Overview

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Physical Problem Description

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).

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:

 

Fig 54: Problem studied.

Analysis, Assumptions and Modeling Description

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Modeling Methodology

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 the following diagram.

The following are tested for each model:

Fig 55: Meshes.

RADIOSS Options Used

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.

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.

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.

The structure’s self-impact is modeled using a type 7 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, the possible edge-to-edge impacts are dealt with using a type 11 self-impacting interface. The edges use the master surface of the type 7 interface as the input surface.

Fig 56: Boundary conditions.

Simulation Results and Conclusions

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The results are compared using three different views:

Three criteria are used to compare the quality of the results obtained:

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 master node.

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

Fig 57: Total energy for a BT_TYPE3 formulation.

Fig 58: Hourglass energy for a BT_TYPE3 formulation.

Fig 59: Force for a BT_TYPE3 formulation.

Influence of Element Formulation Using Mesh 1 and Global Plasticity

Fig 60: Total energy for different element formulation.

Fig 61: Total energy for different element formulation.

Fig 62: Hourglass energy for different BT element formulation.

Fig 63: Force for different element formulation.

Fig 64: Force for different element formulation.

Influence of Plasticity Options Using Mesh 0 and BT_TYPE3 Formulation

Fig 65: Total energy.

Fig 66: Hourglass energy.

Fig 67: Crushing force.

MESH 0

MESH 1

MESH 2

MESH 3

Formulation:  BT_TYPE1

Formulation:  BT_TYPE3

Formulation:  BT_TYPE4

Formulation:  QEPH

Formulation:  BATOZ

Formulation:   DKT18

Formulation:   C0

Conclusion

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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.