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At least 181 records · Page 10

Buckling Load Calculations of the Isotropic Shell A-8 Using a High-Fidelity Hierarchical Approach

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.

Arbocz, Johann↗

Buckling Design Studies of Inverted, Oblate Bulkheads for a Propellant Tank

An investigation of the deformation and buckling characteristics of a composite, oblate bulkhead that has an inverted geometry and is subjected to pressure-only loading is presented for three bulkhead geometries and thicknesses. The effects of a stiffening support ring at the bulkhead to cylinder interface are also evaluated. Buckling analyses conducted using the axisymmetric shell code BOSOR4 are discussed for several bulkhead configurations. These results are analytically verified using results from the Structural Analysis of General Shells (STAGS) code for a selected bulkhead configuration. The buckling characterization of an inverted, oblate bulkhead requires careful attention as small changes in bulkhead parameters can have a significant effect on the critical buckling load. Comparison of BOSOR4 and STAGS results provided a very good correlation between the two analysis methods. In addition, the analysis code BOSOR4 was found to be an efficient sizing tool that is useful during the preliminary design stage of a practical shell structure. Together, these two aspects should give the design engineer confidence in sizing these stability critical structures. Additional characterization is warranted, especially for a composite tank structure, since only one bulkhead configuration was examined closely.

Smeltzer, Stanley S., III↗

Finite Element Modeling of the Buckling Response of Sandwich Panels

A comparative study of different modeling approaches for predicting sandwich panel buckling response is described. The study considers sandwich panels with anisotropic face sheets and a very thick core. Results from conventional analytical solutions for sandwich panel overall buckling and face-sheet-wrinkling type modes are compared with solutions obtained using different finite element modeling approaches. Finite element solutions are obtained using layered shell element models, with and without transverse shear flexibility, layered shell/solid element models, with shell elements for the face sheets and solid elements for the core, and sandwich models using a recently developed specialty sandwich element. Convergence characteristics of the shell/solid and sandwich element modeling approaches with respect to in-plane and through-the-thickness discretization, are demonstrated. Results of the study indicate that the specialty sandwich element provides an accurate and effective modeling approach for predicting both overall and localized sandwich panel buckling response. Furthermore, results indicate that anisotropy of the face sheets, along with the ratio of principle elastic moduli, affect the buckling response and these effects may not be represented accurately by analytical solutions. Modeling recommendations are also provided.

Rose, Cheryl A.↗

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

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

Nemeth, Michael P.↗

Buckling Of Long Compression-Loaded Anisotropic Plates Restrained Against Inplane Lateral and Shear Deformations

An approach for synthesizing buckling results and behavior for thin balanced and unbalanced symmetric laminates that are subjected to uniform axial compression loads and elastically restrained against inplane expansion, contraction, and shear deformation is presented. This approach uses a nondimensional analysis for infinitely long, flexurally anisotropic plates (coupling between bending and twisting) that are subjected to combined mechanical loads and is based on nondimensional parameters. In addition, nondimensional loading parameters are derived that account for the effects of the elastic inplane deformation restraints, membrane orthotropy, and membrane anisotropy on the induced prebuckling stress state. The loading parameters are used to determine buckling coefficients that include the effects of flexural orthotropy and flexural anisotropy. Many results are presented, for some selected laminates, that are intended to facilitate a structural designer's transition to the use of the generic buckling design curves that are presented and discussed in the paper. Several buckling response curves are presented that provide physical insight into the behavior for combined loads, in addition to providing useful design data. An example is presented that demonstrates the use of the generic design curves, which are applicable to a wide range of laminate constructions. The analysis approach and generic results indicate the effects and characteristics of laminate orthotropy and anisotropy in a very general and unifying manner.

Nemeth, Michael P.↗

Experimental Studies of Flutter of Buckled Rectangular Panels at Mach Numbers from 1.2 to 3.0 Including Effects of Pressure Differential and of Panel Width-Length Ratio

Experimental panel flutter data have been obtained at Mach numbers from 1.2 to 3.0 for buckled rectangular panels and the effect of a pressure differential has been determined. Increasing the pressure differential was effective in eliminating flutter on most of the panels tested. The effects of the variables in the panel flutter parameter ((square root of m(exp 2) -1) * (E/q))(exp 1/3) t/l (where M is the Mach number, q is the dynamic pressure, E is Young's modulus, and t and l are the panel thickness and length, respectively) were investigated for buckled panels clamped on the front and rear edges and a critical value of this parameter of 0.44 is indicated at zero pressure differential when the panel width-length ratio is 0.69. An estimated flutter boundary is presented for buckled panels clamped on four edges, with width-length ratios of 0.21 to 4.0. This boundary shows that the panel width is more significant than the panel length when the ratio of width to length is less than approximately 0.5. Panels clamped on four edges and buckled in two half waves in the direction of flow were found to be particularly susceptible to flutter. The results of limited tests on panels with applied damping, curvature, and lengthwise stiffeners are also presented and discussed.

Sylvester, Maurice A.↗

Predicting the Influence of Nano-Scale Material Structure on the In-Plane Buckling of Orthotropic Plates

A multi-scale analysis of the structural stability of a carbon nanotube-polymer composite material is developed. The influence of intrinsic molecular structure, such as nanotube length, volume fraction, orientation and chemical functionalization, is investigated by assessing the relative change in critical, in-plane buckling loads. The analysis method relies on elastic properties predicted using the hierarchical, constitutive equations developed from the equivalent-continuum modeling technique applied to the buckling analysis of an orthotropic plate. The results indicate that for the specific composite materials considered in this study, a composite with randomly orientated carbon nanotubes consistently provides the highest values of critical buckling load and that for low volume fraction composites, the non-functionalized nanotube material provides an increase in critical buckling stability with respect to the functionalized system.

Gates, Thomas S.↗

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↗