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 Investigation of energy absorption properties of thin-walled variable thickness tubes  Determination of the thickness change of variable thickness tubes by optimization method  Comparison of forcedisplacement graphs of fixed thickness and variable thickness tubes Figure A. Mullti-objective optimization process of functionally graded tubs (FGT) Purpose: This study aims to numerically investigate the energy absorption behavior of functionally graded tubes. Theory and Methods: Numerical simulation and multi-objective optimization analysis were performed by Ls_Dyna software included Ls-Opt module. The optimum layer thickness determined according to highest specific energy absorption and lower peak force. Results: As a result of optimization, the optimum layer thicknesses for 0 °, 5 ° and 10 ° taper angles range from 0.53 mm to 3.90 mm, 0.53 mm to 3.96 and 0.55 mm to 3.97 mm, respectively. Conclusion: 5° taper angle tubes gives the highest peak force and absorbed energy values compared 0° and 10° tubes for fixed thickness tubes. Absorbed energy and peak force values increased with increasing layer thickness. It is possible to obtain low peak force and high specific energy absorption at the same time by optimization of VTT layer thicknesses. .

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