RD-E: 1703 Distorted

A steel box beam, fixed at one end and impacted at the other by an infinite mass. Results for distorted meshes 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. Four kinds of mesh and three plasticity formulations are compared (global plasticity, five integration points and iterative plasticity).

Options and Keywords Used

  • Q4 shells
  • 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, the 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_17-56
  • 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 with a fixed velocity (13.3 m/s) in the Z-direction and 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 in 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 (/MAT/LAW2) with 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 beams are modeled with different kinds of mesh, all having 56 elements in length and 8 in height. The layout of the elements is shown in Figure 3.

The following are tested for each model:
  • Element formulation:
    • BT_TYPE1
    • BT_TYPE3
    • QEPH
    • BATOZ
    • C0
    • DKT18
  • Plasticity:
    • Global plasticity
    • Progressive plasticity with five integration points
    • Iterative plasticity with five integration points and variable thickness
Figure 3. Meshes

fig_17-55

Results

The results are compared using three different views:
  • Role and influence of the mesh for a given type of element Formulation
  • Shell element formulations for a given mesh.
  • Plasticity options for a given mesh and element Formulation
Three criteria are used to compare the quality of the results obtained:
  • Crushing force versus displacement

    The crushing force corresponds to the normal force in the Z-direction of the impactor (rigid wall), multiplied by 4 due to symmetry.

    For comparison, displacement corresponds to the Z-direction motion of the rigid wall's main node.

  • Hourglass energy
  • Total energy

    Total absorption energy is the sum of internal energy and hourglass energy.

Mesh Influence of a Given Shell Using Global Plasticity and BT_TYPE3 Formulation

Figure 4. Total Energy for a BT_TYPE3 Formulation

fig_17-57
Figure 5. Hourglass Energy for a BT_TYPE3 Formulation

fig_17-58
Figure 6. Force for a BT_TYPE3 Formulation

fig_17-59

Influence of Element Formulation Using Mesh 1 and Global Plasticity

Figure 7. Total Energy for Different Element Formulation

fig_17-60
Figure 8. Total Energy for Different Element Formulation

fig_17-61
Figure 9. Hourglass Energy for Different BT Element Formulation

fig_17-62
Figure 10. Force for Different Element Formulation

fig_17-63
Figure 11. Force for Different Element Formulation

fig_17-64

Influence of Plasticity Options Using Mesh 0 and BT_TYPE3 Formulation

Figure 12. Total Energy

fig_17-65
Figure 13. Hourglass Energy

fig_17-66
Figure 14. Crushing Force

fig_17-67
Figure 15. MESH 0

ex_17_mesh_000
Figure 16. MESH 1

ex_17_mesh_1-1-1
Figure 17. MESH 2

ex_17_mesh_2-2-2
Figure 18. MESH 3

ex_17_mesh_3-3-3
Figure 19. Formulation: BT_TYPE1

ex_17_mesh_qeph2
Figure 20. Formulation: BT_TYPE3

ex_17_mesh_bt_type3-3
Figure 21. Formulation: BT_TYPE4

ex_17_mesh_4
Figure 22. Formulation: QEPH

ex_17_mesh_batoz
Figure 23. Formulation: BATOZ

ex_17_mesh_dkt18-1
Figure 24. Formulation: DKT18

ex_17_mesh_co-1
Figure 25. Formulation: C0

ex_17_mesh_a

Conclusion

The crash of a box beam using several meshes and finite element formulations was studied in detail. The simulation results for uniform, mapped and transit meshes are classified and compared for each different shell formulation. The results obtained illustrate the sensitivity of the shell elements with respect to the quality of the mesh for a typical crash problem.