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.     

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.     

An efficient design method for obround pressure vessels and their end closures

Obround cross sections find extensive industrial use in pressure vessels and pipings. Yet guidelines for their design are not available in the published literature. The obround shape is inherently unsuitable to withstand internal pressure. Support gussets must be added to such pressure vessels to render their use economical. This paper gives a method to efficiently design a pressurised obround cross section by determining the appropriate gusset plate locations, and the associated bending stresses. Formulae to design the obround flanged end closures are also given.     

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.     

Elasto-plastic analysis of a cracked ductile cylindrical pressure vessel

The deformation of a long cylindrical pressure vessel made of strain hardening material with a long longitudinal crack is analyzed under internal pressure by an FEM code. Stress distributions, the shape of the crack opening, the plastic zone, the J-integral and the CTOD are calculated.The $\text{J}\text{CTOD}$ ratio is found to be practically independent of the amount of pressure load, as well as of the crack height.Comparisons are made with a fully plastic strip yield model which seems to give a reasonable estimate of crack opening. This model suggests that the CTOD is linearly dependent on the radius of cylinder. This implies that the size of the pressure vessel is an important parameter when considering the tolerance of flaws.     

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%.     

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.     

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.     

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.     

Buckling under external pressure of cylinders with either torispherical or hemispherical end closures

In a number of applications, the actual boundary conditions at the ends of a cylinder are not taken into account properly when the structure is being designed against buckling. For example, in the design of submersibles the older theoretical treatments assume that bulkheads are present at the ends of the cylinders, whereas this form of construction is not always used.The purpose of the investigation described here is to study the effect of realistic boundary conditions on the elastic buckling pressure of unstiffened cylinders with torispherical or hemispherical end closures. In the present study only perfect, initially stress-free, structures are considered and their theoretical buckling pressures are obtained from a variational finite-difference program written for the digital computer.The numerical results presented were obtained from a limited parametric survey of the problem. In the main, linear buckling theory was used. However, as is shown, this can sometimes lead to unsafe predictions.The buckling pressures for the cylinders with hemispherical end closures, as predicted by the variational finite-difference technique, are also compared with a modified von Mises formula with corrections for the end closures. The agreement between the two sets of predictions was good within the range of the survey.     

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.     

Limit analysis of flush radial and oblique cylindrical nozzles in spherical pressure vessels. Part 2: Application of results in a design procedure

Using the method of a previously-published paper, optimised lower bounds to the limit pressure of a flush oblique cylindrical nozzle in a spherical pressure vessel have been obtained for a wide range of parameters and the results are presented in graphical form. The same technique of analysis and optimisation is applied to the case of a radial nozzle in a spherical pressure vessel. A very comprehensive parametric survey has been carried out and the results are again presented in graphical form. Methods of interpolation of both sets of results are also given.The use of the parameter is discussed as a means of simplifying the presentation of the results, and its limitations investigated. The results for the oblique nozzle are compared with previously-published experimental results.     

Finite element analysis for buckling of pressure vessels with ellipsoidal head

In this paper, a finite element analysis is performed for buckling of the pressure vessels with ellipsoidal head subjected to uniform pressure. According to the characteristic of deformation of the pressure vessel, it is divided into some identical substructures. The degrees of freedom (DOFs) of joint nodes between the neighboring substructures are classified as master and slave ones. The stress and strain distributions of the whole structure are obtained by solving the static equations for only one substructure by introducing the displacement constraints between master and slave DOFs. The complex constraint method has been used to get the buckling load and mode for the whole structure by solving the eigenvalue problem for only one substructure without introducing any additional approximation. Some numerical examples have been given to illustrate the high efficiency and validity of this method.     

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.     

The design of thickness transition regions for GRP pressure vessels

A computer program (BOSOR4), which allows stress analysis of thin shells of linear elastic material, was used to investigate the design of thickness transitions between the end closure and cylindrical body of GRP pressure vessels. Attention is focussed on the junction of a hemispherical dome and cylinder. A simple geometry and tapered transition is proposed together with a simple but safe design procedure which gives a possible material saving of 16% for hemispherical domes compared with the recommendations of the GRP pressure vessel design code BS4994, 1973.     

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.     

Simulation of JR-curves for reactor pressure vessels steels on the basis of a ductile fracture model

A procedure for the prediction of J_R-curves for reactor pressure vessels (RPVs) steels in the initial and embrittled states is presented. Prediction of the J_R-curves is performed over the ductile fracture temperature range on the basis of a ductile fracture model. A procedure for the determination of ductile fracture model parameters based on tests of smooth and notched cylindrical specimens is proposed. The stress and strain fields near the stationary and growing crack tip are analyzed by FEM. Approximate analytical solutions for stress and strain fields near a growing crack tip are proposed. Comparison of the predicted J_R-curves and experimental 2T–CT data for the initial and embrittled RPV 2Cr–Ni–Mo–V steels for WWER-1000 is performed.     

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.     

Ratcheting limit of flat end cylindrical shell connections under internal pressure

Progressive plastic deformation, or ratcheting, is a failure mechanism in ductile structures usually associated with non-proportional actions. In the case of cylindrical shell flat end connections, with or without opening, ratcheting may occur under the action of cyclically varying pressure from zero to a maximum value, i.e. for single action and, therefore, proportional loading. In this paper the ratcheting limits for this connection under this loading and for two different models are given, for an ideal-elastic ideal-plastic constitutive law, Mises' yield condition and associated flow law. The results are compared with each other and with the limits for global plastic deformation given in the literature.