The limiting state of thin-walled shapes in biaxial bending with torsion
Limiting stress calculated for thin walled shapes in biaxial bending with torsion
TORSIONAL STRESS↗
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Bending strength of large thin-walled pressure- stabilized cylinder beyond onset of compressive skin wrinkling.
Ultimate bending moment capability of thin walled pressure stabilized cylinder with typical axial loads demonstrated to be 50 percent greater than bending moment at which compressive wrinkling occurs
THIN WALLED SHELL↗
Comparative efficiencies of aerospace pressure vessel design concepts.
Comparative efficiencies of thin wall aerospace pressure vessels, emphasizing primary structural weight
PRESSURE VESSEL↗
Stiffness matrices for thin triangular elements of nonzero Gaussian curvature.
Stiffness matrix of thin flat triangular elements of nonzero Gaussian curvature derived by reducing geometrical idealization errors
THIN WALLED SHELL↗
Rim-spoke composite flywheels: Stress and vibration analysis
Elementary relations are described to determine the material utilization efficiency of a thin wall rim composite flywheel over other configurations. An algorithm is generated for the automatic selection of the optimum composite material for a given thin rim flywheel environment. Subsequently, the computer program NASTRAN is used to perform a detailed stress and vibration analysis of thin wall cylindrical shell rim spoke, single rim and multirim composite flywheels for a specific application.
Chamis, C. C.↗
Buckling Analysis of a Honeycomb-Core Composite Cylinder with Initial Geometric Imperfections
Thin-walled cylindrical shell structures often have buckling as the critical failure mode, and the buckling of such structures can be very sensitive to small geometric imperfections. The buckling analyses of an 8-ft-diameter, 10-ft-long honeycomb-core composite cylinder loaded in pure axial compression is discussed in this document. Two loading configurations are considered configuration 1 uses simple end conditions, and configuration 2 includes additional structure that may more closely approximate experimental loading conditions. Linear eigenvalue buckling analyses and nonlinear analyses with and without initial geometric imperfections were performed on both configurations. The initial imperfections were introduced in the shell by applying a radial load at the midlength of the cylinder to form a single inward dimple. The critical bifurcation buckling loads are predicted to be 924,190 lb and 924,020 lb for configurations 1 and 2, respectively. Nonlinear critical buckling loads of 918,750 lb and 954,900 lb were predicted for geometrically perfect configurations 1 and 2, respectively. Lower-bound critical buckling loads for configurations 1 and 2 with radial perturbations were found to be 33% and 36% lower, respectively, than the unperturbed critical loads. The inclusion of the load introduction cylinders in configuration 2 increased the maximum bending-boundary-layer rotation up to 11%.
Cha, Gene↗
Post University On-the-Job Training for Engineers
Our national need for qualified scientists and engineers is greater now than at any other time in our history. Fortunately, we can point with pride to this need as a measure of the impact of science and technology on our way of life. In effect, we have made such rapid strides In advancing established sciences and in opening new technological fields that we have proved the value of the scientist and engineer to society, and, as a-result, have created an expanding demand for their services which we must now attempt to satisfy. This demand we face is also due to the changing skills and high degree of specialization required to perform in these new technological fields. The colleges and universities are doing their part to provide current graduates with a modern technical foundation, but we cannot afford to ignore the thousands of experienced engineers and scientists already employed by private industry and government. As employers, we have an obligation to these men and women to see that they are provided with an understanding of the latest advances that modern technology has to offer; that we develop them in particular specialty areas characteristic of a given field of work; and, equally important, that we assist them in the transition from one field to another as the technological emphasis shifts. Practically all technological industries have experienced and continue to experience rapid changes in their activities. The aerospace business, in particular, has been characterized by extremely rapid, in fact revolutionary, changes during the relatively short period of its existence0 At the National Aeronautics and Space Administration, successor to the National Advisory Committee for Aeronautics, for example, we have encountered the fun impact of a changing science and technology. Indeed, as a research organization, we have undoubtedly contributed, in some measure, to this change. Within the NASAs Lewis Research Center, we have approximately 800 research scientists and engineers who have matured professionally in an environment which is essentially one of continuous learning - an experience which comes close to being a form of post graduate training in itself. This environment, in addition to providing continuous evolutionary changes, has also provided two major revolutions which have made this development picture more complex. We will describe these environmental changes which have occurred at the Lewis Research Center and discuss the various techniques and programs we have employed to provide for the professional development of our staff. The Lewis Research Center has had an Interesting and exciting l8-year history of aerospace propulsion research and development. It began during the early years of World War II as an expansion of the Power Plant Division of the NCA Langley Center with the mission of conducting research required for the development of improved reciprocating engines and to study the associated problems of subsonic propulsion aerodynamics, It was only a few years later, however, that turbojet and ramjet propulsion and supersonic flight research became our main concern. This transition to jet type engines and higher speeds was our first major technological change. The aerodynamics of propellers became the aerodynamics of high speed turbine and compressor blades; the fuel ignition and carbon deposition problems were transferred from a cyclical or Intermittent high compression combustion chamber to a continuous combustion zone within a thin-walled metal shell; aerodynamics problems were thrust into the supersonic range; and high temperature materials began to play an increasingly critical role. Although this transition still required the same basic knowledge and principles as before, the new engine types did involve a different emphasis and variety of consideration not generally familiar to our scientists and engineers.
Manganiello, Eugene J.↗
Buckling Knockdown Factors for Composite Cylinders
The buckling performance of thin-walled cylindrical shells is well known to be sensitive to small geometric and loading imperfections. During design, this sensitivity is typically accounted for by multiplying the predicted buckling load of a geometrically perfect structure by an empirical design factor known as a buckling knockdown factor (KDF). The most widely used source of KDFs for cylindrical launch-vehicle structures is NASA SP-8007. However, general composite shells are outside the original scope of SP-8007, and a universal KDF of 0.65 for all composite shell designs has been used in several recent NASA studies, though the technical justification is unclear. If the NASA SP-8007 is used to calculate KDFs for composite cylinders, the original assumptions and limitations should be understood and care must be taken. Additionally, the universal KDF of 0.65 is thought to be unconservative for certain designs and is therefore not recommended .
Buckling Knockdown Factors↗
Some Studies on the Nonlinear Dynamic Response of Shell-type Structures
Nonlinear flexural vibrations of thin walled circular cylinders, and buckling of shallow, conical and spherical shells subjected to uniform, impulsive pressures
CONICAL SHELL↗
High-Fidelity Nonlinear Analysis of Compression-Loaded Composite Shells
The results of an experimental and analytical study of the effects of initial imperfections on the buckling and postbuckling response of unstiffened thin-walled compression-loaded graphite-epoxy cylindrical shells are presented. The shells considered in the study have four different shell-wall laminates and two different shell-radius-to-thickness ratios. The shell-wall laminates include two different orthotropic laminates and two different quasi-isotropic laminates. The shell-radius-to-thickness ratios include shell-radius-to-thickness ratios equal to 100 and 200. The results identify the effects of traditional and nontraditional initial imperfections on the nonlinear response characteristics and buckling loads of the shells. The traditional imperfections include the geometric shell-wall mid-surface imperfections that are commonly discussed in the literature on thin shell buckling. The nontraditional imperfections include shell-wall thickness variations, local shell-wall ply-gaps associated with the fabrication process, shell-end geometric imperfections, nonuniform applied end loads, and variations in the boundary conditions including the effects of elastic boundary conditions. A high-fidelity nonlinear shell analysis procedure that accurately accounts for the effects of these traditional and nontraditional imperfections on the nonlinear response characteristics and buckling loads of the shells is described. The analysis procedure includes a nonlinear static analysis that predicts the stable response characteristics of the shells, and a nonlinear transient analysis that predicts the unstable response characteristics. The results of a local shell-wall stress analysis used to estimate failure stresses are also described.
Hilburger, Mark W.↗
ON THE POSTBUCKLING BEHAVIOR OF THIN CYLINDRICAL SHELLS
Results of tests on postbuckling equilibrium positions of isotropic thin-walled circular cylindrical shells under axial compression, external pressure and combined loading are reported and compared with available theoretical results.
CYLINDRICAL SHELL↗
Effects of Imperfections on the Buckling Response of Compression-Loaded Composite Shells
The results of an experimental and analytical study of the effects of initial imperfections on the buckling and postbuckling response of three unstiffened thin-walled compression-loaded graphite-epoxy cylindrical shells with different orthotropic and quasi-isotropic shell-wall laminates are presented. The results identify the effects of traditional and non-traditional initial imperfections on the non-linear response and buckling loads of the shells. The traditional imperfections include the geometric shell-wall mid-surface imperfect ions that are commonly discussed in the literature on thin shell buckling. The non-traditional imperfections include shell-wall thickness variations local shell-wall ply-gaps associated with the fabrication process, sheltered geometric imperfections, non-uniform applied end loads, and variations in the boundary conditions including the effects of elastic boundary conditions. A high-fidelity non-linear shell analysis procedure that accurately accounts for the effects of these traditional and non-traditional imperfections on the nonlinear response, and buckling loads of the shells is described. The analysis procedure includes a non-linear static analysis that predicts stable response characteristics of the shells and a non-linear transient analysis that predicts unstable response characteristics.
Hilburger, Mark W.↗
Effects of Imperfections on the Buckling Response of Compression-Loaded Composite Shells
The results of an experimental and numerical study of the effects of imperfections on the buckling response of unstiffened thin-walled composite cylindrical shells are presented. Results that identify the individual and combined effects of traditional initial geometric shell-wall imperfections and non-traditional shell-wall thickness variations, shell-end geometric imperfections and variations in loads applied to the ends of the shells on the shell buckling response are included. In addition, results illustrating the effects of manufacturing flaws in the form of gaps between adjacent pieces of graphite-epoxy tape in some of the laminate plies are presented in detail. The shells have been analyzed with a nonlinear finite-element analysis code that accurately accounts for these effects on the buckling and nonlinear responses of the shells. The numerical results indicate that traditional and nontraditional initial imperfections can cause a significant reduction in the buckling load of a compression-loaded composite shell. Furthermore, the results indicate that the imperfections couple in a nonlinear manner. The numerical results correlate well with the experimental results. The nonlinear analysis results are also compared to the results from a traditional linear bifurcation buckling analysis. The results suggest that the nonlinear analysis procedure can be used for determining accurate, high-fidelity design knockdown factors for shell buckling and collapse. The results can also be used to determine the effects of manufacturing tolerances on the buckling response of composite shells.
Hilburger, Mark W.↗
Design of a Mars entry 'aeroshell'
The external shell of the Project Viking capsule, which will provide atmospheric deceleration for the 1976 landing of an unmanned spacecraft on the surface of Mars, is a wide-angle, stiffened cone subject to buckling under entry aerodynamic pressure. Complex, highly optimized structural prototype and flight designs were evolved through the application of relatively advanced buckling analysis methodology. Both designs were evaluated through tests and analysis with improved shell-of-revolution computer programs. Deviations between the analyses and experiments were resolved only by modeling the thin-walled rings as shell branches. The results illustrate the great complexity of shell behavior and the designer's need for reliable analysis tools capable of representing detailed structural behavior with greater accuracy than is current practice.
Leonard, R. W.↗
Propagation of flexural and membrane waves with fluid loaded NASTRAN plate and shell elements
Modeling of flexural and membrane type waves existing in various submerged (or in vacuo) plate and/or shell finite element models that are excited with steady state type harmonic loadings proportioned to e(i omega t) is discussed. Only thin walled plates and shells are treated wherein rotary inertia and shear correction factors are not included. More specifically, the issue of determining the shell or plate mesh size needed to represent the spatial distribution of the plate or shell response is of prime importance towards successfully representing the solution to the problem at hand. To this end, a procedure is presented for establishing guide lines for determining the mesh size based on a simple test model that can be used for a variety of plate and shell configurations such as, cylindrical shells with water loading, cylindrical shells in vacuo, plates with water loading, and plates in vacuo. The procedure for doing these four cases is given, with specific numerical examples present only for the cylindrical shell case.
Kalinowski, A. J.↗
Experimental Validation of Exact Burst Pressure Solutions for Thick-Walled Cylindrical Pressure Vessels
Burst pressure is one of the critical strength parameters used in the design and operation of pressure vessels because it represents the maximum pressure that a vessel can withstand before failing. Historically, the Barlow formula was used as a design base for estimating burst pressure. However, it does not consider the plastic flow response for ductile steels and is applicable only to thin-walled cylinders (i.e., the diameter to thickness ratio D/t ≥ 20). A new multiaxial plastic yield theory was developed to consider the plastic flow response, and the associated theoretical (i.e., Zhu–Leis) solution of burst pressure was obtained and has gained extensive applications in the pipeline industry because it was validated by different full-scale burst test datasets for large-diameter, thin-walled pipelines in a variety of steel grades from Grade B to X120. The Zhu–Leis flow theory of plasticity was recently extended to thick-walled pressure vessels, and the associated exact flow solution of burst pressure was obtained and is applicable to both thin and thick-walled cylindrical shells. Many full-scale burst tests are available for thin-walled line pipes in the pipeline industry, but limited pressure burst tests exist for thick-walled vessels. To validate the newly developed exact solutions of burst pressure for thick-walled cylinders, this paper conducts a series of burst pressure tests on small-diameter, thick-walled pipes. In particular, six burst tests are carried out for three thick-walled pipes in Grade B carbon steel. These pipes have a nominal diameter of 2.375 inches (60.33 mm) and three nominal wall thicknesses of 0.154, 0.218, and 0.344 inches (3.91, 5.54, and 8.74 mm), leading to D/t = 15.4, 10.9, and 6.9, respectively. With the burst test data, comparisons show that the Zhu–Leis flow solution of burst pressure matches well the burst test data for thick-walled pipes. Thus, these burst tests validate the accuracy of the Zhu–Leis flow solution of burst pressure for thick-walled cylindrical vessels.
42 ENGINEERING↗
Alignment System for Full-Shell Replicated X-Ray Mirrors
We are developing grazing-incidence x-ray optics for high-energy astrophysical applications using the electroformnickel replication process. For space-based applications these optics must be light-weight yet stable, which dictates the use of very-thin-walled full-shell mirrors. Such shells have been fabricated with resolution as good as 11 arcsec for hard x-rays, and technology enhancements under development at MSFC are aimed at producing mirrors with resolution better than 10 arcsec. The challenge, however, is to preserve this resolution during mounting and assembly. We present here a status report on a mounting and alignment system currently under development at Marshall Space Flight Center designed to meet this challenge.
Gubarev, Mikhail↗
The nonlinear bending response of thin-walled laminated composite cylinders
The geometrically nonlinear Donnell shell theory is applied to the problem of stable bending of thin-walled circular cylinders. Responses are computed for cylinders with a radius-to-thickness ratio of 50 and length-to-radius ratios of 1 and 5. Four laminated composite cylinders and an aluminum cylinder are considered. Critical moment estimates are presented for short cylinders for which compression-type buckling behavior is important, and for very long cylinders for which the cross-section flattening, i.e., Brazier effect, is important. A finite element analysis is used to estimate the critical end rotation in addition to establishing the range of validity of the prebuckling analysis. The radial displacement response shows that the character of the boundary layer is significantly influenced by the geometric nonlinearities. Application of a first ply failure analysis using the maximum stress criterion suggests that in nearly all instances material failure occurs before buckling. Failure of the composite cylinders can be attributed to fiber breakage. Striking similarities are seen between the prebuckling displacements of the bending problem and axial compression problem for short cylinders.
Fuchs, Hannes P.↗