Optimization of internally pressurised torispheres subject to shakedown via GAs

The maximization of the shakedown pressure of an internally pressurised torispherical dome subject to constraints on plastic strain and total mass of the component is presented. The meridional shape is sought in the class of torispherical geometries. Both uniform and piece wise constant wall thicknesses are considered. The Genetic Algorithm (GA) technique is used in which the ABAQUS FE code is a re-analysis tool. The material is elastic-perfectly plastic and the first cycle shakedown definition is adopted for the cost function. In addition to the generic three operator approach, i.e. reproduction, crossover and mutation, other variants of GAs such as the elitist model, the two-point crossover and the combined elitist and two-point crossover models are also discussed. Both the "accept or reject" and penalty function strategies are used for the implicit constraint on the amount of plastic strain. The interim re-analysis results were additionally used to train a neural network. The idea behind this approach was to eliminate further FE analysis if or when the net could be deemed capable of taking over the cost function and constraint evaluations. Comparisons of optimal solutions with standard industrial dome profiles are also provided.