RD-E: 1702 Transitions

A steel box beam, fixed at one end, impacted at the other end by an infinite mass. Results for meshes with different transitions are compared.

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 TYPE 7 interface as the input surface.

    fig_17-28
    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 by a sliding rigid wall using 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

The input files used in this example include:
Mesh 0
<install_directory>/hwsolvers/demos/radioss/example/17_BoxBeam/Transition_mesh/mesh0/.../BOXBEAM*
Mesh 1
<install_directory>/hwsolvers/demos/radioss/example/17_BoxBeam/Transition_mesh/mesh1/.../BOXBEAM*
Mesh 2
<install_directory>/hwsolvers/demos/radioss/example/17_BoxBeam/Transition_mesh/mesh2/.../BOXBEAM*
Mesh 3
<install_directory>/hwsolvers/demos/radioss/example/17_BoxBeam/Transition_mesh/mesh3/.../BOXBEAM*

Model Description

Units: mm, ms, g, N, MPa

The material used follows an isotropic elasto-plastic material (/MAT/LAW2) with the Johnson-Cook plasticity model, having the following characteristics:
Material Properties
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@

fig_17-1
Figure 2. Problem Studied

Model Method

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

fig_17-27
Figure 3. Meshes

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 energy is the sum of all energies.

Mesh Influence for a Given Shell Using Global Plasticity


fig_17-29
Figure 4. Total Energy for a BATOZ Formulation

fig_17-30
Figure 5. Force for a BATOZ Formulation


fig_17-31
Figure 6. Total Energy for a QEPH Formulation

fig_17-32
Figure 7. Force for a QEPH Formulation


fig_17-33
Figure 8. Total Energy for a BT_TYPE1 Formulation

fig_17-34
Figure 9. Hourglass Energy for a BT_TYPE1 Formulation

fig_17-35
Figure 10. Force for a BT_TYPE1 Formulation


fig_17-36
Figure 11. Total Energy for a BT_TYPE3 Formulation

fig_17-37
Figure 12. Hourglass Energy for a BT_TYPE3 Formulation

fig_17-38
Figure 13. Force for a BT_TYPE3 Formulation


fig_17-39
Figure 14. Total Energy for a BT_TYPE4 Formulation

fig_17-40
Figure 15. Hourglass Energy for a BT_TYPE4 Formulation

fig_17-41
Figure 16. Force for a BT_TYPE4 Formulation


fig_17-42
Figure 17. Total Energy for a CO Formulation

fig_17-43
Figure 18. Force for a CO Formulation


fig_17-44
Figure 19. Total Energy for a DKT Formulation

fig_17-45
Figure 20. Force for a DKT Formulation

Influence of Element Formulation Using Mesh 3 and Global Plasticity


fig_17-46
Figure 21. Total Energy for Different Element Formulations

fig_17-47
Figure 22. Total Energy for Different Element Formulations

fig_17-48
Figure 23. Hourglass Energy for Different Element Formulations

fig_17-49
Figure 24. Force for Different Element Formulations

fig_17-50
Figure 25. Displacements for Different Element Formulations

Influence of Plasticity Options Using Mesh 1 and BT_TYPE3 Formulation


fig_17-51
Figure 26. Total Energy for Different Plasticity Computations

fig_17-52
Figure 27. Hourglass Energy for Different Plasticity Computations

fig_17-53
Figure 28. Force for Different Plasticity Computations

ex_17_mesh_00
Figure 29. MESH 0

ex_17_mesh_1-1
Figure 30. MESH 1

ex_17_mesh_2-2
Figure 31. MESH 2

ex_17_mesh_3-3
Figure 32. MESH 3

ex_17_mesh_qeph
Figure 33.

ex_17_mesh_bt_type1
Figure 34. Formulation: QEPH

ex_17_mesh_bt_type3
Figure 35. Formulation: BT_TYPE1

ex_17_mesh_bt_type4
Figure 36. Formulation: BT_TYPE3

ex_17_mesh_co
Figure 37. Formulation: BT_TYPE4

ex_17_mesh_dkt18
Figure 38. Formulation: C0

ex_17_mesh
Figure 39. Formulation: DKT18

ex_17_table
Figure 40.

ex_17_table2
Figure 41.