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This monograph indicates current practices for predicting buckling of uniform stiffened and unstiffened circular cylindrical shells under various types of static loading, and suggests the procedures that yield estimates of static buckling loads considered to be conservative. The buckling of truncated conical shells and shells of double curvature will be treated in separate monographs.
The results of an experimental investigation on the fracture behavior of unidirectional and multidirectional laminated graphite/epoxy composites is reported. Critical tensile fracture stresses for constant head rate uniaxial specimens containing single-edge notches, double-edge notches, and centrally located circular holes are presented. Results are reported for loads and notches at various angles to the fiber direction. Evidence of notch sensitivity and stable crack growth is presented. Self-similar crack growth is shown to occur for only a limited set of circumstances. Critical stresses are compared to the theories of Waddoups et al and Whitney et al. These comparisons are presented using isotropic and orthotropic stress concentration factors together with a finite width correction factor. The results tend to show that use of only isotropic correction factors allow good correlation between theory and experiment.
Major areas of study include: (1) edge effects in finite width laminated composites subjected to mechanical, thermal and hygroscopic loading with temperature dependent material properties and the influence of edge effects on the initiation of failure; (2) shear and compression testing of composite materials at room and elevated temperatures; (3) optical techniques for precise measurement of coefficients of thermal expansion of composites; (4) models for the nonlinear behavior of composites including material nonlinearity and damage accumulation and verification of the models under biaxial loading; (5) compressive failure of graphite/epoxy plates with circular holes and the buckling of composite cylinders under combined compression and torsion; (6) nonlinear mechanical properties of borsic/aluminum, graphite/polyimide and boron/aluminum; (7) the strength characteristics of spliced sandwich panels; and (8) curved graphite/epoxy panels subjected to internal pressure.
Stresses were calculated for finite size orthotropic laminates loaded by a frictionless steel pin in a circular hole of the same diameter. The calculations were based on finite element analyses for six laminates. Stress concentration factors, based on nominal bearing stress, were determined for wide ranges of the ratios of width to diameter, w/d and edge distance to diameter, e/d. An infinite laminate case was analyzed for each laminate. Orthotropy had a significant influence on the tensile stress concentration at the hole. For example, the stress concentration factors for the infinite laminate cases ranged from 0.82 to 2.16, compared with 0.87 for the quasi-isotropic laminate. The finite widths and edge distances strongly influenced the tensile stress concentration. For the practical range w/d or = 3, the peak tensile stresses were as much as 80% larger than the infinite laminate reference value. For e/d or = 3, these stresses were amplified by as much as 50%. In contrast, the finite width and edge distance had little effect on shear-out and bearing stress concentrations.
The elasticity problem for a thick plate consisting of two bonded dissimilar homogeneous layers is considered. It is assumed that the plate is infinite, contains a circular hole, and is subjected to axisymmetric external loads. A technique suitable to the formulation of three-dimensional boundary value problems is introduced and applied to the three-dimensional elasticity solution of an infinite plate with a hole. The effect of Poisson's ratio is studied in some detail, and the axisymmetric problem of a laminated plate is solved. The stresses at the interface are calculated and are observed to become unbounded at the hole boundary. An approximate treatment of the singularity is presented and the stress intensity factors are computed. Some of the results are compared with those found from the finite element method. The agreement between the two sets with regard to trend and magnitude is found to be very satisfactory.
An understanding was developed of the factors that determine the semi-circular edge-notched compressive strength and the associated failure mode(s) were identified of thermoplastic composite laminates with multidirectional stacking sequences. The experimental observations and the detailed literature review suggest at least four factors that affected the determination of the strain levels at which fiber microbuckling initiates and thus, partially control the composite's compression strength. The dependent variables studied are the compressive strength of a reduced gage section compression specimen and the compression strength of a compression specimen with two semi-circular edge notches (no opposite free edges) centered along the gage section. In this research, specimens containing two semi-circular edge notches (no opposite free edges) were loaded in compression at a relatively slow rate to provide more stable development of fiber microbuckling damage. The results indicate that the local constraints (free surfaces, supporting ply orientation, and resin-rich regions) significantly affect the strain level for the initiation of in-plane fiber microbuckling. Preliminary results at an elevated temperature, 77 C, showed the shear stress yield strength of the resin was reduced and consequently, the resistance to fiber microbuckling was also reduced. The finite element analysis of the perfectly straight fiber problem indicates that the free surface effect causes a 10 percent reduction in the critical buckling strain. However, the experimentally measured reduction for fibers with an initial fiber curvature, was 35 percent.
The potential gain in buckling resistance is explored by using the curvilinear format with a plate containing a centrally located circular hole and subjected to a uniaxial compressive load. The buckling loads for a uniform stress loading and simple support boundary conditions were examined. The method of analysis is outlined for the buckling improvement study. Several designs that represent an improvement over a baseline quasi-isotropic design (a design that is quite good for buckling resistance) are discussed. The tensile load of these designs is examined. A recommended design is presented that not only shows an improved buckling capacity, but also shows improved tensile performance. Follow-on activities are also discussed.
The deformation and complete stress distribution are determined for each of the following edge loaded thin shells of revolution: (1) a right circular cylinder, (2) a frustum of a right circular cone, and (3) a portion of a sphere. The locations of the maximum circumferential and meridional stresses on both the inner and outer surfaces are also found. The basic equations for the above were selected from the published literature on the subject and expanded to produce to resultant-stress equations in closed from where practicable to do so. Equations are also developed for the discontinuity shear force and bending moment at each of the following junction: (1) axial change of thickness in a circular cylinder, (2) axial change of thickness in a cone, (3) change of thickness in a portion of a sphere, (4) a cylinder and a cone, (5) a cylinder and a portion of a sphere(6) a cylinder and a flat head, and (7) a cone and a portion of a sphere.
An experimental investigation of the compression behavior of laminated specimens made from graphite-epoxy tape (AS4-3502), graphite-thermoplastic tape (AS4-PEEK), and graphite-thermoplastic fabric (AS4-PEEK) was conducted. Specimens with five different stacking sequences were loaded to failure in uniaxial compression. Some of the specimens had central circular holes with diameters up to 65 percent of the specimen width. Other specimens were subjected to low speed impact with impact energy up to 30 J prior to compressive loading. This investigation indicates that graphite-thermoplastic specimens with holes have up to 15 percent lower failure stresses and strains than graphite-epoxy specimens with the same stacking sequence and hole size. However, graphite-thermoplastic specimens subjected to low speed impact have up to 15 percent higher failure stresses and strains than graphite-epoxy specimens with the same stacking sequence and impact energy. Compression tests of graphite-thermoplastic specimens constructed of unidirectional tape and of fabric indicate that the material form has little effect on failure strains in specimens with holes or low speed impact damage.
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.
Surface pressure distributions were obtained with model-scale STOL-OTW configurations using various nozzles designed to promote flow attachment to the wing/flap surface. The nozzle configurations included slot-types and both circular and slot nozzles with external flow deflectors. The wing aerodynamic loading caused by the jet-induced lift is presented in conventional terms of delta p/q as a function of chordwise surface distance in the nozzle centerline plane as well as outboard of the nozzle centerline. Nozzle roof/deflector angle, chordwise location of the nozzle, wing size, and flap deflection angle are included in the geometric variables affecting the wing loading.
Surface pressure distributions were obtained with model-scale STOL-OTW configurations using various nozzles designed to promote flow attachment to the wing-flap surface. The nozzle configurations included slot-types and both circular and slot nozzles with external flow deflectors. The wing aerodynamic loading caused by the jet-induced lift is presented in conventional terms of delta p/q as a function of chordwise surface distance in the nozzle centerline plane as well as outboard of the nozzle centerline. Included in the geometric variables affecting the wing loading are nozzle roof/deflector angle, chordwise location of the nozzle, wing size, and flap deflection angle.
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This paper investigates how stable equilibrium states in the extended and coiled configurations can be predicted in thin-shelled composite booms with parabolic cross-sections. These conic shapes potentially offer greater stiffness properties when compared to circular cross-sections, which is critical for improving the load bearing performance of deployed booms. Inducing bistability through the choice of composite shell layups in parabolic booms would allow for controllable self-deployment due to a less energetic coiled state when compared to monostable booms. An inextensional analytical model is used to predict the stable coiled diameters of tape spring and Collapsible Tubular Mast (CTM) booms with parabolic cross-sections. The parabolic section is discretized into circular segments using biarc spline interpolation, which allows them to be integrated into the strain energy minimization procedure used to obtain the equilibrium states. When the parabolic booms are parametrically compared against circular booms with identical layups, flattened height, and mass, the former are found to generally have better stiffness performance while being less efficient in stowed volume as evidenced by larger coiled diameters. Analytical coiled diameters and their strain energy are verified with finite element simulations for optimal parabolic tape spring and CTM booms.
Stress intensity factor equations are presented for an embedded elliptical crack, a semielliptical surface crack, a quarter elliptical corner crack, a semielliptical surface crack along the bore of a circular hole, and a quarter elliptical corner crack at the edge of a circular hole in finite plates. The plates were subjected to either remote tension or bending loads. The stress intensity factors used to develop these equations were obtained from previous three dimensional finite element analyses of these crack configurations. The equations give stress intensity factors as a function of parametric angle, crack depth, crack length, plate thickness, and, where applicable, hole radius. The ratio of crack depth to plate thickness ranged from 0 to 1, the ratio of crack depth to crack length ranged from 0.2 to 2, and the ratio of hole radius to plate thickness ranged from 0.5 to 2. The effects of plate width on stress intensity variation along the crack front were also included.
Equations describing the stress field and velocity field occurring in a circular cylindrical shell at plastic collapse are derived corresponding to stress states lying on each face of a yield surface for a uniform shell of material obeying the Tresca yield condition. They are then applied to the case of a shell under combined axisymmetric loadings (moment, shear force, and axial force) at one end and uniform internal or external pressure on the lateral surface. For a sufficiently long shell, complete solutions are obtained for a fixed far end, and for a certain range of values of axial force and pressure, they are obtained for a free far end. All the solutions are represented by either closed form or by quadratures. It is shown that in many cases the radial velocity field is proportional to the shear force.
The paper introduces a failure model for laminated composite plates with a cutout under combined compressive and shear loads. The model is based on kinking failure of the load-carrying fibers around a cutout, and includes the effect of local shearing and compressive stresses. Comparison of predictions of the model with available experimental results for quasi-isotropic and orthotropic plates with a circular hole indicated a good agreement. Predictions for orthotropic plates under combined loading are compared with the predictions of a point-stress model. The present model indicates significant reductions in axial load-carrying capacity due to shearing loads for plates with principal axis of orthotropy oriented along the axial load direction. A gain in strength is achieved by rotating the axis of orthotropy to counteract the shearing stress, or by eliminating the compressive-shear deformation coupling.
To help determine the systems requirements for a 300-kWe space nuclear reactor power system, a mission and spacecraft have been examined which utilize electric propulsion and this nuclear reactor power for multiple transfers of cargo between low earth orbit (LEO) and geosynchronous earth orbit (GEO). A propulsion system employing ion thrusters and xenon propellant was selected. Propellant and thrusters are replaced after each sortie to GEO. The mass of the Orbital Transfer Vehicle (OTV), empty and dry, is 11,000 kg; nominal propellant load is 5000 kg. The OTV operates between a circular orbit at 925 km altitude, 28.5 deg inclination, and GEO. Cargo is brought to the OTV by Shuttle and an Orbital Maneuvering Vehicle (OMV); the OTV then takes it to GEO. The OTV can also bring cargo back from GEO, for transfer by OMV to the Shuttle. OTV propellant is resupplied and the ion thrusters are replaced by the OMV before each trip to GEO. At the end of mission life, the OTV's electric propulsion is used to place it in a heliocentric orbit so that the reactor will not return to earth. The nominal cargo capability to GEO is 6000 kg with a transit time of 120 days; 1350 kg can be transferred in 90 days, and 14,300 kg in 240 days. These capabilities can be considerably increased by using separate Shuttle launches to bring up propellant and cargo, or by changing to mercury propellant.