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Static Analysis of a Large-Scale Mold Model

This case study is a linear static analysis in which a uniformly distributed pressure is applied to a mold assembly. Four meshes using second-order tetrahedral elements are provided, ranging from approximately 1 million to approximately 210 million nodes.

The largest model, Mold_200mil, has been run on 13 nodes with 208 processes, making this a case study of the scale at which FrontISTR can handle models with geometries used in practical applications. The four models share the same geometry, material, and boundary conditions and differ only in mesh refinement, so they can also be used to compare how model scale affects accuracy and computational resources.

Overall geometry, lower geometry, and cut section of the mold model

Figure 1. Mold assembly: full parts, lower parts, and cut section.

Analysis Model

The four models share the same geometry, material, and boundary conditions and differ in mesh refinement.

Item Description
Geometry and connections Mold assembly. Parts are connected by shared nodes.
Elements Second-order tetrahedral elements
Material Structural Steel, linear elastic. Young's modulus 200 GPa, Poisson's ratio 0.3
Load Uniform pressure of 1 MPa on the top surface (surface group PRESSURE1)
Constraints All three translational components fixed on the bottom surface (node group CONSTRAINT1)

Mold load and constraint locations and element surface groups on the product surface

Figure 2. Pressure load, displacement constraints, and product surface groups.

Analysis Results

Displacement and Stress by Mesh Scale

Model Minimum Z displacement (mm) Maximum Mises stress, nodal value (MPa) Maximum Mises stress, element value (MPa)
Mold_001mil -0.2527 118.2 75.9
Mold_011mil -0.2638 130.7 101.3
Mold_055mil -0.2659 189.9 156.5
Mold_200mil -0.2666 250.4 213.1

As the mesh is refined, the change in the minimum Z displacement becomes smaller; for the two largest meshes, the difference at the precision shown in the table is 0.0007 mm. In contrast, the maximum Mises stress continues to increase for both the nodal and element values. To determine whether the stress is converging or whether a singularity is present, the location of the maximum value and the surrounding geometry and boundary conditions must be examined.

Mold_001mil Mold_011mil
Close-up of Mises stress: Mold_001mil Close-up of Mises stress: Mold_011mil
Mold_055mil Mold_200mil
Close-up of Mises stress: Mold_055mil Close-up of Mises stress: Mold_200mil
Figure 3. Mesh and nodal von Mises stress for the four model sizes (MPa).

Figure 3 shows nodally extrapolated values (NodalMISES), with the legend fixed at 0–50 MPa in all figures. Differences in the mesh can be compared from the element edges.

Large-Scale Execution Record

The calculations were performed in July 2020 using FrontISTR 5.1.0 with the CG method, a convergence threshold of 1.0E-06, and a maximum of 100,000 iterations. The execution environment was a PC cluster; each node had two Xeon E5-2670 processors (2.6 GHz, 8 cores), 128 GB of memory, and InfiniBand FDR interconnects. The parallel execution mode was Flat MPI (one thread per process).

Model MPI processes (nodes) Preconditioner Iterations Solver time (s)
Mold_001mil 32 (2) AMG (ML) 611 80.16
Mold_011mil 64 (4) AMG (ML) 854 782.65
Mold_055mil 128 (8) AMG (ML) 778 2,015.05
Mold_200mil 208 (13) Diagonal scaling 92,626 96,969.34

The times are the solve values from the execution logs. Mold_200mil ran out of memory even on 13 nodes when AMG was used, so the preconditioner was changed to diagonal scaling; the resulting iteration count was 92,626 and the computation time was approximately 27 hours.

Analysis Data

Model Nodes Elements Compressed size Download
Mold_001mil 1,015,778 638,041 35.6 MB Mold_001mil.tar.gz
Mold_011mil 11,036,922 7,617,345 461 MB Mold_011mil.tar.gz
Mold_055mil 55,508,692 39,271,921 2.41 GB Mold_055mil.tar.gz
Mold_200mil 209,893,102 151,044,460 9.58 GB 5 parts (below)

The data version is 1.0.0.

Obtaining Mold_200mil

Mold_200mil exceeds the per-file limit (5 GB), so it is registered in five 2 GiB parts. Download all files into the same directory and then concatenate them.

for i in 00 01 02 03 04; do
  curl -fLO "https://gitlab.com/api/v4/projects/21515176/packages/generic/Mold_200mil/1.0.0/Mold_200mil.tar.gz.part$i"
done
cat Mold_200mil.tar.gz.part?? > Mold_200mil.tar.gz

The SHA-256 of the concatenated file is c67d5b8990302c84103de7e8a2848449f0035f7813cd122fb443e206f38b8606.

References

Contributors

  • CAD and input data creation: TechnoStar
  • Conversion to FrontISTR and parallel analysis: Yamaguchi and Inagaki