Research On Analysis Of Structure Shakedown Based On The Lower Bound Theorems And Considering Random Factors

The shakedown analysis of structure is of wide-world concern. It is necessary to analyses the mechanical response with complicate load to attain precise result because the need for structure security is higher. And the method of shakedown analysis has presented an effective path to study the mechanical response with complicate load. At the present time, the design procedures for structures are based on reliability theory. So it is necessary to study the problems of shakedown based on reliability theory.First, based on the lower bound shakedown theorems, lower bound analysis method is developed and the domain of shakedown research is also broadened in this paper. Second, combining the lower bound shakedown theorems with stochastic FEM, a method considering the random factors is advanced, which is suit for analyzing the complicate load condition. And a further research on the method for reliability analysis is made in this paper. It consists of:1. Based on the generalized shakedown theorems, lower and upper bound shakedown theorems are discussed. A numerical arithmetic that may reduce the computation scale and enhance computation efficiency is developed. It is discussed the influence of structure geometry topology characters and vary of load action place on shakedown problems. And it is found out that the shakedown value is so sensitive to aforementioned factors.2. Based on the generalized shakedown theorems, the three-dimensional method to study the lower bound problems of shakedown is developed. Aimed at three-dimensional structure a further research is made. How to confirm the shakedown value domain is discussed and it should be based on the variety of load combination.3. A method considering the random factors is advanced, which is suit for analyzing the complicate load condition. From the point of view of reliability, the lower bound problems of shakedown are discussed by means of reliability index and sensitivity. Adopting this method may gain a more reasonable result to the general method. It is so necessary to study the mechanical response with complicate load based on the random factors.4. The lower bound problem of shakedown relates to the axisymmetric structure with different bugs is investigated and the influence of bug characters on structure charring capacity and reliability is discussed too. It is so clear that the influence of bug form and load path is different because of the difference of bug form and load path.