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This book is comprised of two main parts. Firstly, burst pressures in vessel components such as torispheres, shallow spherical caps and toroidal shells are evaluated by analytical, numerical and experimental approaches. Two types of failure mode are investigated, one due to excessive plastic deformation and the other due to plastic instability. Secondly, non-gradient based optimization methods including Simulated Annealing, Particle Swarm Optimization and Differential Evolution have been applied to the design of minimum weight toroidal vessels subject to internal pressure. Constraints are first yield pressure, plastic pressure, burst pressure and volume contained by toroids. Optimality includes geometry and wall thickness. The optimization process is performed by routines written in FORTRAN coupled with ABAQUS software. The book will be useful for those who work in pressure vessel industries and the field of structural optimization
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