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The theoretical critical bending stress of elliptic cylindrical shells is determined on the assumption of infinite shell length and absence of local instability phenomena. The results of the tests on isotropic elliptic cylindrical shells stressed in bending are compared with the theoretical results. The practical applicability of the theory is discussed.
Traditional composite lamination theory was used to predict composite graphite-epoxy laminate stiffnesses for comparison to quasi-experimental stiffnesses developed from cylindrical bottle pressure testing. Stiffness sensitivities were examined for variations in constituent materials and geometric properties. The material component interactions examined were the fiber longitudinal and transverse Young's modulus, the fiber shear modulus and primary Poisson's ratio, the resin Young's modulus, shear modulus, and Poisson's ratio. The geometric variation of the helical winding angle was also examined. Two computer programs were written to generate the data used to demonstrate the stiffness variations.
A mathematical model for the transmission of sound into a thin monocoque cylindrical shell is discussed. The model is used to evaluate an oblique plane wave incident upon a flexible thin cylindrical shell. The solution is applicable to the transmission of sound under actual flight conditions. The model is then used to determine curves of cylinder-transmission loss for heavily damped cylinders. Numerical results are found for several plane-wave incidence angles for a narrow-bodied jet fuselage made of aluminum. It is noted that damping (i.e., the loss factor) increases, dips because of reduced cylinder resonances, and eventually disappears when the loss factor of the shell is large enough.
Axisymmetric vibrations of partially liquid filled flexible cylindrical shell containers with rigid flat bottoms
Theoretical analysis of response of thin cylindrical shell to random vibratory loading
The NASA Shell Buckling Knockdown Factor Project (SBKF) was established in 2007 by the NASA Engineering and Safety Center (NESC) with the primary goal to develop new analysis-based buckling design factors (a.k.a. knockdown factors) and high-fidelity buckling simulations for selected launch-vehicle-like cylindrical shell structures. A series of tests are being conducted on large-scale metallic and composite cylindrical shells in order to provide validation data for these new factors and simulations. However, the validation of these new factors and simulations is quite demanding and requires test data that is commensurate with their fidelity. Traditional instrumentation, such as linear variable displacement transducers (LVDTs) and electrical-resistance strain gages serve a critical role in providing accurate displacement and strain measurements in these tests, but only allow for data to be recorded at a select number of point locations and are not sufficient to provide all the necessary validation data. Advanced measurement technologies can be used effectively to complement traditional instrumentation and gather additional data required to validate these structural simulations. In particular, three-dimensional digital image correlation (DIC) was implemented during SBKF cylinder testing to characterize the full-field displacement and strain behavior. Commercially available VIC-3DTM software and user-written data processing scripts were used to generate valuable data and insight into the complex buckling response of the cylinders that otherwise would be impossible to gather using traditional instrumentation. In addition, the measured data from DIC was used to verify measured test data obtained from other instrumentation, enhance test and analysis correlation, and help identify the root cause of anomalous test results that may have gone unexplained if only traditional instrumentation was used. Selected test results that demonstrate the use of DIC on the SBKF cylinders are presented and a portion of the data processing methods are described.
A cylindrical shell skirt structure 4.57 m (180 in.) in diameter and 3.66 m (144 in.) high was subjected to a design and analysis study using a wide variety of structural materials and concepts. The design loading of 1225.8 N/cm (700 lb/in.) axial compression and 245.2 N/cm (140 lb/in.) torsion is representative of that expected on a typical space tug skirt section. Structural concepts evaluated included honeycomb sandwich, truss, isogrid, and skin/stringer/frame. The materials considered included a wide variety of structural metals as well as glass, graphite, and boron-reinforced composites. The most unique characteristic of the candidate designs is that they involve the use of very thin-gage material. Fabrication and structural test of small panels and components representative of many of the candidate designs served to demonstrate proposed fabrication techniques and to verify design and analysis methods.
The effects of a pulse shape on the transient response of a cylindrical shell are presented. Uniaxial, membrane, and bending theories for isotropic shells were used in this study. In addition to the results of the analytical study, the preliminary results of an experimental study into the generation and measurement of shear waves in a cylindrical shell are included.
Voltage fluctuations in a multi-megawatt quasi-steady MPD accelerator, indicative of increased ablation and a consequent degradation in performance, are found to exist only over a narrow range of currents, above which the ablation continues. Within this range, the discharge is characterized by a thin cylindrical shell, 4.0 cm in diameter, concentric with the cathode surface, containing steep radial gradients in plasma luminosity, number density, current density, electric field and Hall parameter, and within which a significant fraction of the propellant is first ionized. Experiments have shown that this cylindrical shell can be totally eliminated by immersing a small object at critical locations within it, thereby increasing the local mass density by preferential ablation and suggesting further means of improving the accelerator design.
Elastic buckling loads for laminated composite circular cylindrical shells under combined axial compression and torsion are plotted on a dimensionless load plane and determined experimentally from boron/epoxy and graphite/epoxy specimens with symmetric and asymmetric layups. Good correlation is achieved between the theoretical and experimental interaction curves. The theoretical buckling loads are obtained from Fluegge's cylindrical shell equations and for pure torsion there is good correlation, but for the pure axial compression the correlation is rather poor.
The modal theory of acoustoelasticity is applied to the determination of the sound levels caused by a prescribed external sound excitation which is transmitted through a cylindrical shell. A circumferential traveling pressure wave excitation is studied as representative of a propeller sound field. It is shown how other excitations such as point mechanical loading, plane wave and reverberation random may be synthesized by superposition of circumferential waves. Representative numerical results illustrate the importance of structural and acoustic frequency matching in the determination of interior sound levels and clarify the role of the cylindrical shell ring frequency. An exploratory study of a double wall geometry is conducted.
Optimization research at NASA Glenn Research Center has addressed the design of structures, aircraft and airbreathing propulsion engines. The accumulated multidisciplinary design activity is collected under a testbed entitled COMETBOARDS. Several issues were encountered during the solution of the problems. Four issues and the strategies adapted for their resolution are discussed. This is followed by a discussion on analytical methods that is limited to structural design application. An optimization process can lead to an inefficient local solution. This deficiency was encountered during design of an engine component. The limitation was overcome through an augmentation of animation into optimization. Optimum solutions obtained were infeasible for aircraft and airbreathing propulsion engine problems. Alleviation of this deficiency required a cascading of multiple algorithms. Profile optimization of a beam produced an irregular shape. Engineering intuition restored the regular shape for the beam. The solution obtained for a cylindrical shell by a subproblem strategy converged to a design that can be difficult to manufacture. Resolution of this issue remains a challenge. The issues and resolutions are illustrated through a set of problems: Design of an engine component, Synthesis of a subsonic aircraft, Operation optimization of a supersonic engine, Design of a wave-rotor-topping device, Profile optimization of a cantilever beam, and Design of a cylindrical shell. This chapter provides a cursory account of the issues. Cited references provide detailed discussion on the topics. Design of a structure can also be generated by traditional method and the stochastic design concept. Merits and limitations of the three methods (traditional method, optimization method and stochastic concept) are illustrated. In the traditional method, the constraints are manipulated to obtain the design and weight is back calculated. In design optimization, the weight of a structure becomes the merit function with constraints imposed on failure modes and an optimization algorithm is used to generate the solution. Stochastic design concept accounts for uncertainties in loads, material properties, and other parameters and solution is obtained by solving a design optimization problem for a specified reliability. Acceptable solutions can be produced by all the three methods. The variation in the weight calculated by the methods was found to be modest. Some variation was noticed in designs calculated by the methods. The variation may be attributed to structural indeterminacy. It is prudent to develop design by all three methods prior to its fabrication. The traditional design method can be improved when the simplified sensitivities of the behavior constraint is used. Such sensitivity can reduce design calculations and may have a potential to unify the traditional and optimization methods. Weight versus reliability traced out an inverted-S-shaped graph. The center of the graph corresponded to mean valued design. A heavy design with weight approaching infinity could be produced for a near-zero rate of failure. Weight can be reduced to a small value for a most failure-prone design. Probabilistic modeling of load and material properties remained a challenge.
The objective of the study was to develop a more accurate model for the prediction of the compressive behavior of filament-wound composite cylindrical shells. Results from a closed-form analytical model and a three-dimensional finite element model show that the extensional and bending stiffness of the laminate is significantly reduced in tow cross-over regions and that bending-extension coupling is increased in comparison with classical lamination theory. The material properties predicted by a micromechanics analysis are included in a global finite element model of a filament-wound circular cylindrical shell which also incorporates variations in the laminate stacking thickness. Results from the global shell analysis are compared with experimental data.
The linear elastic response is determined for an internally pressurized, long circular cylindrical shell stiffened on the inside by a regular arrangement of identical stringers and identical rings. Periodicity of this configuration permits the analysis of a portion of the shell wall centered over a generic stringer-ring joint; i.e., a unit cell model. The stiffeners are modeled as discrete beams, and the stringer is assumed to have a symmetrical cross section and the ring an asymmetrical section. Asymmetery causes out-of-plane bending and torsion of the ring. Displacements are assumed as truncated double Fourier series plus simple terms in the axial coordinate to account for the closed and pressure vessel effect (a non-periodic effect). The interacting line loads between the stiffeners and the inside shell wall are Lagrange multipliers in the formulation, and they are also assumed as truncated Fourier series. Displacement continuity constraints between the stiffeners and shell along the contact lines are satisfied point-wise. Equilibrium is imposed by the principle of virtual work. A composite material crown panel from the fuselage of a large transport aircraft is the numerical example. The distributions of the interacting line loads, and the out-of-plane bending moment and torque in the ring, are strongly dependent on modeling the deformations due to transverse shear and cross-sectional warping of the ring in torsion. This paper contains the results from the semiannual report on research on 'Pressure Pillowing of an Orthogonally Stiffened Cylindrical Shell'. The results of the new work are illustrated in the included appendix.
Progressive wove and reverberant acoustic fields ore often used in the laboratory for qualification testing of aerospace structures that are subjected to unsteady aerodynamic environments which occur during flight through the atmosphere. Acoustic simulation of these in-flight environments i s achieved i f the structural vibration response to acoustic excitation is equivalent, over the frequency range of interest, to the response caused by aerodynamic turbulence. To determine the degree of response simulation that could be expected for such qualification testing of the Apollo Spacecraft, responses of a segment of the Apollo structure were estimated theoretically for both acoustic and flight environments. The vibration analysis presented in this report was performed for the Spacecraft Lunar Module Adaptor; and the three environments treated are turbulence at Mach 1 and Mach 2, a reverberant acoustic field, and a modified acoustic progressive wave field. The progressive wave field is assumed to be generated within a specially designed shroud of sixteen axially oriented ducts which is constructed around and contoured to the external skin of the vehicle. Each duct is open on the side adjacent to the skin and is driven acoustically at one end by an independent noise source, thus allowing for different pressure correlation patterns around the circumference of the vehicle. The purpose of the analysis was to determine the effects of surface pressure correlation lengths on the response characteristics of representative Apollo structure, and to select on this basis, the optimum acoustic environment for structural vibration qualification tests of the Apollo in the Spacecraft Acoustic Laboratory at MSC. The method of analysis employed consists of determining, independently, the space average, mean-square acceleration spectral density for each of the significant modes of vibration of an equivalent cylindrical shell, and then expressing the total structural response as a linear summation of these modal responses. Approximately 570 classical modes of a pinned-end cylinder were used in order to find the spectral response characteristics of the structure throughout the frequency range of 10 - 1,000 Hz. The effective forcing functions or joint acceptances of the various modes of vibration were computed and are presented graphically for each of the pressure excitation environments. A brief development of the response equations used is presented in the report. Space average acceleration response spectra were computed for twelve different cases including aerodynamic turbulence at Mach 1 and Mach 2, reverberant acoustic field, five duct correlation patterns, two cases of an axially damped progressive wave field, and two cases in which the structural damping constant was varied from the expected value. The response spectra were computed and plotted by a high speed digital computer far a flat excitation pressure spectrum; and the response spectra were numerically integrated to give one-third octave bond average responses. A complete set of digital computer programs has been developed for both flat plate and cylindrical shell structures for the above environments, and each requires run times of three minutes or less. Thus, the work presented herein, along with the results, constitutes a practical advancement to the existing state-of-the-art of vibration prediction.
Standard plate or shell theories were used as a starting point to study the fracture problems in thin-walled cylindrical and spherical shells, assuming that the plane of the crack is perpendicular to the surface of the sheet. Since recent studies have shown that local shell curvatures may have a rather considerable effect on the stress intensity factor, the crack problem was considered in conjunction with a shell rather than a plate theory. The material was assumed to be isotropic and homogeneous, so that approximate solutions may be obtained by approximating the local shell crack geometry with an ideal shell which has a solution, namely a spherical shell with a meridional crack, a cylindrical shell with a circumferential crack, or a cylindrical shell with an axial crack. A method of solution for the specially orthotropic shells containing a crack was described; symmetric and skew-symmetric problems are considered in cylindrical shells with an axial crack.
Donnell type stability equations for thin circular orthotropic conical shells are presented and solved for external pressure, axial compression and combined loading. The solution is likewise applied to stiffened conical shells. Correlation with equivalent cylindrical shells yields a simple approximate stability analysis for orthotropic or ring-stiffened conical shells under hydrostatic pressure. The general instability of stiffened conical shells under hydrostatic pressure is also analysed by a more accurate approach. Preliminary experimental results for buckling of ring-stiffened conical shells under hydrostatic pressure are presented and discussed.
Structural design of stiffened cylindrical shells, discussing minimum weight, prevention of buckling modes, etc