On the mechanical and thermal transient analysis of cylinder-to-cylinder vessels by a finite plate method

Abstract

A problem common to the pressure vessel analyst is the evaluation of stresses in nozzle-to-cylinder structures subjected to internal pressure, nozzle axial force and nozzle moments. In this paper, the finite plate method—discussed by Brown 31 in a paper on nozzle-to-cylinder structures subjected to internal pressure—is extended to include axial force and moments at the nozzle terminus. The purpose is to provide an economical alternative to 3-D geometric analytical and experimental stress analysis of such structures. The finite plate concept explored by Rodabaugh 25 as a geometric approximation of a finite region of the cylinder about the nozzle is used as the axisymmetric attachment to the nozzle. The variable plate parameters are the outer radius dimension and the harmonic loading at the outer radius of the plate. The parameters are determined for the pressure problem by utilising the shell solution of stresses about a circular hole in a cylinder as data for matching in the flat plate with a hole solution. The parameters for the axial force and moment loading of the nozzle problem are determined by utilising the cylindrical shell series solution of Bijlaard 32 for radial force and moment loading and the series solution for asymmetrically loaded axisymmetric plates. Once the parameters are determined, the structural stresses may be calculated by means of an interfacing numerical axisymmetric geometry, asymmetric loading shell or finite element program. In this paper the theoretical development of the geometric and pressure load parameters is briefly reviewed. The analytical development of the parameters for axial force, inplane moment and out of plane moment is presented in detail. The range of applicability is reviewed for the various types of loading. Examples are presented for nozzle-to-cylinder structures loaded by pressure, axial nozzle force, inplane moment at the nozzle and out of plane loading at the nozzle. Finite plane results are compared with the ORNL model No. 3 data obtained by strain gauge and 3-D finite element methods and loaded by nozzle loads. The finite plate results versus the experimental data obtained by Van Campen 27 and 3-D finite element data for internal pressure are briefly discussed. In all instances the data compare favourably at the critically stressed location which is at the nozzle-to-cylinder juncture. A comparison of 3-D finite element, 2-D finite element with the finite plate assumptions and some 2-D finite element nozzle-to-hemisphere data from thermal loading is presented. Finally, some observations were made with respect to the assessment of nozzle loads not analytically treated.