Limit loads of circumferentially flawed pipes and cylindrical vessels under internal pressure

Published limit load formulae for circumferential defects overestimate the burst pressure for penetrating defects in pipes by the factor two in the short crack limit, because they only consider axial stress. Therefore, a class of limit load solution is discussed which takes the triaxial state of stress into account. The solutions for pressure loaded crack faces are improved analytically. Primal–dual limit analysis with the finite element method is used to adjust all solutions to numerical results. Limit loads are obtained for circumferential cracks of all sizes in thick-walled cylinders.     

Bursting pressure of mild steel cylindrical vessels

An accurate prediction of the burst pressure of cylindrical vessels is very important in the engineering design for the oil and gas industry. Some of the existing predictive equations are examined utilizing test data on different steel vessels. Faupel’s bursting pressure formula is found to be simple and reliable in predicting the burst strength of thick and thin-walled steel cylindrical vessels.     

Orthotropic cylindrical pressure vessels under line load

The work carried out earlier in this field is reviewed. Equations of equilibrium in terms of displacement components are derived for an orthotropic thin circular cylindrical shell subjected to a load that is not symmetric about the axis of the shell. Solutions that satisfy the boundary conditions are assumed in the form of exponential and trigonometric terms. Line loads along generator, as well as, circumference are considered. Eighth order differential equations in terms of parameter ‘p’ are obtained. These equations may be solved using suitable numerical methods.     

Fatigue failure criteria for thick-walled cylindrical pressure vessels

The fatigue failure of simple thick-walled cylinders under repeated internal pressure is considered with a view to establishing general criteria for failure which can be of use in design. The factors controlling the endurance limit and the limited life range are considered separately, utilising current thinking on the fatigue process. It is found that the fatigue behaviour of cylinders can be adequately predicted from conventional material fatigue data when the complexities of the elastic-plastic stress-strain state in a pressurised cylinder are taken into account. The importance of pressurising medium in assisting crack development is noted.     

Plastic collapse pressures for conical ends of cylindrical pressure vessels and their relationship to design rules in two british standard specifications

A numerical method is used to calculate lower bounds to collapse loads for cone-cylinder intersections. The method incorporates Carroll's optimisation procedure³ as developed by Robinson.⁵ Current methods of designing cone intersections, used in BS 1515,¹ BS 5500,² are discussed in relation to the results.     

Elasto-plastic analyses of cylindrical pressure vessels with reversed dished ends

Finite element stress analyses are presented which allow for elastic and elasto-plastic material behaviour for axisymmetric problems of pressure vessels using isoparametric quadrilateral elements with linear, parabolic and cubic displacements. The traditional method of analysis and design of cylindrical pressure vessels with reversed dished ends is based on the well known British Standard BS 5500 Code.¹ The stresses and displacements, especially at and near the junctions, are of great interest to designers. In view of the immense usefulness of such containers, a detailed post yield study has been made based on the stress-strain idealisation for isotropic strain hardening materials—H′= 0·0047E and Von Mises and Tresca yield criteria. The basis for the prediction of load increment sizes for the elasto-plastic analysis and the upper bound for collapse pressure are presented, as well as the excessive deformation and shakedown criteria suitable for the design of reversed dished end containers.     

Elastic analysis of cylindrical pressure vessels with various end closures

The well-known problem of the elastic analysis of cylindrical pressure vessels with hemispherical, torispherical and ellipsoidal heads, involving the partial differential equations for the classical theory of thin shells of revolution axisymmetric in character, is attempted here using a step-by-step integration procedure and a segmentation technique. The numerical results are obtained with a generalised computer program for a number of cases and for a given set of values of elastic moduli, Poisson's ratio and $\text{thickness}\text{diameter}$ ratio. The results are compared with the known results available in literature and also with the stresses predicted by the ASME Code.     

Parametric studies of cylindrical pressure vessels with different end closures

Recent developments in the finite element technique using incremental elements permit an easier and more precise determination of stresses, strains and displacements in cylindrical pressure vessels having different end closures. In this paper the geometry analysed is a cylindrical pressure vessel having hemispherical, torispherical, semiellipsoidal and toriconical heads. An axisymmetric solid finite element program employing incremental elements was used for a useful range of vessel parameters.

The formulation of the method used and the results of the parametric study obtained when internal pressure is applied to the vessel are presented. Results are reported in the form of stress intensity parameters based upon the mean circumferential stress of the cylindrical portion of the vessel away from the cylinder head junction.     

Strength behaviour of flawed pipes under internal pressure and external bending moment: Comparison between experiment and calculation

Experimentally determined failure curves for pipes weakened by surface longitudinal or circumferential defects, were compared with results calculated with the aid of engineering approximation methods. Considering the scatter bands of the mechanical properties and the geometrical dimensions, then by use of the engineering approximation methods, one can make only rough estimates of the load bearing behaviour.     

Plastic behaviour of oblique flush cylindrical nozzles in cylindrical pressure vessels: An experimental investigation

Results of seven tests on cylindrical pressure vessels with flush cylindrical nozzles are reported. Two of the test specimens had radial nozzles and the rest had nozzles oblique to a radial line but normal to the longitudinal axis of the vessel. The specimens were machined out of solid 8 in diameter aluminium alloy bar. Electrical resistance strain gauges were used to measure the distribution of strain. Deflections were measured using clock-gauges and displacement transducers.     

A comparative study on failure pressure estimations of unflawed cylindrical vessels

There is a need to design a reliable lightweight solid rocket motor case, pressure vessel for a launch vehicle or a missile system. The rocket motor case used in the advanced solid propulsion system is essentially a lightweight shell acted upon by static internal pressure and dynamic and thermal loads during flight, but for practical structural integrity purposes, consideration of internal pressure is all that is necessary. This paper examines existing test data, theories and procedures, frequently used for evaluating the maximum pressure in closed ended cylindrical vessels.     

Minimization of stress concentration factor in cylindrical pressure vessels with ellipsoidal heads

The paper presents the problem of stress concentration in a cylindrical pressure vessel with ellipsoidal heads subject to internal pressure. At the line, where the ellipsoidal head is adjacent to the circular cylindrical shell, a shear force and bending moment occur, disturbing the membrane stress state in the vessel. The degree of stress concentration depends on the ratio of thicknesses of both the adjacent parts of the shells and on the relative convexity of the ellipsoidal head, with the range for radius-to-thickness ratio between 75 and 125. The stress concentration was analytically described and, afterwards, the effect of these values on the stress concentration ratio was numerically examined. Results of the analysis are shown on charts.     

Sample scale testing method to prevent collapse of plastic liners in composite pressure vessels

Type IV pressure vessels are commonly used for hydrogen on-board, stationary or bulk storages. When pressurised, hydrogen permeates through the materials and solves into them. Emptying then leads to a difference of pressure at the interface between composite and liner, possibly leading to a permanent deformation of the plastic liner called “collapse” or “buckling”. This phenomenon has been studied through French funded project Colline, allowing to better understand its initiation and long-term effects. This paper presents the methodology followed, using permeation tests, hydrogen decompression tests on samples, and gas diffusion calculation in order to determine safe operating conditions, such as maximum flow rate or residual pressure level.     

Finite element analysis of cylindrical pressure vessels having a misalignment in a circumferential joint

Finite element analysis (FEA) has been carried out to obtain the elastic stress distribution at cylinder-to-cylinder junction in pressurized shell structures that have applications in space – vehicle design. To validate the finite element modeling and analysis results, three joint configurations, (viz., unfilleted butt joint with equal thickness, unfilleted butt joint with unequal thickness and filleted butt joint with equal thickness) having test results in open literature were considered. The peak stress values for these configurations obtained from FEA are close to that of test results. The peak stress value is found to reduce due to filleted butt joint as expected and also confirmed through test results.     

Shape optimisation of axisymmetric cylindrical nozzles in spherical pressure vessels subject to stress constraints

In this study, optimal shapes of intersecting pressure vessels are sought using a novel topology/shape optimisation method, called Metamorphic Development (MD). An industrial benchmark design problem of finding the optimal profile of variable thickness that connects a spherical shell pressure vessel to a cylindrical nozzle is considered. Two types of intersecting structures, distinguished by flush and protruding nozzles, are investigated. The optimum profiles of minimum mass intersecting structures are found by growing and degenerating simple initial structures subject to stress constraints. The optimisation seeks to eliminate the stress peaks caused by the opening. The optimised structures are developed metamorphically in specified infinite design domains using both rectangular and triangular axisymmetric finite elements that are ideally suited for modelling continua with curved boundaries. It is shown that the design with a protruding nozzle would produce a better stress distribution than the design with a flush nozzle. The results demonstrate the success of the method in generating suitable, practical solutions to the design problem.     

Elasto-plastic analysis as a basis for design of cylindrical pressure vessels with different end closures

The elasto-plastic investigations described in this paper have been carried out in order to study the performance of unfired cylindrical steel pressure vessels with hemispherical, torispherical, semi-ellipsoidal and toriconical end closures concave to pressure, using the finite element method. The various aspects covered by the study include spread of plastic zones, load-deflection characteristics, head-height growth characteristics, redistribution of effective stresses, effective plastic strain, limit analysis, excessive deformation and shakedown criteria of pressure vessel design. Based upon the results of this analysis, guidelines for the design of cylindrical pressure vessels are indicated in the form of various non-dimensional curves which will be useful for the better design of pressure vessels.     

Stress analysis in cylindrical pressure vessels with loads applied to the free end of a nozzle

This paper contains a stress analysis of a cylindrical pressure vessel loaded by axial and transverse forces on the free end of a nozzle. The nozzle is placed such that the axis of the nozzle does not cross the axis of the cylindrical shell. The method of finite elements was applied to determine the state of stress in the cylindrical shell. The values obtained for stress in the nozzle region were used to determine the following: envelopes of maximum stress values; maximum values on these envelopes; and distances between maximum values on envelopes and the outer edge of the nozzle. Algebraic functions were determined, which enable easy and simple determination of these numerous stress values. The stress values obtained from the algebraic function were within −12.5 and +12.8% of those from finite elements. The difference between stresses deduced from strain gauge readings on experimental and calculated stresses was a maximum of 12%.     

Failure correlation between cylindrical pressurized vessels and flat plates

Utilizing the theory of thin shell structures, a failure criterion is presented which one may use to predict, analytically, catastrophic failures, or unzipping, in cylindrical pressurized vessels, based on the fracture toughness profile K obtained from tests carried out on flat plates of the same material and thickness. These test results are plotted as a function of the characteristic ratio (h/c), where h represents the specimen thickness and c one-half of the crack length. Comparison with carefully controlled experimental data substantiates its validity and its potential use. The advantage of such an approach is that considerable amount of time and money can be saved.