Cylindrical Pressure Vessels Research Articles

A Study of Dimethyl Ether-Steam Coinjection Using a Large-Scale Physical Model

Summary Dimethyl ether (DME) as a water-soluble solvent has been studied as a potential additive to steam for improving the energy efficiency of steam-assisted gravity drainage (SAGD). The main objective of this research was to study in-situ flow characteristics and energy efficiency of DME-SAGD using a large-scale physical model. Results from DME-SAGD were compared with the control experiment of SAGD with no solvent injection using the same experimental setup. The main novelty of this research lies in the experimental data that demonstrated enhanced bitumen drainage by DME-SAGD in comparison with SAGD. The experiment was conducted in a cylindrical pressure vessel with a diameter of 0.425 m and a length of 1.22 m, which contained a sandpack with a porosity of 0.34 and a permeability of 5.0 darcies. The DME-SAGD experiment used a DME concentration of 10 mol% and a steam coinjection rate of 27.6 cm3/min [cold-water equivalent (CWE)] at 3000 kPa. Temperature distributions within the sandpack, along with injection and production histories, were recorded during the experiment. Subsequently, numerical simulations were performed to history match the experimental data, and the calibrated simulation model was used to analyze the details of compositional flow characteristics. Results showed that the 10 mol% DME-SAGD experiment yielded a recovery factor (RF) of 92.7% in 4.2 days, and the SAGD experiment yielded an RF of 68.6% in 6.0 days; for both experiments, the first 2 days were the preheating and the steam-only injection (SAGD) stages. The peak rate of bitumen production was 43.8 mL/min in the DME-SAGD experiment, which was more than twice greater than the peak rates observed in the SAGD experiment. The substantially increased rate of bitumen production resulted in a cumulative steam/oil ratio in DME-SAGD that was less than half of that in SAGD. Analysis of experimental results indicated that the solubility of DME in the aqueous and oleic phases caused different flow characteristics between DME-SAGD and SAGD. For example, the oleic and aqueous phases were more uniformly distributed in the sandpack in the former. Simulations indicated that DME-SAGD had a greater distribution of grid-scale inverse mobility ratio and increased oleic-phase mobilities in comparison with SAGD.

Strength and elastic buckling of a sandwich cylindrical pressure vessel with an individual functionally graded core

The paper is devoted to a sandwich cylindrical pressure vessel with hemispherical and superellipsoidal dished heads loaded with external uniformly distributed pressure. The distinguishing feature of this sandwich structure is an individual functionally graded core. The strength and buckling problems are numerically FEM studied in the linear range. The calculations are carried out for vessels with aluminium faces and aluminium foam core. As a result stress distributions along the meridian and through the thickness of the shell have been generated as well as the buckling modes and buckling loads. Based on the obtained plots it is seen that the stress distribution is more favourable for the tank with superellipsoidal head especially when the shear stress in the core is considered. Moreover, the distribution of shear stress through the thickness of the tank changes considerably depending on the part of the tank in which it is measured.

A new analytical tool for the elastic/plastic buckling design of pressure vessels subjected to external pressure

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.

Compact cryogenic hydrogen test environment for small devices and material characterization

Currently, there is a great need for testing capabilities for material samples and components in LH2. This includes low temperature compatibility at 20 K, H2 compatibility and potential degradation or permeation effects. The test environment required for this is challenging and quite costly due to LH2 supply. Therefore, an alternative test concept was developed whereby the required amount of LH2 (typically 2–3 L) is generated directly on-site by simple condensation. This is achieved with a power-controlled cryocooler (115 W @ 80 K, 18 W @ 20 K). A cylindrical pressure vessel with an inner diameter of d = 109 mm and a length of approx. 500 mm designed for 2.1 MPa is used to hold the LH2 bath and the samples. The cryocooler and the sample chamber are installed in a common vacuum cryostat and are thermally coupled at the lower end. At the 20 K level, thermal coupling is achieved by a sophisticated thermosiphon arrangement. Hydrogen is taken from a pressure reservoir, pre-cooled at the cryocooler 80 K level, and then injected and liquefied within a couple of hours.

Effect of Pad Thickness and Width Variations on Plastic Limit Moment in Cylindrical Pressure Vessels Due to Nozzle In-Plane Load

This study investigates how different pad thicknesses and diameters affect the maximum stress a cylindrical pressure vessel can handle without failing, particularly around the areas where nozzles are attached. Nozzles on these vessels often face directional stress from loads applied in a specific plane, and these stresses mustn’t push the nozzle material beyond its breaking point. The research used computer simulations to see how these vessels, with various pad sizes and a set shell and nozzle size, behave under increasing stress until they reach their breaking point. Findings indicate that making the pad thicker or wider increases the vessel’s resistance to breaking up to a certain point; beyond this optimal size, making the pad larger doesn’t provide any additional benefit. This information helps design better and safer pressure vessels by identifying the best pad size to prevent failure. The study contributes to understanding how to avoid design issues and optimize the construction of these vessels, adhering to specific industry standards.

Burst pressure prediction of carbon/natural fiber and hybrid composite pressure vessels by theoretical and numerical analysis

This study utilized finite element modeling to assess the stress and burst strength of a composite pressure vessel (CPV). The fiber type and its sequences were considered while developing the best CPV. The stress produced inside the CPV may cause damage to the vessel as well as loss of life and property. Therefore, it is critical to guarantee that the CPV's stress output does not surpass the vessel material's maximum allowable stress value. The primary goal of this research is to investigate the stresses induced in composite pressure vessels and then examine the stress using three different solutions: von Mises, Tresca, and ASSY. The theoretical burst strength is first established, and then a numerical solution is developed using ABAQUS. To confirm the correctness of FEA, the outcomes of the theoretical technique and the finite element method are compared. The six-layer carbon fiber-reinforced CPV shows twelve times higher burst strength than four layers but an equal thickness of jute fiber-based CPV. On the other hand, the hybrid combination of CPV (jute and carbon) shows a strength improvement over jute fiber based CPV by almost four times. Other jute fiber-based hybrid CPVs with glass, banana, and aluminum foil show very comparable strength relative to only jute CPV. This study's primary goal is to examine the failure phenomena and burst strength of thin, cylindrical pressure vessels.

Correlations to estimate the ground loading from small scale propane BLEVE experiments

This paper presents small-scale propane BLEVE (Boiling Liquid Expanding Vapor Explosion) experiments coupled with an investigation into ground loading dynamics. The experiments utilized cylindrical aluminum pressure vessels, with a diameter of 50 mm and a length of 300 mm. The controlled variables included burst pressure, liquid fill level, and weakened length. Both high and low-speed measurements of internal pressure and ground force were conducted during the experiments. The dependent variables analyzed were peak total ground load, force duration, and impulse. The findings from the study show trends in ground force and impulse with alterations in failure pressure, fill level and weakened length. Specifically, ground force and impulse exhibit an upward trend with increasing failure pressure, fill level and weakened length (cut length). For the first time, comprehensive correlations have been developed, incorporating the controlled variables, as well as theoretical boiling wave speed and vapor speed, to estimate the dependent variables, which represents a significant contribution in the field. However, the study does acknowledge the presence of scatter in the data, which are believed to be associated with the intricacies of the vessel opening process. It should be noted that this correlation has not been validated for larger scales. Once validated on a larger scale, these correlations can be directly applied in the design and practice of civil infrastructure to enhance the structural integrity. Additionally, the research has direct implications for industrial applications, allowing for the quantitative assessment of risks associated with bridge collapse during the transportation of PLGs.

A thermo-mechanically loaded rotating FGM cylindrical pressure vessels under parabolic changing properties: An analytical and numerical analysis

This study aims to develop an exact analytical solution for steady-state thermo-mechanical stress in a functionally graded (FG) thick-walled cylindrical vessel. The cylinder is subjected to combined rotational speed and internal pressures while the thermal load is with convective and radiative boundary conditions. The dimensionless governing equations and boundary conditions, represented as a quartic equation, are derived and solved using Ferrari's method. The temperature, displacement, and stress fields across the thick-walled cylindrical vessel are calculated by finding the roots of the quartic equation. In order to investigate the accuracy of the exact analytical solution, a numerical model is constructed based on a standard Galerkin discretization approach of the finite element method (FEM). The analytical solutions and the results obtained through FEM show a high level of agreement. Furthermore, the study analyzes the effects of material parameters on temperature, displacement, and stress fields. Displacement, temperature, and stress fields are presented in the form of dimensionless graphs along the radial direction. For the considered parametric studies, results revealed that parabolic grading is beneficial than conventional grading. This study reveals that for the thermal loading, the maximum temperature, displacement, and tangential stress decrease for the parabolic grading. A similar but lower value of temperature, displacement, and tangential stress is also observed in the case of thermomechanical loading. This study is expected to assist in the assessment of the reliability of load calculations and contribute to the overall durability of pressure vessels.The results obtained from this study can provide valuable insights into thermo-elasticity and the thermo-mechanical behavior of thick-walled cylindrical vessels and can aid in the design and optimization of such systems.

DESIGN AND STATIC THERMAL ANALYSIS OF PRESSURE VESSELS WITH VARIOUS MATERIALS USING FEM

Stress assessments are required for a great deal of plant components, including the pressure vessel. A pressure vessel is a container designed to store liquids or gases at pressures much higher than the surrounding air. The finite element analysis of pressure vessels with various types of heads that maintain the same cylindrical volume and thickness is the focus of this project. The intended pressure vessel is made for 8 bar of pressure and 24 lit of volume in accordance with ASME standard section VIII, division I. In order to identify the source of the stress concentration zone in each kind of pressure vessel head at the same volume and reasonable pressure, certain end connections are evaluated under FEA. The project's goal is to use Ansys software to analyse various designs and static and thermal data. It finds that elliptical and flat head pressure vessels have lower distributed stresses than other types of heads, making them the preferred choice for most applications. It displays the fundamental construction and uses finite element modelling to analyse pressure vessels made of various materials, such as Nimonic 80A and SA516 Gr70, and with several types of heads under high stress conditions. In this project, we use the Finite Element tool to compute the estimated stresses that occur in cylindrical pressure vessels supported by two saddles under various end connection types. In order to determine the appropriate design and material, static structural analysis and thermal analysis are performed to compute the stresses in the vessel.

Analysis of Orientation Changes of S-Net Accelerometers due to Earthquake Motions

S-net is a large-scale seafloor observation network for earthquakes and tsunamis around the Japan Trench, consisting of 150 observatories equipped with seismometers and pressure gauges. The sensors have been set up inside cylindrical pressure vessels, which have been buried in the shallow-water regions (water depth <1,500 m), while the vessels have been laid freely on the seafloor in the deeper-water regions. Previous studies showed that the cylindrical pressure vessels rotate during strong shakings due to poor coupling with the seabed sediments, thus making it difficult to retrieve the actual ground motions. We investigated the static changes in the orientations of S-net accelerometers due to shakings from 1,878 earthquakes of Mj greater than 4 that occurred around the network, and found that rotations as large values as 16° were observed during the 2022, Mj 7.4, off-Fukushima Prefecture earthquake. We estimated the threshold acceleration levels after which the sensors are likely to rotate at all S-net stations separately and found that the threshold values lie mostly between 5 and 50 cm/s2. Finally, we discussed the observed peak accelerations and velocities at the S-net stations with those recorded on land, where high-quality records were obtained, during the 2022, Mj 7.4 earthquake, which was also the largest magnitude earthquake to occur in the region after the network commenced operation. The results presented herein complement several previous studies and form the basis for more comprehensive future investigations.

Exact solutions for the symmetric elastoplastic response of functionally graded pressure vessels

With the development of functionally graded (FG) composite material technology, mechanical analyses of FG pressure vessels have attracted attention. Due to the non-uniform stress distributions inside such vessels, irreversible plastic deformation first occurs in some zones of the structure under the action of external loads. It is necessary to perform an elastoplastic analysis of FG structures to determine their load-bearing capacities. In this paper, exact solutions are obtained for the purely elastic, partially plastic, and fully plastic deformation of FG cylindrical and spherical shell pressure vessels under mechanical loads. The material properties (elastic modulus and yield strength) are assumed to vary nonlinearly in the radial direction of the vessel and the Poisson's ratio is assumed to be constant due to Poisson's ratio slight variations in the engineering materials. The novelty of the current work lies in the presentation of complete exact elastoplastic solutions for FG thick cylindrical and spherical shell pressure vessels, taking into account all deformation zones. Tresca's yield criterion is used to formulate four different deformation zones for an ideal plastic material. All of these states of deformation are studied in detail. It is shown that the elastoplastic response of the FG pressure vessels is notably affected by the radial variation of the material properties. With an increase in the FG parameter β, the first yielding position of the FG pressure vessels changes from the inner surface to the outer surface. The conclusions of this work should help with developing designs of FG pressure vessels to prevent yielding under excessive circumferential stresses.

A systematic comparison of solvents and their concentrations in bitumen gravity drainage under controlled thermodynamic conditions

Solvent-assisted SAGD (SA-SAGD) has been studied as an alternative to improve the efficiency of SAGD. This paper reports a new set of experimental data for SA-SAGD and analyzes the characteristics of bitumen-solvent mixing in the experiments using history-matched numerical models. The dimensions of the sand pack were 3 in. in diameter and 15 in. in length, and the sand pack was contained in a 25-L cylindrical pressure vessel. An annular void space surrounded the sand pack with a gap thickness of 1 in., within which a steady state flow of the injected vapor phase maintained the controlled pressure, temperature, and composition. Therefore, the gravity drainage in the sand pack occurred at a set of specified thermodynamic conditions for the surrounding annular steam chamber, unlike transient conditions near the edge of a steam chamber in larger-scale steam injection processes. In addition to SAGD as the base case, five sets of SA-SAGD were performed: 20 mol% C4, 40 mol% C4, 10 mol% C8, 20 mol% C8, and 10 mol% condensate coinjected with steam at 3500 kPa.The peak oil production rate was 9.84 cm3/min with SAGD, 14.61 cm3/min with 20 mol% C4-SAGD, 16.34 cm3/min with 40 mol% C4-SAGD, 31.33 cm3/min with 10 mol% C8-SAGD, 12.36 cm3/min with 20 mol% C8-SAGD, and 12.33 cm3/min with 10 mol% condensate-SAGD. SAGD was the least effective in bitumen gravity drainage, while the 10 mol% C8-SAGD was the most effective. Increasing the C4 molar concentration from 20 to 40 mol% slightly increased the peak rate; however, the peak rate in C8-SAGD significantly was decreased by increasing the C8 concentration from 10 to 20 mol%. This counter-intuitive result was reported in a few simulation studies with heavy solvents (e.g., C7 and C12) in the literature, but had not been experimentally confirmed before this research.Although the condensate contained 93 mol% C7-like pseudo component (C7, eq), the peak rate of 10 mol% condensate-SAGD was much smaller than that of 10 mol% C8-SAGD. These experimental observations highlight the practical importance of understanding the sensitivity of bitumen gravity drainage to heavy-solvent concentrations near the edge of a steam chamber in SA-SAGD.

Exact solutions of burst pressure for thick-walled cylinders in power-law strain hardening steels

Exact solutions of burst pressure for defect-free, thick-walled cylindrical pressure vessels with capped ends are developed using the flow theory of plasticity in terms of the Tresca, von Mises, and Zhu-Leis yield criteria. The material is assumed to obey a power-law strain hardening rule, and the finite strain theory is adopted to describe large plastic deformation. On this basis, internal pressure is obtained as a complex polynomial function of effective strains on the inside and outside surfaces of the pressure vessel with the use of the Bernoulli numbers. At burst failure, the effective strains and stresses on the inside and outside surfaces are first determined, and then three flow solutions of burst pressure are obtained as a power series function of the diameter ratio (Do/Di), strain hardening exponent (n), and ultimate tensile stress (UTS). The power series solution is confirmed to agree well with the exact flow solution of burst pressure in a closed-form for each yield criterion, and the results show that the von Mises flow solution is an upper bound prediction, the Tresca flow solution is a lower bound prediction, and the Zhu-Leis flow solution is an intermediate prediction of burst pressure. Two sets of full-scale burst test data are then utilized to evaluate and validate the proposed flow solutions of burst pressure for both thin-walled pipes and thick-walled cylindrical pressure vessels.

Analysis of a thick cylindrical FGM pressure vessel with variable parameters using thermoelasticity

Abstract In this study, a closed-form analytical solution is derived to compute the stress formulations for a thick cylindrical pressure vessel made of functionally graded material (FGM) with varying parameters, which are mechanical and thermal boundary conditions. The assumed mechanical boundary condition is the time-dependent pressure acting on the internal surface of the cylinder, while the assumed thermal boundary condition is the transient temperature distribution over the cylinder thickness. The material properties are considered to be graded exponentially in the radial direction, except Poisson’s ratio which is assumed to be constant. The stress and displacement formulations are evaluated using Mathematica software for the uncoupled thermo-mechanical analysis. The results of radial, hoop, and axial stress are plotted at various times for two FGM cylinders, the SS304-Alumina FGM cylinder and the TZM-SIC FGM cylinder, to study the impact of using different materials for the same boundary conditions on the results. The results obtained in this study are beneficial as these contribute to the design and modeling of cylinders that are exposed to time-dependent internal pressure and transient temperature profiles.

Exact solution of magneto-elastoplastic problem of functionally graded cylinder subjected to internal pressure

With the development of composite material technology, the multi-field coupling analysis of functionally graded (FG) structures has attracted extensive attention. For FG cylindrical pressure vessels, due to the non-uniform distribution of stresses filed in the structure, plastic deformation occurs irreversibly under external load, and Lorentz's force under static magnetic field is also one of the key factors affecting the elastoplastic state. Assuming that the elastic modulus of FG cylinder changes as a power function along the thickness and Poisson's ratio is constant, the hollow cylinder under the combined action of applied magnetic field and internal pressure may have four deformation states containing pure elastic deformation, partial plastic deformation yielding from the inner surface, partial plastic deformation yielding from the outer surface, and full plasticity. In this paper, analytical solutions of stress and displacement fields of the FG cylinder under these four different elastoplastic states are given, and the critical load conditions corresponding to the transition between these four different states are proposed. The correctness of the present analytical solution in this paper is verified by comparing it with the existing results of related simplified problems. In addition, the analytical solution of residual stress distribution caused by unloading internal pressure is discussed for self-reinforcing processing. Based on the analytical solution in this paper, the influence of FG parameter, applied magnetic field and internal pressure on the elastoplastic state, plastic zone size, stresses and displacements distribution of FG cylinder is analyzed in detail. This study shows that for this magneto-elastoplastic problem of FG cylinder, plastic deformation may appear from the inner surface or outer surfaces. With the increase of FG parameter, the first yielding position of FG cylinder changes from the inner surface to the outer surface. In addition, the existence of an applied magnetic field reduces the critical internal pressure required for FG cylinders to yield, making the FG hollow cylinder more prone to plastic deformation.

Thermally Assisted Rotational Autofrettage of Long Cylinders With Free Ends

Abstract Autofrettage is a widely employed process for strengthening cylindrical or spherical pressure vessels. The process involves applying a uniform load to the inner wall of a vessel to cause a controlled plastic deformation, where the vessel yields starting from the inner wall up to an intermediate radius. When the load is removed, elastic recovery takes place and compressive residual stresses are induced in the vicinity of the inner wall, which strengthen the vessel against high static and pulsating loads during service. Based on the load employed, autofrettage can be of five types—hydraulic, swage, explosive, thermal, and rotational. This work analyzes a rotational autofrettage augmented by a thermal load where the load is applied by rotating the cylinder about its axis while maintaining a temperature gradient across the wall. The combined centrifugal and thermally induced stresses cause plastic deformation in the cylinder. When the cylinder is unloaded by bringing it to rest and cooling down to room temperature, compressive hoop residual stresses are introduced in the vicinity of the inner wall. A finite element method model of the proposed thermally assisted rotational autofrettage is developed for a cylinder made of AH36 mild steel in a commercial package ABAQUS®. The results indicate that the thermal load reduces the rotational speed required for autofrettage, when compared to a conventional pure rotational autofrettage. The thermal load also mitigates the tensile axial residual stresses, which are typical in a purely rotational autofrettage. A conceptual design of the experimental setup is also presented.

Stress linearization application of oblique nozzles with welded pad reinforcement in cylindrical pressure vessels

In pressure vessel applications, one of the most feasible and economical ways of reinforcing an isolated nozzle is to use a pad or compensating plate. Where a pad is used, the extra material is considered to as effective as provided by a thick vessel plate, so a good fit in the vessel shell is required. Considering this information, in this study, welded pad reinforcement is applied to the oblique nozzle-cylinder intersections in the cylindrical pressure vessels and membrane stress and total stress (membrane + bending) cases are examined. It is well-known that the maximum stress is at the crotch corner (nozzle-cylinder junction) in the vertical junction of the radial nozzle. However, as the nozzle connection angle increases, the direction and magnitude of the stress should be investigated. For this reason, six critical paths were determined for the nozzle-cylinder junction and the stress distributions along these paths were examined with the help of Stress Linearization Analysis. In the analysis, cases such as oblique nozzle angle, pad reinforcement rates according to shell thickness, effect of increase in pad diameter are examined in detail. In conclusion, this study provides researchers with an alternative stress analysis for critical locations in the intersection area in the design and analysis of cylinder-oblique nozzle connections.

Thermo-elastic analysis of functionally graded porous thick-walled cylindrical pressure vessels with variable thickness subjected to mechanical and thermal loading by higher-order shear deformation theory

The aim of this research is to analyze the displacements, strains, and stresses is made in the thick-walled cylindrical pressure vessels with a variable thickness subjected to mechanical and thermal loading created of functionally graded porous materials with clamped-clamped boundary conditions. Linear profile is considered for variable thickness. Initially, the governing equations of thick-walled cylindrical shells are extracted using the energy method for a non-homogeneous functionally graded porous material (FGPM) with the power law function of mechanical and thermal properties under mechanical and uniform thermal loading. In this research, by utilizing the application of higher-order shear deformation theory (HSDT) and multi-layers method (MLM), a semi-analytical solution is provided to analyze symmetrical deformations and stresses. Due to the lack of analytical solution for differential equations of the variable thickness cylindrical shell, using the multi-layers method, the variable thickness cylindrical shell is divided into fixed thick disks. Finally, the solutions of each disk are analytically obtained and sum of them are employed for the whole cylindrical shell. The material used in the cylindrical vessel is a porous ceramic-metal, with alumina (Alumina, alpha Al2O3,99.5%) for ceramic and aluminum for metal that is a novel idea for thick-walled cylindrical pressure vessels with a variable thickness. Apart from the Poisson ratio, the characteristics of the materials are believed to change following a power law function in the radial direction of the cylindrical shell. The governing equations, which make up a system of differential equations with variable coefficients, have been resolved using MLM. The research explored how high-level approximations affect different parameters, such as radial and axial displacements, stresses, and strains. To demonstrate the efficiency and precision of the MLM and accurateness of the results, a result comparison is carried out between MLM method and MAM and FEM method. To study the mechanical behavior of the cylindrical pressure shell, some numerical findings were presented, examining the impact of different amounts of non-homogeneity (gradient index), porosity, and mechanical and thermal loads on it.

Strength and elastic buckling of a sandwich cylindrical pressure vessel with dished heads

The paper is devoted to a sandwich cylindrical pressure vessel closed with a dished head at both ends and loaded with external uniformly distributed pressure. Non-standard construction of the vessel is presented characterised by an asymmetric cross-section and superellipsoidal dished heads. The strength and buckling of such structure is numerically studied with the use of the finite element method limited to the linear range. The calculations are carried out for models with aluminium faces and aluminium foam core. The obtained results revealed the advantage of the superellipsoidal dished head compared to the hemispherical one in terms of stress distribution — the edge effect being a typical problem in such structures is diminished. This opens potential applications of such solution in actual structures. It is pointed out that the application of a superellipsoidal head assure a more favourable shear stress distribution in the core.

Application and accuracy of shell theory in the analysis of stress and deformations in cylindrical pressure vessels

The presented study focusses on the application of the analytical shell theory to the problems of stresses and deformations in cylindrical pressure vessels. Two standard types of dished ends are investigated, torispherical and ellipsoidal. To solve the problem the membrane theory and edge effect theory is applied. The equations of deformations are formulated to calculate the forces in the shells junction. The orthotropic material model is taken into account. Two known solutions of the homogeneous Reissner– Meissner differential equations are studied. The resolved stress and deformation are compared with the numerical results of the finite element method. The accuracy of the analytical solution is highly dependent on the thickness of the pressure vessel, as well as on the shape of the dished end. According to the results discussed, the solution for the structure with torispherical dished ends is accurate only for exceptionally small thickness, beyond the typical values for industrial pressure vessels. This shortcoming has been proven to be the result of the limitations of the membrane theory, despite the thin-walled nature of the shells studied.