RD-E: 1701 Densities
A steel box beam, fixed at one end and impacted at the other end by an infinite mass. Results for mesh with different densities are compared.
A steel box beam fixed at one end, is impacted at the other end by an infinite mass. The dimensions of the box beam are 203 mm x 50.8 mm x 38.1 mm, and its thickness is 0.914 mm. As symmetry is taken into account, only one quarter of the structure is modeled.
Options and Keywords Used
- Shells Q4
- Interfaces (/INTER/TYPE7 and /INTER/TYPE11)
The structure's self-impact is modeled using a TYPE7 interface on the full structure. The interface master surface is defined using the complete model. The slave nodes group is defined using the master surface.
On top of the beam, possible edge-to-edge impacts are dealt with using a TYPE11 self-impacting interface. The edges use the master surface of the TYPE7 interface as the input surface.
Figure 1. Boundary Conditions - Global plasticity, iterative plasticity, and variable thickness
- BT_TYPE1, 3, 4, QEPH, BATOZ, DKT18 and C0 formulation
- Boundary conditions (/BCS)
Take into account the symmetry, all nodes in the Y-Z plan are fixed in a Y translation and an X and Z rotation. One quarter of the structure is modeled.
- Rigid wall (/RWALL)
The impactor is modeled using a sliding rigid wall having a fixed velocity (13.3 m/s) in a Z direction and is fixed for other translations and rotations.
- Imposed velocity (/IMPVEL)
- Rigid body (/RBODY)
The lower (fixed) end is modeled using a rigid body connecting all lower nodes (Z = 0.0). The rigid body is completely fixed using translations and rotations.
Input Files
- Mesh 0
- <install_directory>/hwsolvers/demos/radioss/example/17_BoxBeam/Densities_mesh/mesh0/.../BOXBEAM*
- Mesh 1
- <install_directory>/hwsolvers/demos/radioss/example/17_BoxBeam/Densities_mesh/mesh1/.../BOXBEAM*
- Mesh 2
- <install_directory>/hwsolvers/demos/radioss/example/17_BoxBeam/Densities_mesh/mesh2/.../BOXBEAM*
- Mesh 3
- <install_directory>/hwsolvers/demos/radioss/example/17_BoxBeam/Densities_mesh/mesh3/.../BOXBEAM
Model Description
Units: mm, ms, g, N, MPa
- Material Properties
- Initial density
- 7.8 x 10-3
- Young's modulus
- 210000
- Poisson ratio
- 0.3
- Yield stress
- 206
- Hardening parameter
- 450
- Hardening exponent
- 0.5
- Maximum stress
- 340

Figure 2. Problem Studied
Model Method
Four kinds of meshes are used to model the beam. The initial mesh is uniform using a total of 60 x 8 elements. For the three other meshes, the element length is multiplied by 2, 3 and 4, as shown in Figure 3.
- BT_TYPE1
- BT_TYPE3
- BT_TYPE4
- QEPH
- BATOZ
- C0 (T3 element)
- DKT18 (T3 element)

Figure 3. Meshes
The 3-node shell mesh is obtained by dividing the 4-node shell elements.
Results
- Role and influence of the mesh for a given type of element formulation
- The shell element formulations for a given mesh
- Crushing force versus displacement
The crushing force corresponds to normal force in the Z-direction of the impactor (rigid wall), multiplied by 4 due to the symmetry.
In comparison, the displacement corresponds to the Z-direction motion of the rigid wall's master node.
- Hourglass energy
- Total energy
Total energy is the sum of all energies.
Mesh Influence of a Given Shell

Figure 4. Total Energy for a BATOZ Formulation

Figure 5. Force for a BATOZ Formulation

Figure 6. Total Energy for a QEPH Formulation

Figure 7. Force for a QEPH Formulation

Figure 8. Total Energy for a BT_TYPE1 Formulation

Figure 9. Hourglass Energy for a BT_TYPE1 Formulation

Figure 10. Force for a BT_TYPE1 Formulation

Figure 11. Total Energy for a BT_TYPE3 Formulation

Figure 12. Hourglass Energy for a BT_TYPE3 Formulation

Figure 13. Force for a BT_TYPE3 Formulation

Figure 14. Total Energy for a BT_TYPE4 Formulation

Figure 15. Hourglass Energy for a BT_TYPE4 Formulation

Figure 16. Force for a BT_TYPE4 Formulation

Figure 17. Total Energy for a CO Formulation

Figure 18. Force for a CO Formulation

Figure 19. Total Energy for a DKT Formulation

Figure 20. Force for a DKT Formulation
Influence of Element Formulation using Mesh 3

Figure 21. Total Energy for Different Element Formulations

Figure 22. Total Energy for Different Element Formulations

Figure 23. Hourglass Energy for Different Element Formulations

Figure 24. Displacement for Different Element Formulations

Figure 25. Displacement for Different Element Formulations

Figure 26. MESH 0

Figure 27. MESH 1

Figure 28. MESH 2

Figure 29. MESH 3
MESH 0 | MESH 1 | MESH 2 | MESH 3 | |
---|---|---|---|---|
EI t = 8 ms |
3.25 x 105 | 3.82 x 105 | 4.88 x 105 | 7.23 x 105 |
Ehr t = 8 ms |
- | - | - | - |
EK t = 8 ms |
1.32 x 104 | 1.23 x 104 | 1.26 x 104 | 1.10 x 104 |
Total Energy | 3.38 x 105 | 3.94 x 105 | 5.00 x 105 | 7.34 x 105 |
Error t = 8 ms |
0.3% | 1.1% | 1.6% | 2.9% |
Maximum normal force on the wall (N) | 10350 | 10491 | 10953 | 11555 |
MESH 0 | MESH 1 | MESH 2 | MESH 3 | |
---|---|---|---|---|
EI t = 8 ms |
3.38 x 105 | 4.55 x 105 | 5.49 x 105 | 8.13 x 105 |
Ehr t = 8 ms |
- | - | - | - |
EK t = 8 ms |
1.32 x 104 | 1.36 x 104 | 1.35 x 104 | 0.93 x 104 |
Total Energy | 3.51 x 105 | 4.68 x 105 | 5.63 x 105 | 8.23 x 105 |
Error t = 8 ms |
2.0% | 2.9% | 3.2% | 8.0% |
Maximum normal force on the wall (N) | 10345 | 10574 | 11335 | 11865 |
MESH 0 | MESH 1 | MESH 2 | MESH 3 | |
---|---|---|---|---|
EI t = 8 ms |
3.19 x 105 | 3.60 x 105 | 4.68 x 105 | 5.19 x 105 |
Ehr t = 8 ms |
2.42 x 104 | 4.17 x 104 | 3.87 x 104 | 8.80 x 104 |
EK t = 8 ms |
1.29 x 104 | 1.23 x 104 | 1.16 x 104 | 1.35 x 104 |
Total Energy | 3.32 x 105 | 3.72 x 105 | 4.79 x 105 | 5.32 x 105 |
Error t = 8 ms |
-6.4% | -9.3% | -5.8% | 11.5% |
Maximum normal force on the wall (N) | 10344 | 10505 | 10971 | 11569 |
MESH 0 | MESH 1 | MESH 2 | MESH 3 | |
---|---|---|---|---|
EI t = 8 ms |
3.14 x 105 | 3.73 x 105 | 4.46 x 105 | 4.94 x 105 |
Ehr t = 8 ms |
2.02 x 104 | 3.80 x 104 | 6.56 x 104 | 11.90 x 104 |
EK t = 8 ms |
1.31 x 104 | 1.24 x 104 | 1.32 x 104 | 1.29 x 104 |
Total Energy | 3.27 x 105 | 3.85 x 105 | 4.60 x 105 | 5.07 x 105 |
Error t = 8 ms |
-5.5% | -8.2% | -11.0% | -16.7% |
Maximum normal force on the wall (N) | 10353 | 10526 | 11000 | 11670 |
MESH 0 | MESH 1 | MESH 2 | MESH 3 | |
---|---|---|---|---|
EI t = 8 ms |
3.23 x 105 | 3.52 x 105 | 4.60 x 105 | 5.26 x 105 |
Ehr t = 8 ms |
1.26 x 104 | 1.94 x 104 | 3.74 x 104 | 5.02 x 104 |
EK t = 8 ms |
1.30 x 104 | 1.24 x 104 | 1.21 x 104 | 1.31 x 104 |
Total Energy | 3.36 x 105 | 3.64 x 105 | 4.72 x 105 | 5.39 x 105 |
Error t = 8 ms |
-3.3% | -4.0% | -5.8% | -6.5% |
Maximum normal force on the wall (N) | 10344 | 10538 | 11011 | 11568 |
MESH 0 | MESH 1 | MESH 2 | MESH 3 | |
---|---|---|---|---|
EI t = 8 ms |
3.45 x 105 | 4.56 x 105 | 4.79 x 105 | 8.64 x 105 |
Ehr t = 8 ms |
- | - | - | - |
EK t = 8 ms |
1.29 x 104 | 1.30 x 104 | 1.10 x 104 | 1.12 x 104 |
Total Energy | 3.58 x 105 | 4.69 x 105 | 4.90 x 105 | 8.75 x 105 |
Error t = 8 ms |
0.2% | 0.8% | 1.7% | 2.5% |
Maximum normal force on the wall (N) | 10355 | 10344 | 10875 | 11435 |
MESH 0 | MESH 1 | MESH 2 | MESH 3 | |
---|---|---|---|---|
EI t = 8 ms |
3.21 x 105 | 3.75 x 105 | 3.97 x 105 | 4.32 x 105 |
Ehr t = 8 ms |
- | - | - | - |
EK t = 8 ms |
1.29 x 104 | 1.34 x 104 | 1.13 x 104 | 1.45 x 104 |
Total Energy | 3.34 x 105 | 3.88 x 105 | 4.08 x 105 | 4.47 x 105 |
Error t = 8 ms |
0.5% | 0.8% | 1.6% | 1.9% |
Maximum normal force on the wall (N) | 10348 | 10367 | 10800 | 11139 |

Figure 30.

Figure 31.