Experimental investigation of the buckling of shallow spherical shells

In the present paper, the buckling behavior of clamped thin shallow spherical shells under external pressure is studied. Seventy-nine plastic shells formed by thermovacuum process were tested. The distributions of initial geometrical imperfections and vertical displacements were minutely measured with a differential transformer. It was possible to control the symmetrical initial geometrical imperfection of each specimen.Results indicate that the buckling phenomena of shallow spherical shells vary greatly with the symmetrical initial imperfection parameter η. In the case of the geometrical parameter λ larger than 5.5, the amplitude of the asymmetrical displacement component with the bifurcation buckling wave calculated by Huang becomes large immediately before buckling. The validity of Huang's theory for an initially perfect shell is experimentally demonstrated.     

Experimental buckling of GRP cylindrical shells

During the setup of an experiment, errors may occur. Sources of such errors may be due to several factors which sometimes accumulate and then cause erroneous results. An experimental investigation on buckling of GRP (glass-reinforced-plastic) cylindrical shells, subject to axial compression and/or external pressure loading, has been carried out. At the beginning of the experiment, the initial geometrical imperfections were measured. Because of the small size of these quantities and the great effect these imperfections had on buckling loads, any small errors in the measurement procedure may lead to unreasonable results. Attempts have been made to detect these errors, and to identify and minimize their effect on experimental results. Tables are provided to show a comparison between the final experimental results and the corresponding theoretical ones.     

Experimental investigation of the stability of monocoque domes subjected to external pressure

This paper describes the fabrication techniques, testing procedures and experimental results for eight 16-in.-diam rigid-vinyl plastic monocoque domes subjected to external-pressure loads. The domes tested were spherical, elliptical and torispherical, and all had fixed-edge support. They were fabricated in such a manner that wall-thickness tolerances and residual stresses could be minimized. In the test setup, a backup or support block was used to prevent complete collapse or yielding. The support allowed a complete buckle pattern to form, and the resulting pattern was always characteristic of a particular dome shape.These tests on domes withr/t values ranging from 240 to 600 produced remarkably consistent and high critical buckling coefficients (C) which exceeded 80 percent of the classical value (0.60). The results further indicateC to be independent ofr/t as well as the half-opening angle () of the dome shell over the range of values investigated.Paper was presented at 1965 SESA Spring Meeting held in Denver, Colo., on May 5–7.     

Experimental studies of the buckling of complete spherical shells

Complete spherical shells with radius-to-thickness ratios of from 1570 to 2120 were produced by electroforming. For specimens of good quality and for optimum testing conditions, buckling pressures up to 86 percent of the classical value were obtained.The effect of loading-system characteristics was examined by pressurizing spherical shells in rigid and soft systems and no difference in buckling pressure was observed. It was found that buckling behavior is strongly influenced by the nature and severity of flaws or imperfections; i.e., low buckling pressures can be correlated with the presence of severe flaws or nonuniformities.Paper was presented at 1967 SESA Spring Meeting held in Ottawa, Ontario, Can., on May 16–19.     

Experimental studies on buckling of ring-stiffened conical shells under axial compression

The buckling of integrally external ringstiffened conical shells under axial compression was investigated experimentally. Experimental results were compared with theory to find the effect of the stiffener parameters (e ₂ /h), (A ₂ /a ₀ h) and (I ₂₂ /a ₀ h ³ ) as well as of shell geometry. Agreement between classical linear theory and experiments was found to be governed primarily by the area parameter (A ₂ /a ₀ h), and correlation with theory was significantly affected in the range 0.1<(A ₂ /a ₀ h)<0.5 of that parameter. Beyond this region there is practically no improvement with increase in ring area, whereas the weight of the shell continues to increase linearly. An approximate formula is proposed for calculation of critical loads and found to yield results very close to the more exact critical values calculated by linear theory. A modified “Southwell plot” method was applied and both the intercept method and slope method were used. Critical loads computed from the strain records were found to be below the classical linear-theory predictions and closer to experimental ones.     

Features of the buckling of ribbed shells

The results of stability analysis of ribbed shells performed on the basis of the techniques developed by I. Ya. Amiro and his followers are reviewed. Attention is focused on the features of their buckling due to the discrete arrangement of ribs. S.P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 5, pp. 3–31, May, 2000.     

Experimental investigation of the nonlinear resonance properties of cylindrical shells

The nonlinear resonance properties of cylindrical shells filled with a fluid are experimentally studied. It is proved that travelling waves appear under resonance conditions due to the effect of the gyroscopic moment on the shell. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 2, pp. 111–114, February, 2000.     

An experimental investigation on the dynamic axial buckling of cylindrical shells using a Kolsky Bar

Several experiments were performed with a Kolsky Bar (Split Hopkinson Pressure Bar) device to investigate the dynamic axial buckling of cylindrical shells. The Kolsky Bar is a loading as well as a measuring device which can subject the shells to a fairly good square pulse. An attempt is made to understand the interaction between the stress wave and the dynamic buckling of cylindrical shells. It is suggested that the dynamic axial buckling of the shells, elastic or elasto-plastic, is mainly due to the compressive wave rather than the flexural or bending wave. The experimental results seem to support the two critical velocity theory for plastic buckling, withV _c1 corresponding to an axisymmetric buckling mode andV _c2 corresponding to a non-symmetric buckling mode. The project supported by National Natural Science Foundation of China     

Experimental investigation of edge loading of thick cylindrical shells

A method has been developed whereby the elastic behavior of thick cylindrical shells under edge loadings can be determined. The method permits the application of edge moments and edge shears through a specially designed fixture. Strain readings are recorded in both the circumferential and longitudinal directions of the shell for edge loadings. The experimental results are compared with a modified thick-shell theory with good agreement and tend to confirm the validity of the theory. The experimental procedures and the necessary precautions that must be taken to insure accurate results are discussed.     

An experimental investigation into the buckling of cylindrical shells of variable-wall thickness under radial external pressure

Cylindrical shells, with wall thickness-to-diameter ratios varying in steps from 1:2000 to 1:500 are used in large floating-roof storage tanks, where buckling under partial vacuum is a potential risk. To examine the validity of several methods of analysis, aluminum models with a nominal diameter of 150 mm were tested. Some models exhibited a sudden buckling, at the pressure predicted by one of the methods of analysis, others deformed at increased rate as the critical pressure was approached. A gradual change in, modal-buckling pattern, under decreasing pressure, was also observed.     

薄壳失稳机理浅析

对薄壳失稳问题研究的理论与实验成果进行了总结和讨论，对薄壳后屈曲理论研究结果提出了不同的看法，同时应用动力学原理对薄壳失稳问题进行了探讨，并建立了计算模型。文中应用动力学原理描述了从加载初期的一个呈现静力学特征的薄壳随荷载的增加而逐渐成为一个呈现动力学特征的薄壳的过程，从薄壳受扰振动乃至共振的角度解释了失稳临界荷载实验数据值及其离散并低于失稳临界荷载理论值的原因。     

Some features of the buckling of stringer shells

A technique for stability analysis of stringer shells is proposed. It is used to analyze the minimum critical stresses. The dependence of the dimensionless parameters σ_cr/σ_cl on the number of stringers is plotted. The linear and nonlinear theories of ribbed shells are used to examine the features of how stringer shells lose stability. It is shown that the minimum critical stresses determined using the theory of ribbed shells and a structurally orthotropic model are close within the range of stiffness parameters considered __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 59–64, February 2006.     

On local buckling of thin shells

A class of problems is considered where the buckling initially starts only in a part of the shell—locally. The stability analysis is focused on the zone of initial buckling. This leads to radical simplification. First the basic hypothesis and stability equations are formulated. Closed-form stability criteria asymptotically exact for very thin shells are discussed. This gives sufficient conditions for the local character of buckling and for the adequacy of the asymptotic approximation. The analysis taking into account the variation of stresses and shape inside the buckling zone results in a check of stability by hand calculations or by simple coding of a desk-top computer. The adequacy of the simplest representation of the stress and strain variation in the buckling zone is tested.     

Experimental studies on dynamic plastic buckling of circular cylindrical shells under axial impact

In the present paper, experimental studies on dynamic plasticbuckling of circular cylindrical shells under axial impact are carried out. Hopkinson bar and drop hammer apparatus are used for dynamic loading. Three groups of circular cylindrical shells made of copper are tested under axial impact. From the experiments, the first critical velocity corresponding to the axi-symmetric buckling mode and the second critical velocity corresponding to the non-axisymmetric buckling mode are determined. The present results come close to those of second critical velocity given by Wang Ren^[4–6]. Two different kinds of non-axisymmetric buckling modes oval-shaped and triangle shaped are founded. The buckling modes under two loading cases, viz. with small mass but high velocity and with large mass and low velocity using Hopkinson bar and drop hammer, are different. Their critical energies are also discussed. The project is supported by the National Natural Science Foundation of China (19672039) and the Foundation for Returned Scholar from Abroad of Shanxi Province