Finite Element Analysis of Pressure Vessels J.W. Jones President of Swanson Service Corporation 58th General Meeting in 1989 Category: Design/Fabrication Summary: The following article is a part of National Board Classic Series and it was published in the National Board BULLETIN. ANSYS Case Study: Axisymmetric Analysis of A Pressure Vessel The pressure vessel shown below is made of cast iron (E = 14.5 Msi, ν = 0.21) and contains an internal pressure of p = 1700 psi. (7 printed pages) The following material represents the author only and should not be assumed to be the opinion or policy of The National Board of Boiler and Pressure Vessel Inspectors or the American Society of Mechanical Engineers administration, staff or membership, unless so acknowledged. The use of finite element methods to design and analyze pressure vessels is a relatively recent development in the overall historical perspective of the ASME Code. The finite element method first became a useful tool for the designer in the early 1960s. The advent of the ASME Nuclear Code, Section III, which first appeared in about 1964, provided for a 'design by analysis' procedure. Up until this time, the pressure vessel design codes all used the 'design by formula' approach, which is essentially that now used in Section VIII, Division 1 of the ASME Code. The design by formula method provides explicit rules for calculating wall thicknesses of heads, shells, reinforcement around openings, and other details of a vessel. There are additional rules to handle such features as discontinuities between different components (i.e., the 3:1 taper rule) and allowable construction details are illustrated. The shortcoming of these rules is, of course, that they cannot cover every conceivable detail that the designer may want to use. Johnny pacheco discografia. For example, Section VIII, Division 1 gives numerous warnings and admonitions that the designer shall consider the effects of thermal gradients, piping loads, nozzle loads, rapidly fluctuating loads, seismic, wind, etc., but unfortunately there are few specific guidelines or formulas included in the code to cover such items. Rusty blade ikrar perwira rarity. Further, the allowable stresses given in the code are based on a rather simplistic average membrane stress. Other loads, such as thermal loads, for example, cause a different type of stress that cannot be limited to the S values in the code, if a reasonable design is to be developed. Section III and Section VIII, Division 2, which came out several years after Section III, both use the concept of design by analysis. These rules provide the designer/analyst with a variety of stress limits, each developed to protect against a different mode of failure. Stresses are classified into categories such as Primary, Secondary, Peak, etc. Each category of stress is subjected to different stress limits. Essentially, the Nuclear Code and Division 2 of Section VIII require that the designer/analyst be able to calculate the stresses everywhere in the vessel, not just the average membrane stresses in regular sections (such as cylinders and dished heads). Early evaluation of nuclear vessels was performed using discontinuity analyses. This technique requires that the vessel be approximated by a series of simpler shapes, such as cylinders, cones, rings, etc. The stresses are found by matching the displacement and rotations of each section (compatibility) while satisfying equilibrium of the loads. The method is very useful and forms the basis for the present flange design rules in the current codes. The problem is, however, the time-consuming nature of the technique for the engineer who must set up and solve the equations, and the necessity to approximate complex shapes with simpler geometries, for which analytical (i.e., closed form) solutions are available. Furthermore, it is difficult to include thermal stress effects in a discontinuity analysis. The first commercially useful finite element program was developed about the early to mid-1960s. This early program was actually little more than an automated discontinuity analysis. Conical shell elements were employed to model axisymmetric shapes. Each element was essentially a short conical shell or ring.
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