Plastic Limit And Shakedown Analysis For Curved Pipe Structures

At present, an important subject on plastic limit and shakedown analyses is to study the strategies of applications and to develop efficient and feasible numerical methods so that the limit and shakedown theories can find their applications in engineering practice. Supported by the program of the Ministry of Science and Technology of China, this thesis studies systematically and thoroughly numerical methods for upper bound limit and shakedown analyses and applies them to carry out the plastic analyses of elbow structures.A kind of elbow element is improved in this thesis. The effect of recovery of internal pressure on cross-section deformation of elbow structures wasn't included in elbow element before. To this end, the nonlinear term of internal pressure work is introduced in the formulation to solve this problem. The computing capacity of the element is extended largely. The numerical results show that the limit load-carrying capacities are enhanced after considering this effect.A numerical method is developed for upper bound limit analysis of elbow structures under multi-loading systems. The effect of recovery of internal pressure on cross-section deformation of elbow structures is considered. The limit analysis of elbow structures is formulated as a discrete non-linear mathematical programming problem with equality constraints by means of finite element technique. An optimal direct iterative algorithm is given to solve this formulation. The numerical difficulties caused by the non-linearity and non-smoothness of the objective function are overcome. The load factors and corresponding velocity fields during the iterative processes converge to the upper bounds of the real solutions.A numerical method is proposed for upper bound shakedown analysis of elastic-perfectly plastic elbow structures under complex variable loads. If a structure shakes down under any sequence of vertex loads within the set of vertices, then it shakes down under the whole load domain defined by those vertices. According to the above theorem, the numerical difficulties caused by the time integrals in kinematic shakedown theorem are overcome. The numerical formulation can prevent elbowstructures from ratcheting due to the accumulation of plastic deformation and low cycle fatigue due to the alternating plastic deformation. A direct iterative algorithm is given to solve this formulation. The effect of temperature on the yield stress is considered in the numerical method.In case of the limited kinematic strain hardening material model, a numerical method is proposed for upper bound shakedown analysis of elbow structures under the combined action of constant and complex variable loads. A two-surface yield criterion is used in the formulation, where the yield surface and the moving of corresponding center are respectively limited. A direct iterative algorithm is given to overcome the numerical difficulties caused by the non-linearity and non-smoothness of the objective function. The effect of temperature on the yield stress is included in the numerical method.In light of the developed numerical methods and the improved elbow element, upper bound limit and shakedown analyses are performed for elbow structures under multi-loading systems. A series of computational curves for limit and shakedown loads is obtained. Some valuable conclusions are drawn. The calculated results can provide theoretical foundations for the design and safety assessment of elbow structures.