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This book is a state of the art presentation of theories and methods related to the problem of the behaviour of mechanical structures under variable loads beyond their elastic limit. In particular, the problems of shakedown, ratchetting, transient and asymptotic cyclic states are addressed. Four chapters, each composed of individual articles, treat the material modelling for cyclic loading conditions, general theories of accommodated states of structures, effects of changes of the geometry on the inelastic structural response and numerical techniques with applications to particular engineering problems. The volume is of interest to all mechanical and civil engineers involved in design of mechanical elements and structures exposed to variable mechanical and thermal loads and which may suffer inelastic deformations during their lifetime.