Shakedown, integrity and design of elastic plastic damaged structures as subjected to cyclic loading

A method for direct design (i.e. without detailed investigation of the deformation process) of structures of elastic plastic isotropically damaged materials as subjected to cyclic loading is developed. The material is assumed to be stable. Shakedown and integrity conditions provide the possibility of obtaining the interval of safe values of a parameter (b) in design for which the structure preserves its safety. The damage process is assumed to be coupled with the plastic deformation development. Features of the post-adaptation stage lead to a min-max problem of mathematical programming, whose solution provides a relation between the limit values of the damage and hardening parameters. As the hardening parameter is assumed to be bounded, this relation issues in upper and lower bounds for the local actual limit values of the damage parameter admitted by the yield condition for the given loading program. The bounds result in a priori necessary and sufficient conditions of integrity. As the bounds depend on b, the integrity conditions impose constraints to its safe values. A method for computing the purely elastic damaged response of the structure to the prescribed loading program is proposed. An example of the application of the developed method is given.