Buckling of cylindrical shells with stepwise variable wall thickness under uniform 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 Considering that the existing codes are often outdated and subject to improvement, there is a growing demand for modern solutions that can accurately replicate the stability loss response of equipment subject to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.

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.

Experiments on cylindrical shells under pure bending and external pressure

Longitudinally stiffened corrugated cylindrical shells under uniform external pressure

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.

Figure 191 gives several examples of prismatic shells and panels. These are structures the cross sections of which are thin and do not vary in one of the coordinate directions, generally called the axial direction. In this chapter a method will be described in which a computer program for the analysis of shells of revolution can be used to predict buckling of prismatic shells and panels. Results will be given of convergence studies applied to cylindrical shells subjected to external lateral pressure. These studies demonstrate the validity of the technique. The method will then be applied to yield predictions of bifurcation buckling loads of noncircular cylindrical shells under axial compression or external pressure and failure of corrugated and beaded panels under axial compression. The effect of manufacturing processes on buckling and crippling of corrugated semi-sandwich panels of the type from which the rocket payload shroud shown in Fig. 5 is made will be shown.

Buckling of cracked cylindrical thin shells under combined internal pressure and axial compression

Closed-form solutions for the elastic–plastic buckling design of shell structures under external pressure

An analytical solution to the problem of the stress-strain state of a long cylindrical shell supported by two identical side elements of rectangular cross-section is proposed. As a rule, cylindrical shells have side elements in which the main tensioned reinforcement is placed, which significantly reduces the magnitude of tensile stresses, reduces vertical and horizontal displacements of the shell edges. The choice of the type of side elements depends mainly on the conditions of support of the shell edges. Proposals for accounting for the operation of side elements are presented only in regulatory documents and relevant manuals to them. The algorithm proposed by the authors involves the implementation of two approaches ― calculation according to the general semi-moment-free theory and calculation with simplifying hypotheses for shallow shells of medium length. In the first case, the problem is reduced to a system of four linear equations. From this system, it is possible to determine the forces and displacements due to the action of additional edge forces, as well as add them with individual components of the moment-free stress state, to obtain the total forces and displacements in the shell. Two separate cases are considered: gentle cylindrical shells of medium length (the method of forces and the method of displacements are used, the case when the side element is absolutely flexible in some direction is additionally considered) and multi-wave shells in which the side element is loaded by edge forces from both sides (the method of forces is used, symmetric and skew-symmetric loading are considered).

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

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

A new unified procedure for designing tubular members under combined axial load (compression or tension), bending, and hydrostatic pressure on offshore structures, fixed or compliant, is presented. The equations are applicable to members at all water depths, but are limited to members with outside diameter to wall thickness ratios less than 80. In addition to a pure hydrostatic check against hoop collapse, the procedure recommends only one check each for the axial compression and tension cases. The new design equations have been calibrated to test data from several recently completed test programs, and are thus more reliable than currently available technology. The new equations are also simpler to use. The procedure can replace several subsections in the 18th edition of API RP 2A-ASD and the draft RP 2A-LRFD (yellow copy). The recommended procedure provides unambiguous guidance for determining the member axial, bending, and hoop stresses from a frame analysis in order to check the design adequacy or determine the unity check (member utilization) of the member. The recommended procedure includes a reduced safety factor for hoop compression, but other safety factors in RP 2A-ASD are unchanged. Further examination of the reliability question may be warranted, but it is not envisioned that such an evaluation would alter the proposed procedure so as to become more conservative. A comparative design study using the new equations on a 2500-foot compliant pile tower resulted in about 5% tower steel-weight saving (2300 tons) compared to the approach proposed by Chen, Bubonic, and Sohal. Even larger weight savings can be expected for TLP tendons although a comparative design example is not yet available. The new equations are currently being reviewed as part of an ongoing API PRAC 89-56 study on analysis of the cylindrical shell database and validation of design formulations. INTRODUCTION Both API RP 2A-ASD1 and RP 2A-LRFD2 provide incomplete guidance for the design of tubular members under combined axial compression, bending, and external hydrostatic pressure loads, as shown in Fig. 1. The guidance in both documents is limited to checking local cross-sectional buckling. (Shear forces are not shown in Fig. 1. These forces have negligible impact on the strength of beam-columns.) In addition, there is an inconsistency in both documents relating to the allowable bending capacity term. However, this inconsistency generally results in a conservative design. In addition to hoop stress, external hydrostatic pressure will impose a capped-end axial compression force in a member if the ends are capped, as shown in Fig. 2. On the other hand, external radial pressure only imposes hoop compression in a tubular member and no capped-end compression. Since the hoop and capped-end axial stresses from external pressure are always in compression, they are assumed to have a positive sign.

Simple solution for buckling of orthotropic circular cylindrical shells

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.

This paper deals with the elastic/plastic buckling design of pressure vessels under external pressure loading. The objective is to build a simple analytical tool devoted to the elastic and elastoplastic buckling analysis of pressure equipments. This tool is aimed to provide the critical external pressure of cylindrical pressure vessels with ellipsoidal (or possibly hemispherical) heads. Depending on the geometry of the equipment and material parameters, the first buckling pressure may involve either the cylindrical shell or the closure ends, in the elastic or plastic range. The calculation tool will be thus based on a series of exact or approximate analytical solutions of the critical pressure of each part of the considered equipment. In this paper, the elementary shell structures involved in such pressure equipments are first individually examined. The fundamental critical pressures for each of them are recalled or introduced, both in elasticity and plasticity. The new solutions are validated against reference numerical results obtained through finite element computations. Then, approximate solutions of the critical pressure are derived for the same shells, taking account of specific boundary conditions (and not idealized ones, as before) due to the presence of the remaining part of the equipment. In the end, a VBA Excel software is developed. It is able to provide the mappings of the buckling mode type and the corresponding critical pressures for large ranges of geometric and material parameters in a very efficient way. These analytical solutions are finally confronted to numerical calculations performed on complete pressure equipments and they are shown to give quite reliable results. A discussion is also initiated on the use of such a program to update the current design rules in this scope of application.