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The book is dedicated to the behaviour of ductile materials at cryogenic temperatures, structural stability issues and reliability oriented parametric optimisation of compensation systems containing the corrugated bellows. The problems of local and global stability of systems containing bellows, coupling between the low-cycle fatigue and stability as well as evolution of plastic strain fields, micro-damage and strain induced phase transformation in the corrugated shells at cryogenic temperatures are presented. As a special feature reliability oriented optimum design of compensation systems under strength, stability, fatigue and geometrical constraints is discussed. The relevant applications in the particle accelerators and cryogenic transfer lines are shown.