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.     

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.     

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.     

Equivalent torispherical pressure vessel heads

Lower bounds to limit pressures for ellipsoidal and torispherical heads of cylindrical shells have been calculated using a numerical optimisation technique. These have been used to explore the ideas of equivalence between torispherical and ellipsoidal heads. The geometrical proportions of torispherical heads which have optimum limit pressures have been found and these are compared with the results of three geometrical criteria of ‘equivalence’.     

BUCKLING OF TRUNCATED CONICAL SHELLS UNDER COMBINED PRESSURE AND HEATING

This paper presents a theoretical analysis of the elastic instability of truncated conical shells under combined uniform pressure and thermal loading. The problem is solved by applying a finite difference method to the Donnell-type shell equations with the effect of large prebuckling deflections taken into consideration. It is found that the interaction curve of the buckling loads changes drastically with the loading order for the shallow cones clamped to rigid end plates and constrained in the axial direction. This phenomenon is caused by a remarkable difference in the prebuckling deformation and the buckling pattern of each case with single load.     

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.     

The effect of proof testing on the behaviour of two stainless steel pressure vessel drumheads

Two torispherical drumheads which had previously been used for shakedown testing, have been used to determine the effect of proof testing. One drumhead was pressure cycled at its design pressure prior to undergoing a proof test and subsequent pressure cycling. The second drumhead was subjected to a proof test and subsequently pressure cycled at its design pressure. For the first drumhead, significant incremental strain was evident prior to the proof test but not after the proof test. For the second drumhead, no incremental strain was evident after the proof test.     

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.     

The strength and deformations of torispherical ends for glass-reinforced plastic pressure vessels—Part 2: Effect of torisphere geometry for ends of fixed head height

Four further glass-reinforced plastic cylindrical pressure vessels with torispherical dished ends have been tested to destruction. Together with two vessels already reported on in Part 1 of this paper, these specimens form part of a group with the same head height of 0·25 m but with three different torus radii of 0·1 m, 0·146 m and 0·188 m, giving crown radii of 0·71 m, 0·8 m and 1·0 m, respectively (two vessels of each geometry were tested). As in Part 1, results from the tests were compared with those suggested by the current UK design code (BS 4994) and the predictions of a computer-based elastic stress analysis (BOSOR 4). In contrast to BS 4994, BOSOR 4 indicates that there is little difference in strength between dished ends with the two larger knuckle radii. A torus radius of 0·1 m, however, does produce a significant increase of maximum stress and strain. In fact, of the four additional vessels tested, only those two of this latter geometry ultimately failed in the dished end, those of knuckle radius 0·146 m rupturing in the cylinder.     

The strength and deformations of torispherical ends for glass-reinforced plastic pressure vessels—Part I: Effect of torus radius/cylinder diameter ratio on ends with sphere radius equal to cylinder diameter

Six glass-reinforced plastic cylindrical pressure vessels with torispherical end closures have been tested to destruction. Each vessel was of 0·01 nominal thickness/diameter ratio and had an end geometry with the spherical radius equal to the cylinder diameter of 1 m. Three different torus radii of 0·29, 0·19 and 0·1 m were used to give head heights of 0·32, 0·25 and 0·19 m, respectively (two vessels of each geometry were tested). Results from the tests were compared with those suggested by the current UK design code (BS 4994) and the predictions of a computer-based elastic stress analysis (BOSOR 4). These all confirm that maximum stresses and strains increase with decreasing knuckle radius. It was also found that, because of the high elastic strains of GRP, the change of geometry under pressure makes a significant contribution to the ultimate strength of these ends. The result of this, together with the effect of some local wall thickening, was to strengthen the ends to the extent that failure took place in the torisphere for only three of the six vessels tested.     

利用部件整体耦合法分析柴油机气缸盖热机械强度

为提高气缸盖的热机械性能,采用部件整体耦合法对多缸柴油机气缸盖进行了三维非线性有限元分析。在考虑各部件接触关系的基础上,计算了气缸盖在螺栓预紧力、热载荷、最高燃烧压力多场耦合作用下的应力分布,确定了各影响因素在缸盖上造成应力集中的主要位置及原因,并与发动机实际运行后情况进行了对比,为结构改进提供了理论指导。     

Multiobjective optimal power plant operation through coordinatecontrol with pressure set point scheduling

Coordinated control schemes, at fossil fuel power plants, drive units as a whole through a variable pressure operating policy. Ordinarily, the pressure control loop set-point is obtained from the unit load demand through a fixed nonlinear mapping that does not allow for process optimization under operating conditions different from the originals. This paper presents a procedure to optimally design the power-pressure mapping by defining and solving a multiobjective optimization problem. Both procedure and mapping are realized as a supervisory set-point scheduler. The optimization problem is solved with the nonlinear goal programming method, which provides a single solution from the set of all multiobjective optimal solutions based on the assignment of relative preference values to the objective functions. This approach provides a way to specify the operating policy to accommodate a great diversity of operating scenarios. The procedure is presented through a case study, and its feasibility is demonstrated via simulation experiments     

A pressure-ratio equivalent method for ultra-high pressure hydrogen spontaneous ignition experiment

Increasing hydrogen storage pressure brings high economic benefits and high risks. Pressurized hydrogen leakage spontaneous ignition experiment is an important means to reveal the mechanism of hydrogen leakage spontaneous ignition and improve the safety of hydrogen storage equipment. However, due to the extremely high cost and danger of ultra-high pressure, there is a serious lack of experimental data. In this paper, a pressure-ratio equivalent (PRE) method of experiments is proposed based on the theory of the shock tube problem. By keeping the hydrogen-air pressure ratio constant while reducing the absolute pressure of air and hydrogen, the difficulty of the experiment is greatly reduced. The effectiveness of the PRE method is evaluated theoretically and experimentally. The results show the PRE method retains the ignition characteristics of hydrogen leakage spontaneous ignition largely when the air pressure is within 0.05–0.1 MPa. It is found the pressure ratio of hydrogen to air dominates the leakage spontaneous ignition process. In the experiments of different air pressures, the shock Mach numbers are close to theoretical values. In addition, leakage spontaneous ignition of hydrogen mixed with 30% (vol.) CO is found in experiments using the PRE method, with pressure ratios of up to 250. This indicates that when the storage pressure is high enough, there is also a risk of spontaneous ignition of syngas from high-pressure leakage. The PRE method can widely broaden the pressure scope of experimental research on leakage spontaneous ignition, and it provides a new idea for obtaining the experimental data of gas high-pressure leakage spontaneous ignition.     

Study of the nonlinear responses of a submersible pressure hull

A submarine pressure hull normally experiences hydrostatic pressure at different operating depths and, during wartime, it bears shock loading produced by underwater explosions. In this study we examine the transient dynamic responses of a typical submarine hull subjected to hydrostatic pressure and shock loading, in which geometrically large deformation effects involving elastoplastic material behavior are considered. The finite element procedure based on Hibbitt and Karlsson's methodology is used to analyze the nonlinear response of the entire pressure hull. From the numerical results of a nonlinear static analysis under operating depth hydrostatic pressure, we attempt to provide the maximum operating depth at which the behavior varies from elastic to plastic. In transient dynamic analysis under shock environment, this study not only presents the elastoplastic response of the structure but also the critical region of the model. Finally, the implications of these results for future submarine design and maintenance are discussed.     

Couette flow with frictional heating in a fluid with temperature and pressure dependent viscosity

This study investigates the effects of variable viscosity and frictional heating on the laminar flow in a horizontal channel having a wall at rest and a moving wall subjected to a prescribed shear stress. The wall at rest is thermally insulated, while the moving wall is kept at a uniform temperature. This investigation concerns fluids whose viscosity depends exponentially on the pressure and temperature. An appropriate approximation is introduced to analyze the interplay between the dependence of viscosity on the pressure and temperature and the viscous dissipation. It is shown that the nonlinear term in the equation for the balance of energy representing the frictional heating may lead to the existence of dual solutions of the boundary value problem for fixed values of the material parameters that characterize the fluid. The results obtained are compared with those predicted by the generalization of the Oberbeck-Boussinesq approximation for a fluid with pressure and temperature dependent viscosity. It is found that the results for the approximation carried out in this paper and those that stem from the Oberbeck-Boussinesq approximation are markedly different.     

THERMOELASTIC STABILITY OF ORTHOTROPIC CIRCULAR PLATES

In this article the thermoelastic buckling of a circular orthotropic composite plate is discussed. The plate is assumed to be geometrically perfect. The equilibrium and stability equations, derived via variational formulations, are used to determine the prebuckling forces and the buckling temperatures. The equations are based on the Love-Kirchhoff hypothesis and Sanders' nonlinear strain-displacement relation. Critical buckling temperatures associated with the uniform temperature rise, gradient through-the-thickness temperature, and linear temperature variation along the radius are obtained. The results are validated for the first type of loading with the known data in literature.     

Two types of optimization of a cylindrical shell subjected to lateral pressure

Two types of optimization of thin-walled cylindrical shells loaded by lateral pressure are analyzed in this paper, with arbitrary axisymmetric boundary conditions and the volume being constant. The first is to find the optimal thickness to minimize the maximum deflection of a cylindrical shell. Here expressions of the objective function are obtained by the stepped reduction method. The optimal designs are reduced to nonlinear programming problems with an equality constraint. In minimizing the maximum deflection, the position of the maximum deflection from a previous iteration is used as the next one. The second is to find the optimal thickness to maximize the buckling pressure of shell. A buckling criterion of a shell is derived on the basis of an energy principle. An optimization criterion is formulated as the maximum of the buckling pressure. Moreover, the space of allowable solutions is defined. This procedure converges quickly and numerical results show the effectiveness of the method. Several examples are provided to illustrate the methods.     

水电系统及水库库群优化调度的非线性网络法

利用水电系统各机组出力的非线性目标函数，结合各水库流量和库存量具有网络流特点的约束，采用非线性网络规划对各水电站出水或水库水量进行优化调度，本计算方法可充分 各种因素，具有速度快、收敛精度高，占有内存少的特点。     

Data driven NARMAX modeling for PEMFC air compressor

Air compressor of proton exchange membrane fuel cell (PEMFC) system is usually nonlinear and strong coupled. It is difficult to establish a online optimization oriented model. In order to solve this problem, this paper proposed a nonlinear autoregressive moving average with exogenous inputs (NARMAX) model for air compressor of PEMFC system. The NARMAX model is an equivalent time-varying linear model, and the time-varying parameters are identified by recurrent neural network (RNN). Simulation results show that the proposed method has small fitting error, the error of air flow and pressure ratio approximate zero, while the mean square error (MSE) of air flow and pressure ratio are 1.5171e-07 and 6.3767e-05, respectively. Therefore, the established air compressor model is accurate and effective.     

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.