Analysis of the buckling process of circular cylindrical shells under axial compression
Critical buckling loads for circular cylindrical shells under axial compression
Tennyson, R. C.↗
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New Configuration for Compression-Test Fixture
Gravity-loades axial-compression test fixture is operated by raising lower platen and specimen against weighted upper platen. Wheel turns nut on threaded rod to move lower platen up or down. Limiting rods prevent further upward movement if sample buckles.
Shanks, G. C.↗
The Effect on the Buckling of Perfect Cylinders of Prebuckling Deformations and Stresses Induced by Edge Support
Large deflection theory is used to compute buckling loads of simply supported initially perfect cylinders under axial compression, external hydrostatic pressure, and combinations of axial compression and internal or external pressure. Important results are obtained by taking into account prebuckling deformations and stresses induced by edge support. For example, the presence of these deformations and stresses can decrease the axial-compression buckling load of an unpressurized perfect cylinder by 50 percent or more.
CYLINDER↗
The Influence of Prebuckling Deformations and Stresses on the Buckling of Perfect Cylinders
Large-deflection theory is used to compute buckling loads of simply supported initially perfect cylinders under axial compression, external pressure, and combinations of axial compression and internal or external pressure. Important results are obtained by taking into account prebuckling deformations and stresses induced by edge support. For example, the presence of these deformations and stresses can reduce the axial-compression buckling load of an unpressurized perfect cylinder to 50 percent of the classical value.
BUCKLING↗
Postbuckling of long thick plates in compression including higher order transverse shearing effects
Aluminum plates of various length/width ratios loaded in compression are examined analytically in terms of buckling and postbuckling for comparison with classical theory. The plates are considered to be subjected to longitudinal compressive displacement with no edge stress and are assumed to be simply supported at the side edges. The average longitudinal direct stresses are computed to plot characteristic curves by means of the following theories: 3D flexibility, higher-order shear deformation, first-order shear deformation, and classical von Karman. The 3D flexibility approach yields the lowest results with more unknowns than the higher-order shear-deformation method. The 3D flexibility approach is considered to be the most accurate, and it is shown that the calculated resultants and displacements tend to vary when consideration is given to the effects of transverse shear.
Stein, Manuel↗
Compressive Failure of Fiber Composites under Multi-Axial Loading
This paper examines the compressive strength of a fiber reinforced lamina under multi-axial stress states. An equilibrium analysis is carried out in which a kinked band of rotated fibers, described by two angles, is sandwiched between two regions in which the fibers are nominally straight. Proportional multi-axial stress states are examined. The analysis includes the possibility of bifurcation from the current equilibrium state. The compressive strength of the lamina is contingent upon either attaining a load maximum in the equilibrium response or satisfaction of a bifurcation condition, whichever occurs first. The results show that for uniaxial loading a non-zero kink band angle beta produces the minimum limit load. For multi-axial loading, different proportional loading paths show regimes of bifurcation dominated and limit load dominated behavior. The present results are able to capture the beneficial effect of transverse compression in raising the composite compressive strength as observed in experiments.
Basu, Shiladitya↗
Residual stress in high modulus carbon fibers
The modulus and residual strain in carbon fibers are measured by successively electrochemically milling away the fiber surface. Electrochemical etching is found to remove the carbon fiber surface very uniformly, in contrast to air and wet oxidation. The precision of fiber diameter measurements is improved by using a laser diffraction technique instead of optical methods. More precise diameter measurements reveal that past correlations of diameter and fiber modulus are largely measurement artifact. The moduli of most carbon fibers decrease after the outer layers of the fibers are removed. Owing to experimental difficulties, the moduli and strengths of the fibers at their centers are not determined, and moduli are estimated on the basis of microstructure. The calculated residual stresses are found to be insensitive to these moduli estimates as well as the exact form of regression equation used to describe the moduli and residual strain distributions. Axial compressive residual stresses are found to be very high for some higher modulus carbon fibers. It is pointed out that the compressive stress makes the fibers insensitive to surface flaws when loaded in tension but it may initiate failure by buckling when loaded in compression.
Chen, K. J.↗
Rubberlike elasticity experiment
Four rubber erasers from the campus bookstore, two green and two white, have been cut to have identical dimensions. These are loaded in compression with a mechanical test machine capable of applying cyclic loads and providing output to an X-Y plotter. The anelastic behavior of rubber as well as the relative stiffnesses of composite materials loaded transversely and longitudinally may be demonstrated to beginning students or used as input for computer analysis by students.
Greet, Richard↗
Buckling analysis of fully anisotropic plates containing cutouts and elastically restrained edges
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.
Jones, Kevin M.↗
Comparison of Methods to Predict Lower Bound Buckling Loads of Cylinders Under Axial Compression
Results from a numerical study of the buckling response of two different orthogrid stiffened circular cylindrical shells with initial imperfections and subjected to axial compression are used to compare three different lower bound buckling load prediction techniques. These lower bound prediction techniques assume different imperfection types and include an imperfection based on a mode shape from an eigenvalue analysis, an imperfection caused by a lateral perturbation load, and an imperfection in the shape of a single stress-free dimple. The STAGS finite element code is used for the analyses. Responses of the cylinders for ranges of imperfection amplitudes are considered, and the effect of each imperfection is compared to the response of a geometrically perfect cylinder. Similar behavior was observed for shells that include a lateral perturbation load and a single dimple imperfection, and the results indicate that the predicted lower bounds are much less conservative than the corresponding results for the cylinders with the mode shape imperfection considered herein. In addition, the lateral perturbation technique and the single dimple imperfection produce response characteristics that are physically meaningful and can be validated via testing.
Haynie, Waddy T.↗
Analysis of stability-critical orthotropic cylinders subjected to axial compression
Analytical procedure for determining critical buckling loads of orthotropic cylinders subjected to axial compression loading has been defined. Three modes of instability have been considered - general instability, local instability caused by panel and interframe buckling, and local instability caused by yielding and crippling in areas of stress concentration.
Finley, R. L.↗
The influence of prebuckling deformation on the buckling load of truncated conical shells under axial compression
Influence of prebuckling deformation on buckling load of truncated conical shells under axial compression
DEFORMATION↗
An Energy Absorber for the International Space Station
The energy absorber described herein is similar in size and shape to an automotive shock absorber, requiring a constant, high load to compress over the stroke, and self-resetting with a small load. The differences in these loads over the stroke represent the energy absorbed by the device, which is dissipated as friction. This paper describes the evolution of the energy absorber, presents the results of testing performed, and shows the sensitivity of this device to several key design variables.
Wilkes, Bob↗
Mechanical properties of eutectic bonded boron aluminum
Results are presented of extensive testing recently completed on boron-aluminum composites to determine mechanical property data for structural design and analysis. Average property data and associated test methods are given for unidirectional and cross plied laminates at room temperature and 600 F. Results from crippling tests of hat-shaped stringers and mechanical fastener joint tests of laminates containing titanium interleaves are also presented. Compared to aluminum which has approximately same density, tests show that boron-aluminum loaded in compression is 4 1/2 times stronger and 3 1/2 times stiffer. When loaded in tension it is 2 times stronger and 3 times stiffer.
Bohlmann, R. E.↗
Innovative design of composite structures: Further studies in the use of a curvilinear fiber format to improve structural efficiency
Further studies to determine the potential for using a curvilinear fiber format in the design of composite laminates are reported. The curvilinear format is in contrast to the current practice of having the fibers aligned parallel to each other and in a straight line. The problem of a plate with a central circular hole is used as a candidate problem for this study. The study concludes that for inplane tensile loading the curvilinear format is superior. The limited results to date on compression buckling loads indicate that the curvilinear designs are poorer in resistant buckling. However, for the curvilinear design of interest, the reduction in buckling load is minimal and so overall there is a gain in considering the curvilinear design.
Hyer, Michael W.↗
Methods for Determining the Optimum Design of Structures Protected from Aerodynamic Heating and Application to Typical Boost-Glide or Reentry Flight Paths
General equations are developed for the design of efficient structures protected from thermal environments typical of those encountered in boost-glide or atmospheric-reentry conditions. The method is applied to insulated heat-sink stressed-skin structures and to internally cooled insulated structures. Plates loaded in compression are treated in detail. Under limited conditions of plate buckling, high loading, and short flight periods, and for aluminum structures only, the weights of both configurations are nearly equal. Load parameters are found and are similar to those derived in previous investigations for the restricted case of a constant equilibrium temperature at the outside surface of the insulation.
Harris, Robert S., Jr.↗
Effect of Loading Rate on the Open Hole Compression Strength of Quasi-Isotropic Carbon/Epoxy Laminates
This study was undertaken to examine how well the 0.05 inch/min loading rate typically used to develop allowables for open hole compression strength of carbon/epoxy laminates represents structures that may experience a much lower loading rate (such as civil engineering structures) or a much higher loading rate (such as a rocket interstage at liftoff). The Composite Materials Handbook-17 (CMH-17) suggests developing strength allowables at the coupon level (lowest level of the “building block” approach) and using a rigorous statistical analysis to arrive at a strength allowable upon which the structure is to be further designed at higher levels of the building block pyramid. But do these coupon level tests truly represent meaningful stresses at which the composite in the final structure can withstand considering the effects of loading rate? Open hole compression (OHC) strength was chosen for this study since most structures are designed to some damage tolerance criteria and OHC strength testing is rather simple to perform. A quasi-isotropic lay-up was chosen since this is a very common lay-up sequence. The results show that for structures that experience a very small loading rate (0.0005 in/min) the allowables developed at the standard 0.05 in/min loading rate are higher than what the composite can withstand at this lower loading rate. Conversely, at a high loading rate of 10 in/min the strength values found at the standard test rate of 0.05 in/min are slightly lower and not “in family” using the statistics suggested in CMH-17. These results question if standardized test rates are reliable, at least to the fidelity of being “in family” per CMH-17. Some creep rupture tests were also performed to demonstrate that OHC strength values could be lower than the slowest test speed used in this study (0.0005 in/min).
open hole compression strength↗
Combined bearing and bypass loading on a graphite/epoxy laminate
A combined experimental and analytical study was conducted to determine the behavior of a graphite/epoxy laminate subjected to combined bearing and bypass loading. Single-fastener quasi-isotropic specimens were loaded at various bearing-bypass ratios until damage was produced at the fastener hole. Damage-onset strengths and damage modes were then analyzed using local hole-boundary stresses calculated by a finite-element analysis. The tension data showed the expected linear interaction for combined bearing and bypass loading with damage developing in the net-section tension mode. However, the compression bearing-bypass strengths showed an unexpected interaction involving the bearing mode. Compressive bypass loads reduced the bearing strength by decreasing the bolt-hole contact arc and thus increasing the severity of the bearing loads. The bearing stresses at the hole boundary were not accurately estimated by superposition of the stress components for separate bearing and bypass loading. However, superposition produced reasonably accurate estimates for tangential stresses especially near the specimen net-section.
Crews, J. H., Jr.↗