Shape optimisation of axisymmetric cylindrical nozzles in spherical pressure vessels subject to stress constraints

In this study, optimal shapes of intersecting pressure vessels are sought using a novel topology/shape optimisation method, called Metamorphic Development (MD). An industrial benchmark design problem of finding the optimal profile of variable thickness that connects a spherical shell pressure vessel to a cylindrical nozzle is considered. Two types of intersecting structures, distinguished by flush and protruding nozzles, are investigated. The optimum profiles of minimum mass intersecting structures are found by growing and degenerating simple initial structures subject to stress constraints. The optimisation seeks to eliminate the stress peaks caused by the opening. The optimised structures are developed metamorphically in specified infinite design domains using both rectangular and triangular axisymmetric finite elements that are ideally suited for modelling continua with curved boundaries. It is shown that the design with a protruding nozzle would produce a better stress distribution than the design with a flush nozzle. The results demonstrate the success of the method in generating suitable, practical solutions to the design problem.