The development of upper bound and associated finite element techniques for the plastic shakedown of thermally loaded structures.

This thesis is concerned with the behaviour of structures subjected to cyclic or repeated thermal loading in the presence of steady mechanical loads. The present work consists of four main parts; in the first part, the thermal loading problems and the possible solution methods are discussed. The development of shakedown theory and its applications are reviewed with particular attention on the case of thermal actions. By utilising the upper bound shakedown theorem and assuming a broader range of shakedown conditions, a new extended upper bound technique for estimating the extent of plastic shakedown (reversed plasticity) region is developed. The occurrence of the structural and material shakedown and a related structural theory which indicates whether a reversed plasticity region exists, are discussed. In the second part, the influence of cyclic hardening and temperature dependents of material properties on the modes of behaviour of two representative kinematically determinate structures; namely a parallel two-bar assembly and a Bree plate are investigated by means of an empirical cyclic hardening material model and the theory, developed in the first part. Comparing the available experimental data on a two-bar structure with the predictions of perfect plasticity, complete cyclic and cyclic hardening models it is argued that the use of perfect plasticity model may not -always guarantee the safe performance above the shakedown limits. In this region the use of complete cyclic hardening model gives conservative boundary whereas the cyclic hardening model gives the most appropriate boundary. The analytical solutions for the Bree plate with temperature independent material properties show that the boundary between the reversed plasticity and ratchetting is insensitive to the hardening assumption. The influence of the transient thermal loading and the effects of multi-axial state of stress on the Bree solution are also studied. The applications of the upper bound technique to the problems involving transverse and in plane loading in plates are presented and the importance of the shear stresses in this type of loading conditions are emphasized. In the third part, a finite element technique for the computing of shakedown limits and estimation of the corresponding mechanisms of deformation for kinematically highly indeterminate structures is developed. Presenting the main features of the technique which is based upon the upper bound shakedown theorem and linear programming, a number of solutions are given to specific problems to illustrate the types of problems which may be solved by the technique. Some recently reported experimental data on a tube under axisymmetrical loading is compared with the present analytical predictions. Finally, the conclusions and the proposals for future work are presented in the fourth part.