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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.

The present formulation considered four cross-sectional configurations as shown in below picture


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


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  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. Ali 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).
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