Longitudinally stiffened corrugated cylindrical shells under uniform external pressure

Experiments on cylindrical shells under pure bending and external pressure

Based on a systematic literature review, no design guidelines addressing practical issues related to steel circular hollow section (CHS) members under hydrostatic pressure have been documented thus far, except for the design recommendations proposed by the European standard EN 1993-1-6 concerning the strength and stability of shell structures. Considering that the existing codes are often outdated and subject to improvement, there is a growing demand for modern solutions that can accurately replicate the stability loss response of equipment subject to external pressure. The development of a more direct and simple method, augmented by reliable computational techniques, is advisable to avoid the numerous challenges associated with manual calculations. This approach will streamline the design process and mitigate the complexity of current practical or technical approaches. Thus, this research has formulated a method to predict design strength through the direct application of the critical elastic buckling stress, determined from Generalised Beam Theory (GBT) analyses, induced by hydrostatic pressure in custom-crafted equations, finely tuned for this specific objective. The authors present a formulation of GBT to analyze the elastic buckling behavior of CHS subject to both combined axial compression and external pressure. This work provides an extensive study of the behavior of circular cylindrical shells under external loading conditions. It first introduces the analyses of GBT and the theoretical and empirical formulas applicable to this objective. It then describes the steps involved in the development and validation of a numerical model that simulates the response of circular cylindrical shells under hydrostatic pressure, conducting an extensive parametric study using finite element analyses (FEAs). The results from available tests validate the finite element (FE) model. Upon achieving adequate agreement between the generated numerical and experimental results, new resistance reduction curves for cylindrical shell members are developed based on the results of the parametric study. Additionally, the study compares the existing provisions of EN 1993-1-6 for the design of cylindrical shells under hydrostatic pressure. Finally, a statistical approach is adopted to compare the responses of cylindrical shells calculated according to the EN 1993-1-6 code recommendations with those obtained through the newly proposed method.

On the theory of stability of cylindrical thin-walled shells under the action of external pressure

This paper proposes a new type of shell, similar to a cylindrical shell, which has significantly higher buckling strength when subjected to an arbitrary combination of uniform external pressure and axial compression. The underlying principle consists in a slight modification of the perfect cylinder in order to counteract the natural deformations which get larger and larger and lead to the collapse of the structure. Such shells are called ASTER shells. The concept has been validated through experiments, then analyzed numerically in order to explain what was observed and to propose avenues for improvements. The shells were made of electrodeposited nickel. The material was characterized. The chosen specimens were carefully measured to characterize their thickness and initial imperfections, then tested under the various types of loading. Then they were analyzed using finite elements. Thus, we were able to compare the finite element predictions with the experimental results. This comparison shows that plasticity has a decisive influence on the critical load and that linear elastic dimensioning leads to a serious overestimation of the experimental critical load. Contrary to perfect cylindrical shells, this type of shell is not significantly affected by geometric imperfections: this is another advantage of this type of design. Finally, we propose a numerical analysis in order to optimize the choice of the shape and propose shapes which resist buckling much better than a smooth cylinder when subjected to uniform external pressure, axial compression or a combination of both.

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.

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.

Considering that the use of thin-walled shells is expanding every day, it is important to examine the problem of instability in this form of structure. Many steel structures such as high-water tanks, water and oil reservoirs, marine structures, and pressure vessels, including shell elements, are under stress tension. In addition, shell elements are subject to instability owing to the loads applied. Ten thin-walled cylindrical shell specimens in two groups with different dent depths of tc and 2tc, and the different dent number subject to uniform external pressure were tested in the present research (tc is the thickness of cylindrical shell). The samples were modified to include either one or two dent line with amplitudes of h/3 in height (h the height of cylinder shell). Moreover, CFRP Strips on the dent depth was used in one of the groups. The results of testing under different theories and codes are compared.

Global optimum design of externally pressurized isogrid stiffened cylindrical shells with added T-rings

Buckling of cylindrical shells with stepwise variable wall thickness under uniform external pressure

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.

Vertical cylindrical containers are widely used for storage of granular bulk materials. The enclosing side surface of such containers is made in the form of cylindrical metal circular shells with a wall thickness that is constant or piecewise constant along the height of the shell. Known designs for storage of bulk materials of the reservoir type with the installation of a cylindrical shell on the annular foundation with hinged fixed attachment of the shell to the foundation. Thin-walled shells are made suspended from the supporting structures of the storage facilities. To stabilize the cylindrical shape of the shell and its position in space, the suspended shells are pre-tensioned in the vertical direction. During operation, storage facilities are empty and filled with bulk materials, exposed to the environment in the form of wind and temperature climatic influences. The object of study of this work is the enclosing structures of storages of granular bulk materials in the form of vertical circular cylindrical thin-walled metal shells, in the general case of piecewise constant thickness, subject to temperature and climatic influences of the environment ‒ changes in the temperature of the outside air, direct and diffuse solar radiation. The subject of the study is the components of the stress-strain state of the shell due to changes in temperature and climatic influences. The performed studies of the temperature fields of storage shells on models and full-scale objects made it possible to substantiate the assignment of the temperature field of cylindrical storage shells by Fourier series. One-sided solar heating of cylindrical storage shells completely illuminated by the sun induces in the shell wall a flat temperature field symmetrical with respect to the normal of incidence of sunlight, which can be represented by a Fourier series with five terms of the cosine expansion series. In the presence of a structure located next to the shell, which covers half of the shell along the entire height in the circumferential direction, the temperature field is described by a Fourier series containing 10 harmonics of expansion in sines and cosines. The small thickness of the shell, the significant radius of curvature of the shells, the large thermal diffusivity of metals provides a small variability of the temperature of the shell over the thickness, the ability to describe the stress-strain state of the shell, the momentless theory and a simple edge effect. Formulas are obtained in Fourier series for the forces of a momentless state, the residuals of which at the joints of shell chords of different thicknesses and in the support zones are eliminated by a simple edge effect.

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

Experiments on dented cylindrical shells under peripheral pressure

A methodology for evaluating damage in thin-walled cylindrical shells using bounded ultrasonic beam scattering

Collapse behavior of corrugated stiffened pressure shells under external hydrostatic pressure considering actual fabrication imperfections: A reverse modeling technique