Plastic collapse of circular conical shells under uniform external pressure

This paper describes an experimental and a theoretical investigation into the collapse of 22 circular cylindrical composite tubes under external hydrostatic pressure. The investigations were on the collapse of fibre reinforced plastic tube specimens made from a mixture of three carbon and two E-glass fibre layers. The theoretical investigations were carried out using an in-house finite element computer program called BCLAM, together with the commercial computer package, namely ANSYS. It must be emphasised here that BS 5500 does not appear to exclusively cater for the buckling of composite shells under external hydrostatic pressure, so the work presented here is novel and should be useful to industry.The experimental investigations showed that the composite specimens behaved similarly to isotropic materials previously tested, in that the short vessels collapsed through axisymmetric deformation while the longer tubes collapsed through non-symmetric bifurcation buckling. Furthermore it was discovered that the models failed at changes of the composite lay-up due to the manufacturing process of these models. These changes seemed to be the weak points of the specimens.

Buckling behavior of cylindrical steel tanks with concavity of vertical weld line imperfection

5 - Vibration of pressure vessel shells

This paper considers the stability of a toroidal shell subjected to uniform external pressure. Stability equations for a toroidal shell are solved by use of series expansions in the circumferential and meridional directions for the displacement components that develop during buckling. Axially symmetric as well as asymmetric buckling modes are considered. Design curves that give nondimensional buckling pressures for a wide range of the toroidal shell's geometric parameters are presented. In addition, the variation of the mode shapes with the geometric parameters is illustrated. In a comparison between the results of the present theory and the few available tests on toroidal shells, it is shown that test and theory agree to within 10%. For the limiting case of a sphere under external pressure, the well-known classical result (p — 1.21 Eh/a) is obtained numerically for both the asymmetric and axially symmetric buckling modes.

The author deduced approximate formulae for calculating, the collapsing pressure of conical and spherical shells under uniform external pressure from the exact formulae for Cylindrical Shells, and showed that the results of collapsing experiments relating to elastic stability of mild-steel shells of the three typical shapes above mentioned can be represented by a single curve.

Results of theoretical and experimental investigations into problems of underwater optical communication on scattered laser radiation in the Siberian Branch of the Russian Academy of Sciences (SB RAS) are discussed. Theoretical investigations of bistatic communication channels are carried out by statistical simulation of the process of signal propagation from a source to a receiver by the Monte Carlo method. Experiments were carried out under field conditions with different characteristics of radiation sources and receivers, orientations of their optical axes, and immersion depths in water. Ranges of action, probabilities of communication errors, and their SD estimated for winter and spring-and-summer seasons are presented.

In 1970, F. Y. M. Wan derived a single, complex-valued ordinary differential equation for an elastically isotropic right circular conical shell (“On the Equations of the Linear Theory of Elastic Conical Shells,” Studies Appl. Math., 49, pp. 69–83). The unknown was the nth Fourier component of a complex combination of the midsurface normal displacement and its static-geometric dual, a stress function. However, an attempt to formally replace the Fourier index n by a partial derivative in the circumferential angle θ results in a partial differential equation, which is eighth order in θ. The present paper takes as unknowns the traces of the bending strain and stress resultant tensors, respectively, and derives static-geometric dual partial differential equations of fourth order in both the axial and circumferential variables. Because of the explicit appearance of Poisson ratios of bending and stretching, these two equations cannot be combined into a single complex-valued equation. Reduced equations for beamlike (axisymmetric and lateral) deformations are also derived.

The large deflection of a spherical shell loaded with an inward radial point load and a uniform external pressure is investigated by supposing that the shell suffers small deflections from two known exact solutions to the equations for large deflection. These two exact solutions being of a segment whose curvature is completely reversed, for the region in the neighbourhood of the point of application of the point load, and of an unstressed sphere for the remainder of the shell.In the first part of the paper load-deflection curves are obtained for constant external pressures with varying inward point loads. It is found that for certain combinations of the values of pressure and point load, the shell becomes unstable. This is believed to be the first time that the stability of spherical shells under combinations of independently varying load system has been discussed.The results obtained in the first part of the paper are used in the second part to investigate the post-buckling behaviour of perfect and imperfect spherical shells under uniform external pressure acting alone. The behaviour predicted for a perfect shell agrees satisfactorily with the work of previous authors; the behaviour of shells with geometrical imperfection has received no previous satisfactory treatment. It is found that a geometrical imperfection of half the thickness can reduce the buckling pressure to about one-fifth of the classical value for perfect shells.Experiments are described on copper shells having regions thinned by acid etching. Their results are in good agreement with the theoretical predictions.

Internal inversion of thin-walled tubes using a die: experimental and theoretical investigation

Postbuckling characteristics of angle-ply laminated truncated circular conical shells

Longitudinally stiffened corrugated cylindrical shells under uniform external pressure

Vibration and elastic instability of thin-walled domes under uniform external pressure

The solution of the stability problem of a circular sandwich ring under uniform external pressure is given in a refined statement. The need to determinate the precritical stresses in load-bearing layers in the refined statement with regard to the transverse compression of the core is established, which is the basis for the detection of the mixed flexural buckling forms (BFs) with more than two half-waves along the circumferential coordinate (n>2). It is found that sandwich structures with a determining parameter of transverse compression corresponding to the limit of transition from the mixed BFs to synphasic ones are the most efficient from the weight viewpoint.

Stability Analysis of Prefabricated Underground Granary Composite Silo Walls

The main load-bearing structure of submarines is the pressure shell. Shell failures are usually caused by high hydrostatic pressure and its own potential geometric imperfections. This paper proposes a cylindrical shell with a strong corrugated stiffening structure. Two theoretically geometrically identical shells are fabricated using CNC machining to ensure the reproducibility and reasonableness of the results. Firstly, the point cloud data of all the geometric parameters of the corrugated pressure cylindrical shells were obtained using a 3D scanner. Geomagic Control X 3D inspection software was used to determine the geometric deviations of the shells. Geometric reconstruction was performed using Geomagic Design X reverse modeling software to capture potential imperfections of the shells. The aluminum shells were then welded and placed in the pressure chamber. Failure loads were obtained for all shells by constant water injection and pressurization. Considering the confined nature of the pressure chamber, a nonlinear finite element analysis of the corrugated pressure cylindrical shell was carried out using Abaqus/Riks, taking into account actual fabrication imperfections. Finally, the failure behavior of the shells under uniform external pressure was determined. The results show that both corrugated pressure cylindrical shells have high machining accuracy. The numerical simulation results of the critical buckling load of the corrugated pressure cylindrical shells were in good agreement with the test results. The corrugated structure has additional advantages in retarding the generation and expansion of shell surface defects. The equilibrium path of the corrugated pressure cylindrical shell can be maintained in a smooth and continuous state, showing stable buckling behavior. This study will provide new inspiration for the structural design and failure prediction of the submarine pressure shell.