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A survey of the state-of-the-art for the stability of thin-walled conical shells is presented. Known theoretical results are summarized and compared with experiment. The shortcomings of present knowledge and recommended work for the future are discussed.
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%.
Design and analysis results are reported for a panel that is a 16th arc-segment of a full 33-ft diameter cylindrical barrel section of a payload fairing structure. Six such panels could be used to construct the fairing barrel, and, as such, compression buckling testing of a 16th arc-segment panel would serve as a validation test of the buckling analyses used to design the fairing panels. In this report, linear and nonlinear buckling analyses have been performed using finite element software for 16th arc-segment panels composed of aluminum honeycomb core with graphiteepoxy composite facesheets and an alternative fiber reinforced foam (FRF) composite sandwich design. The cross sections of both concepts were sized to represent realistic Space Launch Systems (SLS) Payload Fairing panels. Based on shell-based linear buckling analyses, smaller, more manageable buckling test panel dimensions were determined such that the panel would still be expected to buckle with a circumferential (as opposed to column-like) mode with significant separation between the first and second buckling modes. More detailed nonlinear buckling analyses were then conducted for honeycomb panels of various sizes using both Abaqus and ANSYS finite element codes, and for the smaller size panel, a solid-based finite element analysis was conducted. Finally, for the smaller size FRF panel, nonlinear buckling analysis was performed wherein geometric imperfections measured from an actual manufactured FRF were included. It was found that the measured imperfection did not significantly affect the panel's predicted buckling response
An improved four-node quadrilateral assumed-stress hybrid shell element with drilling degrees of freedom is presented. The formulation is based on Hellinger-Reissner variational principle and the shape functions are formulated directly for the four-node element. The element has 12 membrane degrees of freedom and 12 bending degrees of freedom. It has nine independent stress parameters to describe the membrane stress resultant field and 13 independent stress parameters to describe the moment and transverse shear stress resultant field. The formulation encompasses linear stress, linear buckling, and linear free vibration problems. The element is validated with standard tests cases and is shown to be robust. Numerical results are presented for linear stress, buckling, and free vibration analyses.
Physical phenomena involving rapid and sudden transitions, such as snap buckling of elastic shells, explosions, and earthquakes, are characterized mathematically as a small disturbance causing a large-amplitude response. Because of this, standard asymptotic and perturbation methods are ill-suited to these problems. In the present paper, a new method of analyzing jump phenomena is proposed. The principal feature of the method is the representation of the response in terms of rational functions. For illustration, the method is applied to the snap buckling of an elastic arch and to a simple combustion problem.
To study the buckling and post-buckling behavior of shells and various other structures, one must solve a nonlinear 2-point boundary problem. Since closed-form analytic solutions for such problems are virtually nonexistent, numerical approximations are inevitable. This makes the availability of accurate and reliable software indispensable. In a series of papers Lentini and Pereyra, expanding on the work of Keller, developed PASVART: an adaptive finite difference solver for nonlinear 2-point boundary problems. While the program does produce extremely accurate solutions with great efficiency, it is hindered by a major limitation. PASVART will only locate isolated solutions of the problem. In buckling problems, the solution set is not unique. It will contain singular or bifurcation points, where different branches of the solution set may intersect. Thus, PASVART is useless precisely when the problem becomes interesting. To resolve this deficiency we propose a modification of PASVART that will enable the user to perform a more complete bifurcation analysis. PASVART would be combined with the Thurston bifurcation solution: as adaptation of Newton's method that was motivated by the work of Koiter 3 are reinterpreted in terms of an iterative computational method by Thurston.
Thin-walled stiffened or unstiffened, metallic or composite shells are widely used structural elements in aeronautical and space applications. Buckling strength, which is a major concern in all these areas, is affected by the uncertainties in the definition of loads, material properties, geometric variables, engineering models and the accuracy of the analysis tools used in the design phase. The NASA design criteria monographs from the late sixties account for these design uncertainties by the use of a lump sum safety factor or the so-called "knockdown" factor gamma, which usually results in an overly conservative design. In the present paper a new, reliability based, probabilistic design procedure for buckling critical imperfect isotropic shells is proposed. It essentially consists of a stochastic approach based on a new, improved "knockdown" factor lambda(sub a) that is not as conservative as the traditional one. It is felt that by quantifying and understanding the "problem uncertainties" such as initial imperfections and their influence on the design variables, one can develop a better engineered, better designed and safer system.
Buckling strengths of axially compressed filament wound cylinders determined by linear anisotropic shell theory
Analytical evaluation of buckling modes of shell configurations to determine imperfection sensitivity of optimum structural designs for Mars entry capsule
Axisymmetric plastic deformation of imperfection sensitive spherical shell after elastic buckling, considering load carrying capacity
The paper considers jump phenomena composed of large amplitude responses of nonlinear systems caused by small amplitude disturbances. Physical problems where large jumps in the solution amplitude are important features of the response are described, including snap buckling of elastic shells, chemical reactions leading to combustion and explosion, and long-term climatic changes of the earth's atmosphere. A new method of rational functions was then developed which consists of representing the solutions of the jump problems as rational functions of the small disturbance parameter; this method can solve jump problems explicitly.
This report is a first attempt to devise a calculation method for representing the buckling behavior of cylindrical shells of variable curvature. The problem occurs, for instance, in dimensioning wing noses, the stability of which is decisively influenced by the variability of curvature. The calculation is made possible by simplifying the stability equations (permissible for the shell of small curvature) and by assuming that the curvature 1/R as a function of the arc lengths can be represented by a very few Fourier terms. The formulas for the special case of an ellipse-like half oval with an axis ratio 1/3 ?= e ?= 1 under compression in longitudinal direction,shear, and a combination of shear and compression were evaluated. However, the results can also be applied approximately to an unsymmetrical oval-shell segment under compression, shear, and bending so that the numerical values contained in the diagrams 10 to 12 represent directly dimensioning data for the wing nose.
Results from the testing of cylinder test article SBKF-P2-CYL-TA02 (referred to herein as TA02) are presented. TA02 is an 8-foot-diameter (96-inches), 78.0-inch-long, aluminum-lithium (Al-Li), orthogrid-stiffened cylindrical shell similar to those used in current state-of-the-art launch-vehicle structures and was designed to exhibit global buckling when subjected to combined compression and bending loads. The testing was conducted at the Marshall Space Flight Center (MSFC), February 3-6, 2009, in support of the Shell Buckling Knockdown Factor Project (SBKF). The test was used to verify the performance of a newly constructed buckling test facility at MSFC and to verify the test article design and analysis approach used by the SBKF researchers.
This work presents optimum designs for unstiffened, hat stringer-stiffened and honeycomb sandwich cylinders under axial compression. Optimization results for graphite-epoxy cylinders show about a 50 percent weight savings over corresponding optimized aluminum cylinders for a wide loading range. The inclusion of minimum gage considerations results in a significant weight penalty, especially for a lightly loaded cylinder. Effects of employing a smeared stiffener buckling theory in the optimization program are investigated through comparison of results obtained from a more accurate branched shell buckling computer code. It was found that the stiffener cross-sectional deformations, which are usually ignored in smeared stiffener theory, result in about a 30 percent lower buckling load for the graphite-epoxy hat stiffened cylinder.
The structural performance of two advanced composite tow-steered shells is assessed using experiments and analyses. The fiber angles vary continuously around the shell circumference, and one shell has all 24 tows applied during fabrication, while the second shell uses the fiber placement systems tow drop/add capability to achieve a uniform wall thickness. The shells are tested in compression, and their axial stiffnesses and buckling loads are estimated using linear finite element analyses. Scaled passenger and cargo door cutouts are machined into one side of each shell. Axial stiffnesses and buckling loads of the shells with cutouts are computed using linear finite element analyses. The retested shells carry over 90 percent of the axial stiffness, and 85 percent of the buckling loads, of the shells without cutouts. These small reductions demonstrate the potential of tow steering to mitigate adverse effects of cutouts on the structural performance. The good correlation between experimental buckling loads and linear buckling analyses noted here may result from their circumferential stiffness variation, reducing geometric imperfection sensitivity. Analysis models of both shells were evaluated without and with measured geometric imperfections superposed in different longitudinal orientations. Small variations in prebuckling stiffness and buckling load of the shells are observed.
Skin-stringer Tank Analysis Spreadsheet System (STASS) computer program developed for use as preliminary design software tool that enables quick-turnaround design and analysis of structural domes and cylindrical barrel sections in propellant tanks or other cylindrical shells. Determines minimum required skin thicknesses for domes and cylindrical shells to withstand material failure due to applied pressures (ullage and/or hydrostatic) and runs buckling analyses on cylindrical shells and skin-stringers. Implemented as workbook program, using Microsoft Excel v4.0 on Macintosh II. Also implemented using Microsoft Excel v4.0 for Microsoft Windows v3.1 IBM PC.
Liapunov method used to obtain sufficient conditions for buckling stability of long cylindrical shells with random imperfections