[1] Ru-Yang Yao, Wen-Qian Hao, Guan-Sheng Yin , Bei Zhang. Analytical model of circular tube with wide external circumferential grooves under axial crushing, International Journal of Crashworthiness. DOI: 10.1080/13588265.2019.1617096.
[2]Vivek PATEL, Gaurav TIWARI, Ravikumar DUMPALA .Review of the crushing response of collapsible tubular structures. Front. Mech. Eng. 2020, 15(3): 438–474 https://doi.org/10.1007/s11465-019-0579-1.
[3] Alexander J. An approximate analysis of the collapse of thin cylindrical shells under axial loading. Quarterly Journal of Mechanics and Applied Mathematics, 1960, 13(1): 10–15.
[ 4] Abramowicz W, Jones N. Dynamic axial crushing of circular tubes. International Journal of Impact Engineering. 1984, 2(3): 263–281.
[5] Jones N. Energy-absorbing effectiveness factor. International Journal of Impact Engineering. 2010, 37(6): 754–765 .
[6] Luo X, Xu J, Zhu J. A new method to investigate the energy absorption characteristics of thin-walled metal circular tube using finite element analysis. Thin-Walled Structures. 2015, 95: 24–30.
[7] Singace A A, Elsobky H, Reddy T Y. On the eccentricity factor in the progressive crushing of tubes. International Journal of Solids and Structures. 1995, 32(24): 3589–3602 .
[8] Gupta N, Gupta S. Effect of annealing, size and cut-outs on axial collapse behavior of circular tubes. International Journal of Mechanical Sciences. 1993, 35(7): 597–613.
[9] Karagiozova D, Jones N. Dynamic effects on buckling and energy absorption of cylindrical shells under axial impact. Thin-Walled Structures, 2001, 39(7): 583–610 .
[10] Farmani S M , Babaei H, Alitavoli M, Haghgoo M. Numerical and Experimental Investigation of Deformation of Circular Sandwich Plates with Vertical Metal Tube Core Under Free Blast Load, Modares Mechanical Engineering. 2023;23(12):673-683
[11] H M Wen a , T. X. Yu a , TY Reddy. A Note on Clamped Circular Plates under Impulsive Loading. Mechanics of Structures and Machines: An International Journal. 2007. doi.org/10.1080/08905459508905241.
[12] farmani M, Shamami M Z, Alitavoli M. Experimental and analytical study of transverse displacement of plates in a circular sandwich structure with vertical metal tube cores under free blast load. Modares Mechanical Engineering.
[13] Gerami A.Vahidi H.Ahmadi H.Liaghat G. Experimental Analysis of Impact Loading on Sandwich Panels with Glass/Epoxy Composite Faces and Cork Core. Modares Mechanical Engineering. 2025;25(01):55-63.
[14] Khodaeipour B, Khodarahmi H ,SadeghYazdi M, Ziya-Shamami M. Numerical and Experimental Study of Damage in Multi-Compartment Armor due to UNDEX. Modares Mechanical Engineering. 2024;24(08):499-509.
[15] Motamedi MA , Hashemi R. Evaluation of Temperature Effects on Forming Limit Diagrams of AA6061-T6 Considering the Marciniak and Kuczynski Model. Journal of Testing and Evaluation. 2019 Jun 28;49(2),PP.854-65.
[16] Corbett.b.m, Numerical simulations of target hole diameters for hypervelocity impacts into elevated and room temperature bumpers. International Journal of Impact Engineering. 33 (2006) 431–440.
[17] Farahani A, Hadianfard M A. Blast Loading and Evaluation of Nonlinear Response of Structural Buildings, Ferdowsi Journal of Civil Engineering. 2013;26,1.
[18] Unified Facilities Criteria (UFC). Structures to Resist the Effects of Accidental Explosions, U. S. Army Corps of Engineers, Naval Facilities Engineering Command, Air Force Civil Engineer Support Agency, UFC 3-340-02, 5 December (2008).
[19]. Abramowicz W, Jones N. Dynamic axial crushing of square tubes. International Journal of Impact Engineering. 1984, 2(2): 179–208
[20] Darvizeh.A,Gharababaei.H, Darvizeh. M, Analytical and experimental studies for deformation of circular plates subjected to blast loading. Journal of Mechanical Science and Technology .24 (9) (2010) 1855~1864, DOI 10.1007/s12206-010-0602-2.
[21].F. Mokhtarnezhada, S. Salehghaffaria and M. Tajdari .Improving the crashworthiness characteristics of cylindrical tubes subjected to axial compression by cutting wide grooves from their outer surface . International Journal of Crashworthiness. Vol. 14, No. 6, December 2009, 601–611 ,DOI: 10.1080/13588260902896466.
[22]- Jones. N.Structural impact, Cambridge university press; 2011 Dec 26.
[23] Farmani S M, Alitavoli, M, Babaei H .Investigation of dynamic response of circular sandwich plates with metal vertical tubes core under blast load. J Braz. Soc. Mech. Sci. Eng.2024 ;46, 150 https://DOI.org/10.1007/s40430-024-04707-2

[24] DarvizehA,Gharababaei H. Experimental and Analytical Investigation of Large Deformation of Thin Circular Plates Subjected to Localized and Uniform Impulsive Loading. Mechanics Based Design of Structure and Machines: An International Journal, 38:2, 171-189.
[25] Mirzababaie MT, Babaei H, Alitavoli M. Theoretical analysis on the effect of uniform and localized impulsive loading on the dynamic plastic behavior of fully clamped thin quadrangular plates. Thin-Walled Struct. 109 (2016),PP. 367–376.
[26] Hanssen AG, Langseth M, Hopperstad OS. Static and dynamic crushing of square aluminium extrusions with aluminium foam filler, Int. J. Impact Eng. 24 (5) (1999) 475–507.
[27] Zhang X, Leng K, Zhang H. Axial crushing of embedded multi-cell tubes. Int. J.Mech. Sci. 131–132 (2017) 459–470.
[28] P.s.Westine and W.E. Baker , Energy solution for predicting deformation in blast loaded structures, proc.19 th Explosive safety seminar, Hollywood Beach,Florida,U.S.A, PP.849-879(1974).
[29] Zaera R, Arias A, Navarro C.Analytical Modeling of Metallic Circular Plates to Impulsive Loads. Int. J. Solids and Structures. 2002; Vol. 39, PP 659-672 .
[30] Liaghat G H , Azad S. Z. Analysis of explosive and moldless forming of two-layer circular sheet with Using the principle of energy conservation .Journal of Algorithms and Computation. Modares Mechanical Engineering. 1387;42(1):1862-
10.22059/JAC.2013.7734
[31] Wai Fah C. Plasticity for Structural Engineers. Springer; 1st edition (1988).