## 4 Mechanical Analysis and Strength Check of the Backfilling Hydraulic Support
### Strength Check of the Backfilling Hydraulic Support  
In addition to checking the rationality of the plane structure of the backfilling hydraulic support by the mechanical model, it is necessary to comprehensively test the bearing strength of the whole frame under the combined action of its 3D structure and material manufacturing using the finite element analysis.  
The boundary conditions of the model and the connection between the parts are shown in Figure 9. The displacement boundary conditions are applied at the front and rear of the model, and the load is applied at the top beam. The connection methods between the components include normal hinges and spherical hinges, with spherical hinges used at the columns and normal hinges used at the rest of the model.  
After the pre-processing before ABAQUS modeling, a uniformly distributed load (5160 kN), 1.2 times the working resistance, is added according to the experimental theory of support strength. Figure 10 shows that the maximum stress of the whole frame is 797.8 MPa, which appears at the hinged connection between the base and the rear column. If the connection is weak, it is necessary to give Q960 steel to the connection and thicken it to ensure that it is within the allowable range of the material. The stress of other parts is within 300 MPa, and Q460 steel can be used.  
Figure 9: The boundary conditions of the model and the connection between the components.  
In Figure 11, the stress data of the middle node of each column are selected as a reference. The stress values of the middle nodes of the front, middle and rear columns are 22.09, 14.71, and 41.43 MPa, and the column load ratio is 1:0.67:1.64. The stress of the column is in the descending order of rear, front, and middle columns, proving that the 3D support structure with given materials is in line with the theoretical analysis results.  
Figures 12-14 show the stress clouds of the top beam, the rear top beam and the base, respectively. It can be seen that the force of the top beam is mainly concentrated in the front column and the connection with other components, which is the same as the load distribution of the column. The force of the rear top beam is mainly distributed at the connection with the rear column, and the maximum can reach 610 MPa. This is because the structure is weak here, and the stress concentration occurs easily; therefore, the thickness here can be enhanced appropriately. From the stress distribution of the base, the stress is mainly concentrated in the connection between the base and the rear and front columns. Especially important, the connection between it and the rear column is prone to stress concentration; therefore, the thickness of this area should be increased.  
Figure 11: Stress of columns.  
Figure 10: Stress of the whole support.  
The theoretical stress analysis of the plane structure of the backfilling hydraulic support and the finite element loading analysis of the 3D structure show that the ZC4800/16/30 backfilling hydraulic support after reformation can meet the production requirements in terms of the structure. The design is more reasonable, e.g., the strength of the whole frame within the allowable range, the stress law of each column meeting the requirements, and the sufficient support strength of the rear column.