Thesis
Local loading and saddle supports on cylindrical vessels : (some analytical and finite element studies of local load and saddle support problems with a special emphasis towards generating improved design methods)
- Creator
- Rights statement
- Awarding institution
- University of Strathclyde
- Date of award
- 1999
- Thesis identifier
- T9667
- Qualification Level
- Qualification Name
- Department, School or Faculty
- Abstract
- The study of local loading problems including the support of horizontal vessels on twin saddles was, and continues to be, of considerable interest to pressure vessel designers throughout the world. Whilst design rules are available in codes and standards, the drive is for improved, reliable analysis methods and design procedures by which engineers can produce efficient, commercially competitive, yet structurally reliable components with reasonable ease. The Department of Mechanical Engineering has an international reputation for studies in the field of pressurised systems. This present work continues the work of Emeritus Professor Alwyn S Tooth who commenced an investigation in this area some thirty years ago. The main thrust of this thesis is in two parts. Initially, local load problems are tackled since these are important in their own right. This provides a platform for the other main part, a study on saddle supports. The present work reviews the background to these classes of problem and considers the main contributions in the literature to solutions for the local loading and saddle support problems. Although a major contribution has been made within the Department of Mechanical Engineering at the University of Strathclyde, other pertinent international works are referenced in Chapter 2. In addition, this chapter details the main aims and objectives of the present work. The problem of the stress analysis of a cylindrical pressure vessel is tackled by employing Sanders thin shell theory, which is developed in Chapter 3. Governing differential equations are solved by a matrix method to evaluate the displacements of the shell. Thereafter, these are used to establish strains and thus stress resultants and stresses. Externally applied surface loads are described by employing a double Fourier series approach. The solution is then extended to encompass cases where thermal loading is present. Comments on the limitations of the use of Fourier series and rates of convergence are presented. In Chapter 4, the solution of the governing equations is successfully applied to some difficult local load problems. In this, the interface loading, which is traditionally represented by a radially loaded ‘rectangular patch’, is extended to circular and elliptical regions. In addition, the more complex loading cases of longitudinal and circumferential moment are also presented. Illustrative examples of the use of the solution are detailed and compared with experimental results obtained from the literature. The solution is also used to examine thermal loading on cylindrical shells with the cases of uniform thermal loading acting over discrete areas of the shell. In addition, the fault condition of a ‘hot spot’ with a prescribed thermal profile is outlined and a solution detailed. This form of solution may be used to examine, for example, the case of loss of insulation on a reactor wall. Some comments are also made with respect to modelling this class of problem using finite element analysis. Although the use of this mathematical tool is becoming widespread in engineering design and analysis, there are some drawbacks of the technique when examining local load problems. The important issues pertaining to the use of finite element analysis are examined and some results are thereafter compared with the Fourier series solution. These are fully discussed in this chapter. The design of cylindrical vessels supported on twin saddles is often driven by the magnitude of the stresses located near the uppermost point of the saddle shell junction. Surcharge pressure loading is generally the main design load for most component parts of a vessel. For the saddle supports, however, it is usually ignored and only the liquid fill load is considered since this is the worst situation and tends to exacerbate these junction stresses. In such cases, the major difficulty is the determination of the interaction forces between the saddle and the shell. This is examined in Chapter 5 by considering the interface pressure distribution between the two components. By discretising the contact area and by considering the compatibility of displacements for two bodies in contact and examining the equilibrium equations, an accurate mathematical solution for the interface pressure and subsequent stress analysis can be derived. A choice of models to describe the interface pressure system is detailed - line load, patch load and line plus patch load model. A brief description is given of the implementation of the computer programs. The solution of the saddle support problem requires a reasonably powerful computer to solve the equations, and therefore it is preferable to have a simple design method which can either be undertaken by hand calculation or be easily programmed into a simple spreadsheet. Chapter 6 develops a design methodology and parameter study for a typical range of vessel sizes and configurations as defined by the results of an industrial survey. In this, the scope is clearly identified and the range of parameters defined and justified. A ‘basic stress’ quantity is defined and thereafter modified by the use of a number of factors which describe the influence of the vessel weight, and the leading geometrical factors ~ saddle width, distance to rigid end, saddle interaction, saddle wrapround, and the effect of length change. Some verification and design examples are presented together with a design worksheet and a fatigue example in accordance with British Standard BS 5500. Traditionally, the influence of the stiffness of the vessel end or saddle support have either been ignored or treated in a simplified fashion. Although not included in this section, these topics are covered in Chapters 8 and 9. The main alternative method to the analytical one described above is the finite element method. Chapter 7 presents an overview of the main factors affecting the solution of saddle support problems using finite element analysis. The complications in modelling the geometry, the selection of element type, the choice and specification of boundary conditions and mesh refinement are examined in detail. Some sample results are given and the general influences of the geometric parameters on the deformations of the vessel are described. In addition, a comparison is made between the finite element analysis stress results and other methods. Some comments are made regarding the nature of the stresses obtained from the finite element analysis. The flexibility of the vessel dished end closure and the effect of this on the stresses obtained at the saddle shell junction is considered in Chapter 8. The treatment in the British Standard is outlined and compared to a finite element study for the various end closure types ~ rigid, flat, semi-ellipsoidal and hemispherical end closures. Some details are given on the modelling of such components and a parameter study is undertaken examining the main influencing parameters ~ radius, thickness of end and thickness of attached shell section. Some results are presented and an ‘end flexibility factor’ proposed. The influence of the saddle flexibility is examined in Chapter 9. This causes major difficulty, not least because of the almost infinite number of possible configurations of support. Obviously, the introduction of a flexible saddle affects the distribution of contact pressure. The first step is to adjust the equations developed in Chapter 5 to accommodate flexibility terms. The interface system for flexible saddles, the compatibility equations and the resulting values of strain and stress are fully detailed. The second step is to develop a mathematical model for the saddle flexibility; a fully parametric finite element model is proposed which works in conjunction with the analytical procedure. Thereafter, several alternative versions of the parametric model are described together with their applications and drawbacks. A new finite element approach using shell, solid and surface elements to introduce surface tractions is proposed and revised finite element models described. Thereafter, results are presented which demonstrate the influence of introducing a more flexible saddle can have great benefit of reducing the stresses in the vessel shell. Some overall conclusions and final comments are made in Chapter 10, especially with regards to further work and moves towards implementation, standardisation and improved availability via the Internet and adoption by industry.
- Advisor / supervisor
- Tooth, A. S.
- Resource Type
- DOI
- EThOS ID
- uk.bl.ethos.325680