## 5 Research Progress on Key Technologies of IPPCS
### The Strength Criterion of the Pressurized Capsule Structure Based on Shakedown
#### 5.1.2 Application of Shakedown Theory on Pressurized Capsule Structure  
In structural shakedown, the ideal elastic-plastic structure produces a favorable residual stress field after a certain amount of plastic deformation under cyclic loading, which improves the elastic limit load of the structure. Moreover, the accumulated plastic deformation is stable, which does not affect its initial design function and the failure mode. From the definition, it can be seen that shakedown theory can analyze and evaluate the ultimate load that a structure with plastic deformation can withstand. Therefore, based on the shakedown theory, conducting structural shakedown analysis can evaluate the feasibility and load-bearing safety of the pressurized capsule structure allowing local plastic deformation [23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36]. (1) Shakedown analysis of pressurized capsule structure [23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36]  
The finite element solid model of the large pressurized capsule structure is large in scale, and the shakedown analysis is difficult to be carried out directly in the solid model because the number of independent variables and constraints is above one million levels and the solution time is long and the calculation amount is huge. Since the structure of the pressurized capsule and the load are symmetrical, the axisymmetric model can be used for the shakedown analysis. Compared with the solid model, the axisymmetric model is smaller, the solution time is shorter, and it is more convenient to combine with the parametric modeling method. By comparing the analysis results of the shakedown analysis of the pressurized capsule with the solid model and the axisymmetric model, it is shown that the three-dimensional solid model and the two-dimensional axisymmetric model have similar characteristics in the shakedown numerical analysis, and it is reasonable to transform the solid model into the axisymmetric model. The shakedown analysis model is reduced to a two-dimensional axisymmetric model, which reduces the operation scale and calculation amount, and lays the foundation for the design and optimization of the pressurized capsule structure through shakedown analysis. Through the shakedown analysis, the shakedown load of the pressurized capsule structure is calculated (under this load, the structure is in a shakedown state, and the local stress is higher than the yield strength of the material). The maximum shakedown load is  
Figure 10: Local stress concentration in transition zone under internal pressure load [24]. the elastic shakedown limit of the pressurized capsule structure. The elastic shakedown limit of the pressurized capsule structure is greater than the elastic limit load (the structure is globally in elastic deformation, and the maximum stress is equal to the yield strength of the material). In order to verify the validity of the shakedown numerical analysis method and whether the shakedown limit exists, it is necessary to carry out experimental verification research. To study the shakedown behavior of the structure by experiment, the key is to investigate if residual strain and displacement at all critical locations identified by simulation would stop developing after several load cycles. The design ultimate limit load for the internal pressure is 0.15 MPa, while the calculated stable ultimate limit load is 0.2765 MPa. Therefore, experimental testing will be conducted at the calculated load of 0.2765 MPa. In the study of [36], the research object was a pressurized capsule of reduced size. Firstly, the plastic dissipation of the structure gradually converged after 10 times of shakedown limit cyclic loading through the shakedown analysis (as shown in Figure 11a). Secondly, the strain and displacement changes at locations of interest were observed by cyclic internal pressure loading experiments (as shown in Figure 11b). Finally, the numerical analysis was compared with the experimental results.