Plastic Buckling Of Cylindrical Shells Research Articles

An Analytical Symplecticity Method for Axial Compression Plastic Buckling of Cylindrical Shells

This study is mainly concerned with the analytical solutions of plastic bifurcation buckling of cylindrical shells under compressive load. The analysis is based on the J2 deformation theory with a linear hardening and proportional loading is adopted in the calculation. A symplectic solution system is established and Hamilton's governing equations are derived from the Hamilton variational principle. The basic problem in plastic buckling is converted into solving for the symplectic eigenvalues and eigensolutions, respectively. The obtained results reveal that boundary conditions have a very limited influence on bucking loads but its influence on buckling modes and plastic borders cannot be neglected. Meanwhile, it is demonstrated that the shell material properties significantly affect the plastic buckling behavior. This proposed symplectic method is shown to be a rigorous approach. It also provides a uniform and systematic way to any other similar problems.

Twin-characteristic-parameter solution of axisymmetric dynamic plastic buckling for cylindrical shells under axial compression waves

In the present investigation on the dynamic plastic buckling of cylindrical shells under axial compression waves, the critical axial stress and the exponential parameter of inertia terms in stability equations are treated as a couple of characteristic parameters. The criterion of transformation and conservation of energy in the process of buckling initiation is used to derive the supplementary restraint equation of buckling deformation at the fronts of axial elastic and plastic compression waves. The supplementary restraint equation, stability equations, boundary conditions and continuity conditions constitute the necessary and sufficient conditions of determining the two characteristic parameters. Two characteristic equations are derived for the two characteristic parameters. The critical axial stress or the critical buckling time, the exponential parameter of inertia terms and the initial modes of buckling deformation are calculated quantitatively from the solution of the characteristic equations.

Influence of stress waves on the dynamic progressive and dynamic plastic buckling of cylindrical shells

A new concept is presented for the dynamic elastic–plastic axisymmetric buckling of circular cylindrical shells under axial impact. The phenomena of dynamic plastic buckling (when the entire length of the shell wrinkles before the development of large radial displacements) and dynamic progressive buckling (when the shell folds form sequentially) are analysed from the viewpoint of stress wave propagation resulting from an axial impact. The conditions for the development of dynamic plastic buckling are obtained. A numerical analysis of the buckling phenomena reveals that the material properties together with the geometrical characteristics of the shell determine the particular type of response for high velocity impacts. It is concluded that shells made of strain rate insensitive materials can respond either by dynamic plastic buckling or dynamic progressive buckling, depending on the inertia properties of the shell, while those shells made of strain rate sensitive materials respond always by dynamic progressive buckling. It is shown that the prediction for the peak load, which can develop in a shell for a high velocity impact, depends on the particular yield criterion used in the analysis.

On plastic buckling of cylindrical shells struck axially with a mass

Buckling of elastic-plastic cylindrical shells axially struck with a mass is discussed. The effect of stress wave fronts travelling along the shell is taken into account. This allows us to cast some more light on the mechanism of progressive buckling. Only axisymmetric buckling modes are considered. The analysis is based on the Kirchhoff-Love hypotheses. As a constitutive law, the rate independent elasto-plastic relations with linear strain hardening and von Mises yield condition are adopted. A method for calculating bifurcation times and buckling modes is presented. Numerical examples are given.

Dynamic Pulse Buckling of Cylindrical Shells Subjected to External Impulsive Loading

The dynamic plastic buckling of cylindrical shells (rings) subjected to general initial impulsive velocity and subjected to impulsive loading is studied based on the energy criterion. A simple analysis method is given and the formulas of critical mode numbers ncr and critical impulsive velocity νcr are obtained.

Plastic buckling of cylindrical shells under biaxial loading

The predictions for plastic buckling of shells are significantly affected by the plasticity model employed, in particular in the case of nonproportional loading. A series of experiments on plastic buckling of cylindrical aluminum alloy shells under biaxial loading (external pressure and axial tension), with well-defined loading and boundary conditions, was therefore carried out to provide experimental data for evaluation of the suitability of different, plasticity models. In the experiments, initial imperfections and their growth under load were measured and special attention was paid to buckling detection and load path control. The Southwell plot was applied with success to smooth the results. The results show that axial tension decreases resistance to buckling under external pressure in the plastic region due to ‘softening’ of the material behavior. Comparison with numerical calculations usingJ 2 deformation and incremental theories indicate that both theories do not predict correctly plastic buckling under nonproportional loading.

An experimental study on the dynamic axial plastic buckling of cylindrical shells

This paper deals with an experimental study on the dynamic plastic post-buckling behaviour of a stationary AMΓ aluminium alloy cylindrical shell under axial impact. According to current theory, it is believed that within a certain velocity range, the shell will buckle in a uniform axisymmetrical sinusoidal mode. However, we found that when the impact velocity is less than a certain critical value V c1, the shell will exhibit only uniform plastic deformation in both the axial and radial directions and does not produce the sinusoidal waves. On the other hand, when the impact velocity exceeds another critical value V c2, the shell will change from the axisymmetric mode into a nonuniform type of large deformation, the number of waves decreases slightly and the shell begins to lose its load-carrying capacity. Experimental results on cylinders with three different thicknesses are presented and discussed. An approximate theoretical formula for estimating V c2 based on strain rate reversal is also given.

Plastic Buckling of Cylindrical Shells Under Axial Compression

Analytical and experimental results are presented for the axisymmetric plastic buckling of axially compressed cylinders made from strain hardening materials. Buckling loads predicted by two simple bifurcation buckling formulas (simplified analysis) and by the STAGS finite difference computer program (detailed analysis) are compared with buckling loads measured in room temperature tests on Type 304 stainless steel cylinders. The comparison shows that the loads predicted by Gerard’s bifurcation buckling formula agree well with the test results and the STAGS solution. Thus, the present results provide further confirmation that Gerard’s simple formula furnishes a reasonably good approximation to the load carrying capacity of strain hardening cylinders that buckle axisymmetrically at nominal axial stresses equal to or greater than the yield stress.

Plastic buckling of cylindrical shells in the case of complex loading paths

Plastic buckling of cylindrical shells in the case of complex loading paths

Plastic buckling of cylindrical shells subjected to external fluid pressure

The problem considered here is that of a thin-walled circular cylindrical shell whose external surface is submitted to uniform fluid pressure. The condition under which bifurcation will occur in the shell beyond the elastic limit is examined and the true tangent modulus formula for the plastic buckling is established. Numerical results are presented for the critical pressure, covering both elastic and plastic ranges of buckling.

Plastic Flow Buckling of Cylindrical Shells Due to Impulsive Loading

A theory is postulated to explain the plastic buckling of cylindrical shells caused by uniform radially inward impulses. Experimental results are presented which show that the number of buckles increases with the shell length. A simple formula is derived which predicts preferred mode numbers in agreement with the experimental results for shells with lengths up to about 1 1/2 dia. For longer shells, mode numbers may be obtained by numerical integration of the equation of motion. The increase in mode number with shell length is attributed to the relative effects of the “directional” and hardening contributions to the reactive bending moment, the former stemming from yielding in a biaxial plastic state of stress. In short shells (length < dia), it is shown that the directional moment dominates, whereas in long shells (length > 3 dia) the hardening moment dominates. The mode prediction formula just mentioned applies whenever the directional moment dominates and the difficulty in treating cases where the hardening moment is significant is indicated. Again, for the former case, a simple threshold impulse formula is derived conforming to the experiments.

Dynamic Plastic Buckling of Cylindrical Shells in Sustained Axial Compressive Flow

A theory is postulated to explain the dynamic plastic buckling of cylindrical shells in sustained axial compressive flow. Tube impact experiments are described in which uniform axisymmetric waves were produced. Predicted and experimental wavelengths are in satisfactory agreement. According to the theory presented, wavelengths do not depend strongly on strain-hardening modulus and, based on results for two aluminum alloys, neither do experimental wavelengths. This result is shown to apply also to slow plastic buckling.

Nonsymmetric buckle patterns in progressive plastic buckling

This paper presents the results of a series of experiments on the progressive plastic buckling of cylindrical shells under axial compressive load. It shows that, for shell bodies with anR/t less than 100, the normal axisymmetric ring buckling will develop into nonsymmetric patterns. We demonstrate that there exists also a class of shells within this thickness-radius range for which nonsymmetric plastic buckling always occurs without the prior formation of a ring. It appears from the limited number of tests made that, for a particularR, R/t, material and rate of loading, there is a critical value ofL, above which there is a high probability of the buckle pattern developing in a nonsymmetric fashion. It seems probable, too, that there are bands ofR/t for a particularL/R, R, material and rate of loading for which the buckle number will be constant. The experiments tend to indicate that the postbuckling efficiency of the shell decreases with increasing buckle number. The nonsymmetric patterns demonstrated appear to be inextensional deformations. They are very similar in character to the Yoshimura pattern which occurs as the limiting case for thin shells in axial compression and, under impact loading. Load-displacement histories are presented for some of the various modes of failure demonstrated.

Plastic buckling of axially compressed cylindrical shells

The plastic buckling of cylindrical shells under axial compression is studied analytically and experimentally. Attention is given to both the nonlinear and nonconservative aspects of the stress-strain relation. The effect of unloading is investigated in an exact manner for a hinge model which is proposed and in both an exact and an approximate manner for a geometrically perfect shell. Thirty tests are reported on cylindrical shells of 2024-T4 aluminum with radius to thickness ratios of 120 through 10 and length to radius ratios of 0.20 to 7. Specimens were prepared with three different types of end conditions and were tested either through a ball and socket arrangement or flat ended between smooth bearing blocks. A simple (jy incremental theory gives results very close to J% deformation theory and does predict both buckling strength and the geometry of buckling for thick and moderately thick shells.

Plastic Buckling of Cylindrical Shells

PLASTIC buckling of plates and shells has been worked out by Bijlaard, Ilyushin, Stowell, Handelman and Prager, Gerard and others. Some investigators have assumed deformation type stress‐strain laws while others have used incremental type (flow type) stress‐strain laws. The present work is an extension of the work started by Gerard along the lines initiated by Stowell.