| Summary: | The work presented is concerned with the implementation and exploitation of an iterative non-linear programming technique, based on the elastic compensation method, for solving limit load and shakedown problems. Such solutions are required in the design of structures or components subjected to complex combinations of static and cyclic loading, in structural integrity procedures and life cycle assessment. To achieve these aims, a brief review of the problem, the historical development of shakedown theory and recent developments of methods addressing these issues are given in the early chapters. This is followed by the implementation of the above method to generate limit load solutions for elastic-plastic materials subject to the von Mises yield condition. The method was found to be numerically stable and convergence could be guaranteed for upper bound limit load solutions if a number of sufficient convergence criteria are adhered to. These are stated during the provided convergence proofs. Upon studying the behaviour of the method, i.e. quality and sensitivity of solutions, computational effort as well as identifying error sources, this implementation is extended to solve limit load problems for arbitrary yield surfaces. This was found to be possible, but dependent on the nature of the yield surface and limits to the implementation in its present form were identified. The method was then implemented using a different formulation capable of solving limit and, more importantly, shakedown problems for elastic-plastic materials subject to the von Mises yield criterion. A number of benchmark problems were considered, an example of which is the classic Bree problem, which is concerned with shakedown of components subjected to a static mechanical load in combination with thermal transients. The method performed well and was then used to solve novel shakedown problems, such as shakedown states where creep must be considered. Acceptable creep behaviour for a given shakedown state could also be calculated using minor additions. The final issue considered was cyclic creep solutions. Rapid cycle creep solutions could be generated as a stress history can be considered, which is of a similar form to shakedown. Finally, conclusions were drawn and remaining issues discussed.
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