Axial Crushing of Multi-Cell Multi-Corner Tubes

An analytical formula for the prediction of mean crush force of multicorner multi-cell tubes is derived based on the super folding element theory ^{[1] [2] [3]} The analytical predictions for the mean crush force are found to be in good agreement with the FE solutions. Results also show a strong correlation between the cross-sectional geometry and the crash behavior with the method of connecting the inner to the outer walls having large influence on the energy absorption, as shown in the comparison of two configurations in Figure 1.

Figure 1. Comparison of Crush Behavior for Two Cross-sectional Configurations

The present formulation considered four cross-sectional configurations as shown in Figure 2.

Figure 2. Considered Cross-sectional configurations

Theoretical Aspect

The theoretical aspect including the derivation of equations and the plastic approach can be found in links below:

Multi-CRUSH 			*
|-- README.txt 			*this file
|				
|-- doc				* Documentation: license info, help files, and reports
|   |-- README.doc.txt		* doc README
|   |-- AIAA-2008-2014-577.pdf	* SDM Paper on the early developement of analytical model and finite element results for dynamic cases
|   |-- SDM-Tube_2008_6.ppt	* Presentation file for the above SDM paper
|   |-- Najafi_MS_thesis.pdf	* Master thesis contains detail description and derivation of analytical model
|   |-- TWS_UNDER REVIEW.pdf	* Journal paper that is under review in Thin Walled Structures
|   |-- UserLicence		* Help file to use mathematica codes
`-- src 			* Source files
     |
     |-- README.src.txt		* src README
     |-- mathematica 			* Source files
     |    |				* Mathematica source file
     |    |-- C2CNEW_Revised1.nb	* implementation of the analytical model for corner to corner cross-sectional configuration
     |    |-- C2WNEW_Revised1.nb	* implementation of the analytical model for corner to web cross-sectional configuration
     |    |-- W2CNEW_Revised1.nb	* implementation of the analytical model for web to corner cross-sectional configuration
     |    `-- W2WNEW_Revised1.nb	* implementation of the analytical model for web to web cross-sectional configuration
     `-- lsdyna-validation 			* Source files
          |				* Mathematica source file
          |-- c2cp.k			* lsdyna input file for c2c configuration
          |-- c2wp.k			* lsdyna input file for c2w configuration
          |-- w2cp.k			* lsdyna input file for w2c configuration
          `-- w2wp.k			* lsdyna input file for w2w configuration 

Figure 3. Representative FEA Result of Crush Behavior

References

1. ↑ Ali Najafi, Masoud Rais-Rohani, “Mechanics of axial plastic collapse in multi-cell, multi-corner crush tubes,” Thin-Walled Structures 49 (2011): 1–12.
2. ↑ Najafi, & Masoud Rais-Rohani, (Apr 2008), “Influence of Cross-Sectional Geometry on Crash Characteristics of Crush Tubes”, proceedings of 49th AIAA/ASME/ASC/AHS/ASC Structures, Structural Dynamics and Materials Conference, Schaumburg, Il.
3. ↑ Ali Najafi, “Axial Collapse Of Thin-Walled, Multi-Corner Single- And Multi-Cell Tubes” (Master's thesis, Mississippi State University, 2009).