Buckling of Segments of Toroidal Shells
Nonlinear differential equations of equilibrium and buckling equations for segments of toroidal shells having Gaussian curvature
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Nonlinear differential equations of equilibrium and buckling equations for segments of toroidal shells having Gaussian curvature
Available theories and test data on buckling of curved plates and shells are reviewed. For torsion and external-pressure loadings, the test data are correlated in terms of linear buckling theories for both the elastic and inelastic ranges. The cases which exhibit a marked disagreement between linear theory and test data include those of curved plates and cylinders under axial compression, cylinders under bending, and spherical plates under external pressure. These cases have been analyzed by a unified semiempirical approach for both the elastic and inelastic ranges which is satisfactory for analysis and design purposes. The effects of internal pressure on buckling of elements under uniaxial loads are discussed and data on various combined loadings are presented in interaction form. (author)
Influence of prebuckling deformation on buckling load of truncated conical shells under axial compression
A method is described to computationally simulate probabilistic buckling behavior of multilayered composite shells. The simulation accounts for all naturally-occurring uncertainties including those in constituent (fiber/matrix) material properties, fabrication variables, and structure geometry. The method is demonstrated for probabilistically assessing the buckling survivability of a specific case of a stiffened composite cylindrical shell with and without cutouts. The sensitivities of various uncertain variables on the buckling survivability are evaluated at specified reliability. The results show that the buckling survivability for a shell without cutouts depends primarily on shell skin related uncertainties. However, stringer related uncertainties become important for a shell with cutouts.
Supervised autonomous assembly (SAA) will create a paradigm shift in the planning and design of future persistent assets (PAs), both in near zero-g environments and on planetary surfaces. SAA refers to an autonomy approach that has the benefits of autonomous assembly as well as the benefits provided by a supervisor (operator) who is available to resolve unexpected situations. SAA provides both increased design freedom as well as reduced programmatic risk. SAA enables evolution of future PAs over decades as in-space operations transition from single purpose missions to creation of PAs, such as laboratories and experimental stations which more closely resembling terrestrial laboratories that can easily adapt and evolve to new missions leveraging repeated visits to the PA. The ability to evolve enables PAs to rapidly respond to changing objectives resulting from new questions as our understanding improves. A recently initiated National Aeronautics and Space Administration (NASA) project in the Space Technology Mission Directorate (STMD) Game Changing Development (GCD) Program called the Precision Assembled Space Structure (PASS), leverages the advantages of SAA to develop technologies that enable efficient creation and evolution of hexagonal topologies; both planar (example: fuel depots) and curved (examples: telescopes and shelters). PASS will be used to provide context for the philosophy and concepts discussed as well as the decision and selections made. PASS objectives are: a) Develop confidence in SAA and on-orbit servicing, assembly and manufacturing (OSAM) technologies by executing a test campaign that uses a path-to-flight autonomous precision assembly process directly applicable to future space telescopes. b) Test autonomous technologies including automated path planning and error recovery, to emphasize a robust approach that relies on generic robots and special purpose tools. c) Validate critical component models using a digital twin that includes the assembled primary mirror support structure and assembly process. A digital twin is a high-fidelity simulation of the asset capable of predicting the on-orbit performance. The paper concludes after identifying the critical need for a modest assembly flight experiment to validate and develop confidence in the SAA paradigm, thus accelerating adoption of the benefits described. SAA is a game changing paradigm that enhances the ability of an organization to infuse new technology through rapid evolution of PAs while leveraging OSAM technologies.
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Structural analysis of thermal buckling of orthotropic, multilayered, stiffened cylindrical shell using finite differences and determinant plotting or modal iteration
The present paper deals with the buckling of a circular cylindrical shell under axial compression from the viewpoint of energy and the characteristics of deformation. It is shown first, both theoretically and experimentally, that the reason why the buckling of a cylindrical shell is quite different from that of a flat plate is attributable to the existence of a nearly developable surface far apart from the original cylindrical surface. Based upon this result, the experimental fact that the buckling is really not general but local, that is, that the buckled region is limited axially to a range of 1.5 times the wave length of the lobe, is explained by the theoretical result that the minimum buckling load is smaller in the local buckling than in the general buckling case. The occurrence of local buckling is affirmed also from the viewpoint of the energy barrier to be jumped over during buckling, and from a comparison of the theoretical post-buckling state with the experimental results. Finally, the local buckling with the load applied by a spring is analyzed, and it is proved that the minimum buckling load increased with an increase of rigidity of the spring.
Elastic stability of clamped shallow spherical shells under concentrated load, noting buckling modes
Elastic stability of clamped shallow spherical shells under concentrated load, noting buckling modes
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.
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.
Initial postbuckling behavior of double curvature shell segments under several loading conditions determined, using Koiter theory
A rigorous analytical study of cones stiffened by many thin-gage, open-section rings is presented. The results are compared with data previously obtained from uniform pressure tests of the Viking mission flight aeroshell and of the Viking structural prototype aeroshells. A conventional analysis, in which the rings are modeled as discrete rigid cross sections, is shown to lead to large, unconservative strength predictions. A more sophisticated technique of modeling the rings as shell branches leads to much more realistic strength predictions and more accurately predicts the failure modes. It is also shown that if a small initial imperfection proportional to the shape of the buckling mode is assumed, the critical buckling modes from analysis and test are in agreement. However, the reduction in buckling strength from the perfect-shell predictions is small.
Buckling and initial postbuckling behavior of thin elastic cylindrical shells of elliptical cross section
A system of 6th-order quasi-linear Ordinary Differential Equations is analyzed to show the global existence of axisymmetrically buckled states. A surprising nodal property is obtained which shows that everywhere along a branch of solutions that bifurcates from a simple eigenvalue of the linearized equation, the number of simultaneously vanishing points of both shear resultant and circumferential bending moment resultant remains invariant, provided that a certain auxiliary condition is satisfied.
The effects of imperfections on the buckling strength of pressurized cylinders under axial compression are studied. The imperfection factor is considered in the finite-deflection compatibility equation, as well as in the equilibrium equation. A new relation to express the imperfection as an explicit exponential function of pressure and radius thickness ratio is proposed. A method for finding the exponential function is described, and the solution for the critical stress is found in a fairly simple form. The relation of decrease of stability with respect to magnitude of imperfections if found.
Elastic buckling load of cylindrical shells with dimple imperfections under external pressure, applying perturbation expansion to Karman-Donnell equations