Document Type : Research Paper

Authors

Faculty of Materials and Manufacturing Technologies, Malek Ashtar University of Technology, Tehran, Iran.

Abstract

In this paper, the parametric analysis of the impact on cylindrical sandwich shells with the FML face sheet and functionally graded core using a new shell theory is discussed. In this research, two new, simple and engineering models have been presented to predict the history of the contact force caused by a quasi-static transverse impact by an elastic and isotropic impactor in the shape of a sphere, with a low speed, to a composite cylindrical shell. These two models are the half-sine model (or H-S) and the improved mass and spring model with two degrees of freedom (or IS-M). In the H-S model, the maximum contact force and contact duration have been extracted analytically. In the IS-M model, first the mass and the effective stiffness of the shell at the contact point are calculated analytically, then using the successive method and reaching convergence, the modified contact stiffness is obtained. Validation of the present research results was done by comparing the theoretical and experimental results of other researchers and the results of the ABAQUS software, and a good match has been achieved. The results show that the more accurately the effect of (z/R + 1) terms are calculated, the higher the accuracy of estimating the impact response.

Keywords

Main Subjects

[1] Gong S.W., Lam K.Y., “Rotating multilayered cylindrical shells to impact loading”, AIAA Journal, Vol. 41, No. 1: Technical Notes, pp. 139-142, 2002.
[2] Krishnamurthy K.S., Mahajan P., Mittal R.K., “Impact response and damage in laminated composite cylindrical shells”, Composite Structures, Vol. 59, pp. 15-36, 2003.
[3] Dubinin V.V., Bannikov S.N., “The experimental investigation of the impact of a particle or a rigid body on a cylindrical shell”, Progress in Nuclear Energy, Vol. 43, No. 1-4, pp. 253-260, 2003.
[4]Tsunokake H., Kobayashi H., Araki H., “Impact response of transversely isotropic circular cylindrical shells”, Structures and Materials, Vol. 15, Structures Under Shock and Impact VIII, pp. 485-493, 2004.
[5] Gning P.B., Tarfaoui M., Collombet F., Davies P., “Prediction of damage in composite cylinders after impact”, Journal of Composite Materials, Vol. 39, No. 10, pp. 917-928, 2005.
[6] Jafari A.A., Khalili S.M.R., Azarafza R., “Transient dynamic response of composite circular cylindrical shells under radial impulse load and axial compressive loads”, Thin-Walled Structures, Vol. 43, pp. 1763–1786, 2005.
[7] Azarafza R., "Weight and dynamic optimization of multi-layer composite cylindrical shells", PhD thesis, Khajeh Nasiruddin Toosi University of Technology, Tehran, Iran, 2014, In persian.
[8] Kumar S., Nageswara Rao B., Pradhan B., “Effect of impactor parameters and laminate characteristics on impact response and damage in curved composite laminates”, Journal of Reinforced Plastics and Composites, Vol. 26, No. 13, pp. 1273-1290, 2007.
[9] Khalili S.M.R., Azarafza R., Davar A., “Transient dynamic response of initially stressed composite circular cylindrical shells under radial impulse load”, Composite Structures, Vol. 89, pp. 275–284, 2009.
[10] Ahmadi I., Sadighi M., “Finite element analysis of low-velocity impact on functionally graded cylindrical shell”, 17th Annual (International) Conference on Mechanical Engineering, Tehran Universiy, Tehran, Iran, Paper code: ISME-2009-2520, May 19-21 2009.
[11] Setoodeh A., Enferadi M., “Effect of structural damping on dynamic response of laminated cylindrical shell subjected to low velocity impact”, 17th Annual (International) Conference on Mechanical Engineering, Tehran Universiy, Tehran, Iran, Paper code: ISME-2009-1722, May 19-21 2009.
[12] Rahmani O., Khalili S.M.R., Malekzadeh K., “Free vibration response of composite sandwich cylindrical shell with flexible core”, Composite Structures, Vol. 92, pp. 1269-1281, 2010.
[13] Bayat M.R., Rahmani O., Mousavi Mashhadhi M., “dynamic analysis of composite cylinders reinforced with carbon nanotubes under low speed impact”, 24th annual international conference of mechanical engineering of Iran, Yazd, May 2015, In persian.
[14] Mamandi A., Salimzadeh M., “Analysis of nonlinear vibrations of composite cylindrical shell with internal pressure against low speed impact using analytical methods and finite elements”, Aerospace Mechanics, Volume 16, Number 3, pp. 59-73, 2019, In persian.
[15] Zhao, G., Hooman, M., Yarigarravesh, M., Algarni, M., Opulencia, M.J.C., Alsaikhan, F., Jalil, A.T., Mohamed, A., AboRas, K.M., Rahman, M.L. and Sarjadi, M.S., “Vibration analysis of size dependent micro FML cylindrical shell reinforced by CNTs based on modified couple stress theory”. Arabian Journal of Chemistry, 15(10), p.104115, 2022.
[16] Suresh S., Mortensen A., “Fundamentals of functionally graded materials”, London, UK: IOM Communications Limited, 1998.
[17] Rao S.S., “Mechanical vibrations”, 2nd edition, Addison Wesley, 1990.
[18] Gong S.W., “A study of impact on composite laminated shells”, Ph.D. Dissertation, National University of Singapore, 1995.
[19] Chandrashekhara K., Schroeder T., “Nonlinear impact analysis of laminated cylindrical and doubly curved shells”, Journal of Composite Materials, Vol. 29, pp. 2160-2179, 1995.
[20] Kistler L.S., Waas A.M., “Impact response of cylindrically curved laminates including a large deformation scaling study”, International Journal of Impact Engineering, Vol. 21, No. 1-2, pp. 61-75, 1998.
[21] Ganapathy S., Rao K.P., “Interlaminar stresses in laminated composite plates cylindrical spherical shell panels damaged by low velocity impact”, Composite Structures, Vol. 38, No. 1-4, pp. 157-168, 1997.
[22] Matemilola S.A., Stronge W.J., “Impact response of composite cylinders”, International Journal of Solids and Structures, Vol. 34, No. 21, pp. 2669-2684, 1997.
[23] Christoforou A.P., Swanson S.R., “Analysis of simply-supported orthotropic cylindrical shells subjected to lateral impact loads”, Journal of Applied Mechanics, Vol. 57, Issue 2, pp. 376-382, 1990.
 
[24] Shivakumar K.N., Elber W., Illg W., “Prediction of impact force and duration due to low-velocity impact on circular composite laminates”, Journal of Applied Mechanics, Vol. 52, pp. 674-680, 1985.
 [25] Apetre N.A., Sankar B.V., Ambur D.R., “Low-velocity impact response of sandwich beams with functionally graded core”, International Journal of Solids and Structures, Vol. 43, pp. 2479–2496, 2006.
[26] Choi I.H., Hong C.S., “New approach for simple prediction of impact force history on composite laminates”, AIAA Journal , Vol. 32, No. 10, pp. 2067-2072, 1994.
[27] Choi I.H., Lim C.H., “Low-velocity impact analysis of composite laminates using linearized contact law”, Composite Structures, Vol. 66, pp. 125–132, 2004.
[28] Yang S.H., Sun C.T., “Indentation law for composite laminates”, In Composite Material: Testing and Design, pp. 425-449, ASTM STP 787, Philadelphia PA, 1982.
[29] Greszczuk L.B., “Impact Dynamics”, John Wiley & Sons, pp. 55-94, New York, 1982.
[30] Pashah S., Massenzio M., Jacquelin E., “Prediction of structural response for low velocity impact”, International Journal of Impact Engineering, Vol. 35, pp. 119–132, 2008.
[31] Soedel W., “Vibrations of shells and plates”, 3rd Edition, Revised and Expanded, Marcel Dekker, Inc., New York, 2004.
[32] Zhou D.W., Stronge W.J., “Low velocity impact denting of HSSA lightweight sandwich panel”, International Journal of Mechanical Sciences, Vol. 48, pp. 1031–1045, 2006.
[33] Swanson S.R., “Limits of quasi-static solutions in impact of composite structures”, Composites Engineering, Vol. 2, No. 4, pp. 261–267, 1992.
[34] Abrate S., “Impact on composite structures”, Cambridge University Press, US, 1998.
[35] Khalili S.M.R., Mittal R.K., Mohammad Panah N., “Analysis of fiber reinforced composite plates subjected to transverse impact in the presence of initial stresses”, Composite Structures, Vol. 77, pp. 263–268, 2007.