern aircraft because they help reduce weight and increase durability. In addition, hat-stiffened panels provide the stability that the airframe skin needs. However, they can be subject to delamination in the post-buckling regime. Progressive damage analysis (PDA) methods can help predict interlaminar and intralaminar failure events. Many aircraft structures are subject to cyclic loading in the post-buckling regime. Hence, fatigue life prediction becomes essential for design and sustainment purposes. Under the NASA Advanced Composites Project (ACP), composite panels stiffened with single hat-stringers were subject to a cyclic loading sequence from a pre-buckling state to a post-buckling state. This test campaign aimed to provide damage initiation and growth data for three initial damage scenarios: nominally pristine, initial Teflon inserts representing manufacturing defects, and impact-induced damage. This work uses the Abaqus FEA Virtual Crack Closure Technique (VCCT), capabilities enhanced through a novel empirical method integrating fatigue R-curve effects (different from R-ratio) into the Paris Law via user-defined subroutine to simulate the fatigue response of the panels with single hat-stringers. The analysis predictions were within 5% of the test results using this novel method.

single hat↗

Integration of Fatigue R-Curve Effects into VCCT for Durability Predictions, Part 2: Buckled Composite Multi-Stringer Stiffened Panels

Composite structures with hat-stiffened panels have gained traction in modern aircraft because they help reduce weight, increase durability, and provide stability to airframe skins. For weight reduction, skins should be designed to operate in the post-buckling regime. This causes possible interlaminar and intralaminar failure. However, composite panels stiffened with multiple hat-stringers are subject to cyclic loading even in the post-buckling regime. Under the NASA Advanced Composites Project (ACP), composite panels with multiple hatstringers were subject to a cyclic loading sequence from a pre-buckling state to a post-buckling state. This effort aimed to predict interlaminar failure for cyclic compression loading with pre-existent impact-induced damage. This work uses the Abaqus FEA Virtual Crack Closure Technique (VCCT), capabilities enhanced through an empirical method to integrate fatigue R-curve effects (different from R-ratio) into the Paris Law via user-defined subroutine to simulate the fatigue response o

ACP↗

Hierarchical domain structures in buckled ferroelectric free sheets

Flat elastic sheets tend to display wrinkles and folds. From pieces of clothing down to two-dimensional crystals, these corrugations appear in response to strain generated by sheet compression or stretching, thermal or mechanical mismatch with other elastic layers, or surface tension. Extensively studied in metals, polymers and, — more recently — in van der Waals exfoliated layers, with the advent of thin single crystal freestanding films of complex oxides, researchers are now paying attention to novel microstructural effects induced by bending ferroelectric-ferroelastics, where polarization is strongly coupled to lattice deformation. Here we show that wrinkle undulations in BaTiO3 sheets bonded to a viscoelastic substrate transform into a buckle delamination geometry when transferred onto a rigid substrate. Using spatially resolved techniques at different scales (Raman, scanning probe and electron microscopy), we show how these delaminations in the free BaTiO3 sheets display a self-organization of ferroelastic domains along the buckle profile that strongly differs from the more studied sinusoidal wrinkle geometry. Moreover, we disclose the hierarchical distribution of a secondary set of domains induced by the misalignment of these folding structures from the preferred in-plane crystallographic orientations. Our results disclose the relevance of the morphology and orientation of buckling instabilities in ferroelectric free sheets, for the stabilization of different domain structures, pointing to new routes for domain engineering of ferroelectrics in flexible oxide sheets.

36 MATERIALS SCIENCE↗

SOME RESULTS ON BUCKLING AND POSTBUCKLING OF CYLINDRICAL SHELLS

In this summary paper, the effects of initial deformations on the buckling and postbuckling characteristics of circular cylindrical shells under hydrostatic pressure is determined in an approximate manner. The influence of initial axisymmetric deformations is stressed. Also, the classical buckling of an axially compressed, noncircular (oval) cylindrical shell is studied. The results show that the major-minor axis ratio of the cross section has a marked effect on the critical load, and that use of the maximum radius of curvature in the formula for the classical buckling stress of a circular cylindrical shell leads to good results for moderate eccentricities.

BUCKLING↗

Local Circumferential Buckling of Thin Circular Cylindrical Shells

The problem of circumferential buckling of a thin circular cylindrical shell due to compressive hoop stresses which vary in the axial direction is examined. For extremely localised compressive hoop stress distributions resulting from thermal discontinuity effects, or from a uniform, radial line loading, the buckle pattern should also be localised. Simplified analyses into these two types of problem are considered which show that only a limited number of buckle deflection modes needs to be assumed.

CYLINDRICAL SHELL↗

BUCKLING OF CONICAL SHELLS UNDER EXTERNAL PRESSURE

It is shown that the initial and the buckled shapes of a certain element of a conical shell can be considered as similar to those of an element of a cylindrical shell of which the radius and length are conservatively determined. It is concluded that therefore the buckling pressure of the conical shell is equal to that of the comparable cylindrical shell. A simple method for finding the buckling pressure if it varies along a generatrix is also given.

CONICAL SHELL↗

ON THE INFLUENCE OF NON-SYMMETRICAL MODES ON THE BUCKLING OF SHALLOW SPHERICAL SHELLS UNDER UNIFORM PRESSURE

In view of the wide discrepancy between theoretical and experimental results that still exists, the problem of buckling of shallow spherical shells under uniform external pressure is reexamined with the introduction of non-symmetrical deflection modes. The basic idea is that, for a symmetrical shell under gradually increasing symmetrical loading, the deformation will be symmetrical up to and after buckling, but it is feasible that a non-symmetrical mode participates in the snap-through process. Including this possibility in the governing equations may lower the theoretical buckling load. Some analytical results are presented and compared with experiment.

SPHERICAL SHELL↗

SOME RECENT RESULTS ON THE BUCKLING MECHANISM OF SPHERICAL CAPS

The curve of pressure versus deformation for a spherical cap subjected to external pressure is frequently assumed to be similar to that of Fig. 1. Here P is a loading parameter and D(P) is a measure of the deformation (e.g. maximum displacement). This curve implies that for P > P(U) and for P < P(L) there is only one equilibrium state. For each P in P(L) < P < P(U) there are three equilibrium states and the cap must buckle at some P in this interval. We call P(L) and P(U), respectively, the upper and lower buckling loads. Points on the branch 0U correspond to unbuckled equilibrium states, those on the branch LN to buckled states and those on UL to unstable states.

BUCKLING↗