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 main surface is defined using the complete model. The secondary nodes group is defined using the main surface.

    On top of the beam, possible edge-to-edge impacts are dealt with using a TYPE11 self-impacting interface. The edges use the main surface of the TYPE7 interface as the input surface.
    Figure 1. Boundary Conditions

    fig_17-3
  • 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

Before you begin, copy the file(s) used in this example to your working directory.

Model Description

Units: mm, ms, g, N, MPa

The material used follows an isotropic elasto-plastic material (/MAT/LAW2) using the Johnson-Cook plasticity model, with the following characteristics:
Material Properties
Value
Initial density
7.8 x 10-3 [ g m m 3 ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada WcaaqaaiaadEgaaeaacaWGTbGaamyBamaaCaaaleqabaGaaG4maaaa aaaakiaawUfacaGLDbaaaaa@3BBC@
Young's modulus
210000 [ MPa ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWadaqaai Gac2eacaGGqbGaaiyyaaGaay5waiaaw2faaaaa@3BE6@
Poisson ratio
0.3
Yield stress
206 [ MPa ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWadaqaai Gac2eacaGGqbGaaiyyaaGaay5waiaaw2faaaaa@3BE6@
Hardening parameter
450 [ MPa ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWadaqaai Gac2eacaGGqbGaaiyyaaGaay5waiaaw2faaaaa@3BE6@
Hardening exponent
0.5
Maximum stress
340 [ MPa ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWadaqaai Gac2eacaGGqbGaaiyyaaGaay5waiaaw2faaaaa@3BE6@
Figure 2. Problem Studied

fig_17-1

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.

For each model, several element formulations are tested:
  • BT_TYPE1
  • BT_TYPE3
  • BT_TYPE4
  • QEPH
  • BATOZ
  • C0 (T3 element)
  • DKT18 (T3 element)
Figure 3. Meshes

fig_17-2

The 3-node shell mesh is obtained by dividing the 4-node shell elements.

Results

The results are compared using two different views:
  • Role and influence of the mesh for a given type of element formulation
  • The shell element formulations for a given mesh
Three criteria are used to compare the quality of results obtained:
  • 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 main 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

fig_17-4
Figure 5. Force for a BATOZ Formulation

fig_17-5
Figure 6. Total Energy for a QEPH Formulation

fig_17-6
Figure 7. Force for a QEPH Formulation

fig_17-7
Figure 8. Total Energy for a BT_TYPE1 Formulation

fig_17-8
Figure 9. Hourglass Energy for a BT_TYPE1 Formulation

fig_17-9
Figure 10. Force for a BT_TYPE1 Formulation

fig_17-10
Figure 11. Total Energy for a BT_TYPE3 Formulation

fig_17-11
Figure 12. Hourglass Energy for a BT_TYPE3 Formulation

fig_17-12
Figure 13. Force for a BT_TYPE3 Formulation

fig_17-13
Figure 14. Total Energy for a BT_TYPE4 Formulation

fig_17-14
Figure 15. Hourglass Energy for a BT_TYPE4 Formulation

fig_17-15
Figure 16. Force for a BT_TYPE4 Formulation

fig_17-16
Figure 17. Total Energy for a CO Formulation

fig_17-17
Figure 18. Force for a CO Formulation

fig_17-18
Figure 19. Total Energy for a DKT Formulation

fig_17-19
Figure 20. Force for a DKT Formulation

fig_17-20

Influence of Element Formulation using Mesh 3

Figure 21. Total Energy for Different Element Formulations

fig_17-21
Figure 22. Total Energy for Different Element Formulations

fig_17-22
Figure 23. Hourglass Energy for Different Element Formulations

fig_17-23
Figure 24. Displacement for Different Element Formulations

fig_17-24
Figure 25. Displacement for Different Element Formulations

fig_17-25
Figure 26. MESH 0

ex_17_mesh_0
Figure 27. MESH 1

ex_17_mesh_1
Figure 28. MESH 2

ex_17_mesh_2
Figure 29. MESH 3

ex_17_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
Table 1. Formulation: QEPH
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
Table 2. Formulation: BT_TYPE1
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
Table 3. Formulation: BT_TYPE3
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
Table 4. Formulation: BT_TYPE4
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
Table 5. Formulation: C0
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
Table 6. Formulation: DKT18
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.

ex_17_mesh_table2-1
Figure 31.

ex_17_mesh_table2-2