First, each component is modeled individually. The finite element model of each subcomponent is assembled, and then the degrees of freedom at the joint areas are coupled at the bolt positions of the respective components, forming a rough structural model. Once the rough model is established, constraints and loads are applied to perform an initial analysis. A detailed submodel is then created for the local regions of interest, such as the bolted joints. This submodel must align with the corresponding area in the rough model, and a cut boundary is defined for interpolation. This step is crucial in the submodeling approach. The user defines the nodes on the cut boundary, and the program uses the results from the rough model—such as displacements—to interpolate the boundary conditions for the submodel. After setting up the submodel, it is solved, and the distance between the cut boundary and the stress concentration region is verified. It should be sufficiently far away. To ensure accuracy, the results (e.g., stress) on the cut boundary are compared with those from the rough model. If discrepancies exist, the cut boundary is redefined further away from the area of interest, and the submodel is recalculated.
This method offers several advantages. When dealing with structures that have many bolted joints, there's no need to model detailed features like screw holes, significantly reducing modeling effort. Meshing near the bolt holes can also be coarser, which reduces the number of elements. This avoids complications arising from modeling numerous bolts separately. For the critical areas, a more accurate model can be built with finer meshing, independent of the overall model’s unit count. This not only helps overcome hardware and software limitations in complex analyses but also improves the precision of the results.
A calculation example was conducted using the coupled node submodel method to analyze the quasi-static stress distribution in a cabinet and assess the strength reserve of the electronic equipment rail fixing parts near the bolt connections. The cabinet has four sides, with the rail fixing parts on the left and right connected via 21 bolts to the front pillars and fixing members. The rail fixing parts of the electronic equipment are connected to the front fixing parts of the cabinet through two bolts. The rail fixing members are mounted to the front pillars at different sizes and positions, with three pairs of mounting holes reserved on each side—making a total of four pairs per side. Additionally, five pull members on both sides of the cabinet are connected to the front and rear columns via bolts. During operation, the cabinet is subjected to up to 9g of acceleration.
The calculation procedure using the coupled node submodel method involved creating and analyzing a rough model of the cabinet. During meshing, attention was given to the bolt joint locations so that when coupling the degrees of freedom later, the node positions could match the actual bolt positions. All six degrees of freedom of the corresponding nodes were coupled. The resulting rough model, made up of shell elements, contained 44,515 nodes, 32,831 elements, and 2,481 coupling points.
After establishing the rough model, the first few natural frequencies were calculated to verify the model's accuracy, check for missing bolt connections, and ensure proper node coupling. The first-order natural frequency of the entire cabinet was found to be 15.9 Hz, representing a lateral bending mode. This closely matched the experimental result of approximately 15.0 Hz, confirming the high accuracy of the finite element model. A static load of 9g was then applied to the rough model to examine the strain and stress distribution across the entire structure.
For the submodel, a cut boundary was selected in an area where the joint between the rail fixing member and the front fixing member had a relatively low stress gradient. The submodel was directly extracted from the rough model. A comparison of the finite element models of the submodel and the rough model is shown. These two bolts were simulated using solid elements. After meshing, the submodel contained 13,486 nodes and 3,118 elements.
Verification of the submodel involved comparing the von Mises stress at the nodes on the cut boundary between the rough model and the submodel. The table below lists the stresses at the corresponding nodes. The maximum equivalent stress near the screw hole of the joint in the rail fixing member was found to be 280.7 MPa. The entire calculation process was completed successfully.
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