Stress Classification at Cylindrical Intersections Using Primary Structure Method: A Parametric Study Using Finite Element Method

Stress classification at shell and nozzle interface has always been an interesting and challenging problem for Engineers. Basic shell theory analyses shell stresses as membrane with local bending stresses developed at locations of discontinuity and load applications. Since in a shell structure, bending stresses develop to mainly maintain compatibility of deformation and membrane stresses to equilibrate the applied load, a simple stress classification will be to categorize the bending stresses as secondary stresses. This is because by definition, secondary stresses develop to maintain compatibility of deformation and primary stresses develop to maintain equilibrium with the applied load. This simplified analysis can result in errors as in real world 100% primary stress as well as 100% secondary stress is rare if not impossible. The widespread use of Finite Element Analysis has made this problem become even more challenging. In this paper the work done by Chen and Li [1], using the two step primary structure method has been used to analyze the problem of stress classification of a shell and nozzle. This paper is a continuation of the author’s previous work on this topic [21]. In the previous paper, the sensitivity of modelling and the effect of the same on the results were investigated. However, the various approaches adapted in the paper [21], were not exactly in the true spirit of the method i.e in all the models, stresses in the vessels and nozzles were checked separately and compared against the stresses in the vessel and nozzle in the original model where by “original “model we mean the model with the vessel and nozzle modelled together i.e. connected along the space curve of intersection in all six degrees of freedom. The spirit of the method requires that the comparison has to be with reference to maximum M+B stresses in the original and reduced structure ( a “reduced” structure means where the vessel and the nozzle are not connected along some degrees of freedom along the space curve of intersection) and not individually in the vessels and nozzles and the M+B stresses have to be evaluated anywhere on the structure and not just at and close to the space curve of intersection. It is because of these reasons that [21] in not exactly in spirit of the method. In other words, the development of this paper was motivated by the fact that the previous paper did not use the exact spirit of the method and hence to investigate how its exact implementation changes results. This is the approach followed in this paper. A point to note; not in spirit of the method does not necessarily mean that the approach taken in [21] was not correct. It’s just that it was not in line with the way this method was defined by Chen and Li [1] and the present authors used their subjective approach to the problem. Additionally, this paper investigates the effect of geometric parameters like D/T, d/t and t/T on the results which was not investigated in the previous paper.