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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 [[image:Crush.JPG|right]] element theory <ref>
[http://www.sciencedirect.com/science/article/pii/S0263823110001126 'Ali Najafi, Masoud Rais-Rohani, “Mechanics of axial plastic collapse in multi-cell, multi-corner crush tubes,” ''Thin-Walled Structures'' 49 (2011): 1–12.] </ref>,<ref>[[Media:AIAA-2008-2014-577.pdf| 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.'']]</ref>,<ref>[[Media:NajafiFinalA.pdf| Ali Najafi, “Axial Collapse Of Thin-Walled, Multi-Corner Single- And Multi-Cell Tubes” (Master's thesis, Mississippi State University, 2009).]]
</ref>. 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


[[image:Multi-celltubes.JPG|left]]




















==Theoretical Aspect==



















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

 

<pre>
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
</pre>

[[image:Crush1.JPG]]



[[SRCLID:Simulation-Based Design Optimization|go back to Simulation-Based Design Optimization]]

= References =
<references/>

[[Category:Structural Scale]]