Lower-bound Shakedown Analysis Of Vessels Containing Defects Subjected To Multitypes Of Variable Loads

Pressure vessels widely used in many fields of industry are usually subjected to multitypes of variable loads. It is very important to assess their shakedown carrying capacities for safety in operation. Because of large difficulties in numerical algorithm, shakedown analysis only for some simple problems has been solved up to now, which is still far away from engineering application. Especially, the investigations in the effects of 3-dimensional defects such as pits or gas holes on the limit carrying capacities of the pressure vessels are usually simplified to plane problems but not quantitative analysis. Due to the lower-bound shakedown analysis has important meaning for guarantee for the safety of structures, therefore in this thesis, plastic shakedown analysis in a finite element computational form is presented for axi-symmetric and 3-dimensional structures based on lower-bound shakedown theorem, and the effects of various kinds of 3-dimensional defects on the carrying capacities of spherical and cylindrical shells are investigated. The effects of multitypes of variable loads acting on the structures can be considered. The reduction of yield limit with the rising of material temperature is taken into account as well.In this thesis following steps are adopted to overcome the numerical difficulties. The pseudo-temperature field is put into a structure and the resulting thermo-elastic stress is considered as a residual-stress field. The nonlinear yield condition is piece wise linearized, so that shakedown analysis is transformed into a linear programming problem whose strategic variable is pseudo-temperature and object variable is loading multiplier.In axi-symmetric problems, two kinds of piece wise linearized schemes to the yield condition are presented, and the selection of the schemes based on the particular stress state is investigated, then the sources of computational errors are analyzed. In 3-dimensional problems, the pseudo temperature field is assumed as a harmonic function satisfying the uniqueness theorem. So the nodal temperature vector of the whole structurecan be expressed by the boundary nodal temperature. Therefore, the quantity of strategic variables can be significantly decreased. Then the quantity of constraints is decreased by removing the unnecessary constraints of linearized yield conditions for the particular stress state. Therefore, the optimization on a very large scale can be solved by using 486 PC and the shakedown analysis is applicable to the engineering structures.By the above computational form, the effects of internal, external pits and gas holes on carrying capacities of spherical shells, and the effects of external pits on carrying capacities of cylindrical shells under internal pressure are investigated. The computational schemes and programs are proved to be reliable by comparison between the computational results and the experimental ones. Then several suggestions on carrying capacities of pressure vessels are presented after comparing the numerical results with current codes and standards. The shakedown behaviors of structures under single loading case are obtained based on the shakedown theorems. Further, the shakedown domains in 3-dimensional loading space are obtained through investigating the axi-symmetric structures subjected to the combination of three kinds of loads, constant and pulsative internal pressure, and pulsative temperature fields.In a word, a series of computational graphs, tables and curves presenting the relationship between defects and the carrying capacities of structures are given in the thesis, which can make an important improvement on the safety assessment methods of pressure vessels.