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Low-velocity impact analysis of laminated composite plates and shells with generalized differential quadrature method

Year 2020, Volume: 3 Issue: 1, 1 - 24, 30.06.2020

Abstract

In this article, low-velocity impact analysis of laminated composite plates and shells for small and large displacements is investigated using Generalized Differential Quadrature (GDQ) method. Equation of motion for impact system is derived using virtual work principle. First-order shear deformation theory (FOST) is employed to consider transverse shear effects and Von-Karman nonlinear strain-displacement relationships are used in large displacement analyses. Spatial derivatives are expressed with GDQ method and time integration of dynamic equations is performed using Newmark average acceleration method. Several laminated composite impact problems from the literature are solved with the proposed method. Very close results are obtained with the
literature using only limited number of grids, showing the efficiency of the method in contact-impact problems.

References

  • [1]Karas, K. (1939). Platten unter seitlichen stoss. Ingenieur Archiv, 10, 237-250. doi:10.1007/bf02084907 [2] Chen, J.K., Sun, C. T. (1985). Dynamic large deflection response of composite laminates subjected to impact. Composite Structures, 4(1), 59-73. doi: 10.1016/0263-8223(85)90020-0 [3] Sun, C. T., Chen, J. K. (1985). On the Impact of Initially Stressed Composite Laminates. Journal of Composite Materials, 19(6), 490-504. doi:10.1177/002199838501900601 [4] Wu, H.-Y. T., Chang, F.-K. (1989). Transient dynamic analysis of laminated composite plates subjected to transverse impact. Computers & Structures, 31(3), 453-466. doi: 10.1016/0045-7949(89)90393-3 [5] Cairns, D. S., Lagace, P. A. (1989). Transient response of graphite/epoxy and kevlar/epoxy laminates subjected to impact. AIAA Journal, 27( 11), 1590-1596. doi: 10.2514/3.10306 [6] Liou, W. J. (1997). Impact analysis of laminated composite plates with statical indentation laws. Computers & Structures, 62 (5), 817-829. doi: 10.1016/S0045-7949(96)00317-3 [7] Chun, L., Lam, K. Y. (1998). Dynamic response of fully-clamped laminated composite plates subjected to low-velocity impact of a mass. International Journal of Solids and Structures, 35(11), 963-979. doi: 10.1016/S0020-7683(96)00231-4 [8] Vaziri, R., Quan, X., Olson, M. D. (1996). Impact analysis of laminated composite plates and shells by super finite elements. International Journal of Impact Engineering, 18(7), 765-782. doi: 10.1016/S0734-743X(96)00030-9 [9] Karmakar, A., Sinha, P. K. (1998). Finite element transient dynamic analysis of laminated composite pretwisted rotating plates subjected to impact. International Journal of Crashworthiness, 3 (4), 379-392. doi: 10.1533/cras.1998.0085 [10] Her, S.-C., Liang, Y. C. (2004). The finite element analysis of composite laminates and shell structures subjected to low velocity impact. Composite Structures, 66(1–4), 277-285. doi: 10.1016/j.compstruct.2004.04.049 [11] Choi, I. H., Lim, C. H. (2004). Low-velocity impact analysis of composite laminates using linearized contact law. Composite Structures, 66(1–4), 125-132. doi: 10.1016/j.compstruct.2004.04.030 [12] Karmakar, A., Kishimoto, K. (2006). Transient dynamic response of delaminated composite rotating shallow shells subjected to impact. Shock and Vibration, 13(6), 619-628. doi: 10.1155/2006/645949 [13] Tiberkak, R., Bachene, M., Rechak, S., Necib, B. (2008). Damage prediction in composite plates subjected to low velocity impact. Composite Structures, 83(1), 73-82. doi: 10.1016/j.compstruct.2007.03.007 [14] Kumar, S. (2008). Analysis of impact response and damage in laminated composite shell involving large deformation and material degradation. Journal of Mechanics of Materials and Structures, 3(9), 1741-1756. [15] Khalili S. M. R., Soroush M., Davar A., Rahmani O. (2011). Finite element modeling of low-velocity impact on laminated composite plates and cylindrical shells. Composite Structures, 93(5), 1363–1375. doi: 10.1016/j.compstruct.2010.10.003 [16] Dey, S., Karmakar, A. (2014). Effect of oblique angle on low velocity impact response of delaminated composite conical shells. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 228(15), 2663-2677. doi: 10.1177/0954406214521799 [17] Park, H. (2017). Investigation on low velocity impact behavior between graphite/epoxy composite and steel plate. Composite Structures, 171, 126-130. doi: 10.1016/j.compstruct.2017.03.032 [18] Mao, Y., Hong, L., Ai, S., Fu, H., Chen, C. (2017). Dynamic Response and Damage Analysis of Fiber-Reinforced Composite Laminated plates under low-velocity oblique impact. Nonlinear Dynamics, 87(3), 1511-1530. doi: 10.1007/s11071-016-3130-5 [19] Rout, M., Karmakar, A. (2017). Low velocity impact performance of delaminated composite stiffened shell. Procedia Engineering, 173, 306-313.doi: 10.1016/j.proeng.2016.12.021 [20] Serge, A. (2005). Impact on composite structures. Cambridge University Press, Cambridge.. [21] Bellman, R., Casti, J. (1971). Differential quadrature and long-term integration. Journal of Mathematical Analysis and Applications, 34(2), 235-238. doi: 10.1016/0022-247X(71)90110-7 [22] Bellman, R., Kashef, B. G., Casti, J. (1972). Differential quadrature: A technique for the rapid solution of nonlinear partial differential equations. Journal of Computational Physics, 10(1), 40-52. doi: 10.1016/0021-9991(72)90089-7 [23] Shu, C. (2000). Differential quadrature and its applications in engineering, Springer-Verlag, Great Britain. [24] Bert, C. W., Malik, M. (1996). Differential quadrature method in computational mechanics: A review. Applied Mechanics Reviews, 49(1), 1-28. doi: 10.1115/1.3101882 [25] Chen, C.N. (2006). Discrete element analysis methods of generic differential quadratures. Springer, The Netherlands. [26] Tornabene, F., Fantuzzi, N., Ubertini, F., Viola, E. (2015). Strong formulation finite element method based on differential quadrature: A survey. Applied Mechanics Reviews, 67(2), 020801. doi: 10.1115/1.4028859 [27] Zong, Z., Zhang, Y. (2009). Advanced differential quadrature methods. CRC Press. [28] Hong, C. C. (2010). Transient responses of magnetostrictive plates by using the GDQ method. European Journal of Mechanics - A/Solids, 29(6), 1015-1021. doi: 10.1016/j.euromechsol.2010.07.007 [29] Kurtaran, H. (2015). Large displacement static and transient analysis of functionally graded deep curved beams with generalized differential quadrature method. Composite Structures, 131, 821-831. doi: 10.1016/j.compstruct.2015.06.024 [30] Kurtaran, H. (2015). Geometrically nonlinear transient analysis of thick deep composite curved beams with generalized differential quadrature method. Composite Structures, 128, 241-250. doi: 10.1016/j.compstruct.2015.03.060 [31] Kurtaran, H. (2015). Geometrically nonlinear transient analysis of moderately thick laminated composite shallow shells with generalized differential quadrature method. Composite Structures, 125, 605-614. doi: 10.1016/j.compstruct.2015.02.045 [32] Civalek, Ö. (2005). Geometrically nonlinear dynamic analysis of doubly curved ısotropic shells resting on elastic foundation by a combination of harmonic differential quadrature-finite difference methods. International Journal of Pressure Vessels and Piping, 82(6), 470-479. doi: 10.1016/j.ijpvp.2004.12.003 [33] Civalek, Ö. (2007). Nonlinear analysis of thin rectangular plates on winkler–pasternak elastic foundations by DSC–HDQ methods. Applied Mathematical Modelling, 31(3), 606-624. doi: 10.1016/j.apm.2005.11.023 [34] Viola, E., Miniaci, M., Fantuzzi, N., Marzani, A. (2014). Vibration analysis of multi-stepped and multi-damaged parabolic arches using GDQ. Curved and Layered Structures, 2(1), 28-49. doi: 10.1515/cls-2015-0003 [35] Xing, Y., Liu, B. (2009). High-accuracy differential quadrature finite element method and its application to free vibrations of thin plate with curvilinear domain. International Journal for Numerical Methods in Engineering, 80(13), 1718-1742. doi: 10.1002/nme.2685 [36] Reddy, J. N. (2003). Mechanics of laminated composite plates and shells: theory and analysis, CRC Press.

Tabakalı kompozit levha ve kabukların genelleştirilmiş diferansiyel kuadrature metodu ile düşük çarpma hızlarındaki analizleri

Year 2020, Volume: 3 Issue: 1, 1 - 24, 30.06.2020

Abstract

Bu çalışmada tabakalı kompozit levha ve panellerin düşük çarpma hızlarındaki nonlineer dinamik davranışı Genelleştirilmiş Diferansiyel Kuadrature (Generalized Differential Quadrature) yöntemi ile incelenmektedir. Sistemin dinamik denklemleri Virtüel iş ilkesi ile elde edilmektedir. Düzleme dik doğrultudaki kalınlık etkisi 1. mertebe kayma deformasyon teorisi ile dikkate alınmaktadır. Büyük yer değiştirmeler Von-Karman nonlineer birim şekil değişimleri ile dikkate alınmaktadır. Konumsal türevler Genelleştirilmiş Diferansiyel Quadrature yöntemi ile zaman integrasyonu da Newmark metodu ile hesaplanmaktadır. Önerilen metotla birçok çarpma problemi çözülmüş ve literatürdeki sonuçlarla karşılaştırılmıştır. Önerilen metodun çarpma problemlerinin incelenmesinde etkili ve verimli bir yöntem olduğu gösterilmiştir.

References

  • [1]Karas, K. (1939). Platten unter seitlichen stoss. Ingenieur Archiv, 10, 237-250. doi:10.1007/bf02084907 [2] Chen, J.K., Sun, C. T. (1985). Dynamic large deflection response of composite laminates subjected to impact. Composite Structures, 4(1), 59-73. doi: 10.1016/0263-8223(85)90020-0 [3] Sun, C. T., Chen, J. K. (1985). On the Impact of Initially Stressed Composite Laminates. Journal of Composite Materials, 19(6), 490-504. doi:10.1177/002199838501900601 [4] Wu, H.-Y. T., Chang, F.-K. (1989). Transient dynamic analysis of laminated composite plates subjected to transverse impact. Computers & Structures, 31(3), 453-466. doi: 10.1016/0045-7949(89)90393-3 [5] Cairns, D. S., Lagace, P. A. (1989). Transient response of graphite/epoxy and kevlar/epoxy laminates subjected to impact. AIAA Journal, 27( 11), 1590-1596. doi: 10.2514/3.10306 [6] Liou, W. J. (1997). Impact analysis of laminated composite plates with statical indentation laws. Computers & Structures, 62 (5), 817-829. doi: 10.1016/S0045-7949(96)00317-3 [7] Chun, L., Lam, K. Y. (1998). Dynamic response of fully-clamped laminated composite plates subjected to low-velocity impact of a mass. International Journal of Solids and Structures, 35(11), 963-979. doi: 10.1016/S0020-7683(96)00231-4 [8] Vaziri, R., Quan, X., Olson, M. D. (1996). Impact analysis of laminated composite plates and shells by super finite elements. International Journal of Impact Engineering, 18(7), 765-782. doi: 10.1016/S0734-743X(96)00030-9 [9] Karmakar, A., Sinha, P. K. (1998). Finite element transient dynamic analysis of laminated composite pretwisted rotating plates subjected to impact. International Journal of Crashworthiness, 3 (4), 379-392. doi: 10.1533/cras.1998.0085 [10] Her, S.-C., Liang, Y. C. (2004). The finite element analysis of composite laminates and shell structures subjected to low velocity impact. Composite Structures, 66(1–4), 277-285. doi: 10.1016/j.compstruct.2004.04.049 [11] Choi, I. H., Lim, C. H. (2004). Low-velocity impact analysis of composite laminates using linearized contact law. Composite Structures, 66(1–4), 125-132. doi: 10.1016/j.compstruct.2004.04.030 [12] Karmakar, A., Kishimoto, K. (2006). Transient dynamic response of delaminated composite rotating shallow shells subjected to impact. Shock and Vibration, 13(6), 619-628. doi: 10.1155/2006/645949 [13] Tiberkak, R., Bachene, M., Rechak, S., Necib, B. (2008). Damage prediction in composite plates subjected to low velocity impact. Composite Structures, 83(1), 73-82. doi: 10.1016/j.compstruct.2007.03.007 [14] Kumar, S. (2008). Analysis of impact response and damage in laminated composite shell involving large deformation and material degradation. Journal of Mechanics of Materials and Structures, 3(9), 1741-1756. [15] Khalili S. M. R., Soroush M., Davar A., Rahmani O. (2011). Finite element modeling of low-velocity impact on laminated composite plates and cylindrical shells. Composite Structures, 93(5), 1363–1375. doi: 10.1016/j.compstruct.2010.10.003 [16] Dey, S., Karmakar, A. (2014). Effect of oblique angle on low velocity impact response of delaminated composite conical shells. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 228(15), 2663-2677. doi: 10.1177/0954406214521799 [17] Park, H. (2017). Investigation on low velocity impact behavior between graphite/epoxy composite and steel plate. Composite Structures, 171, 126-130. doi: 10.1016/j.compstruct.2017.03.032 [18] Mao, Y., Hong, L., Ai, S., Fu, H., Chen, C. (2017). Dynamic Response and Damage Analysis of Fiber-Reinforced Composite Laminated plates under low-velocity oblique impact. Nonlinear Dynamics, 87(3), 1511-1530. doi: 10.1007/s11071-016-3130-5 [19] Rout, M., Karmakar, A. (2017). Low velocity impact performance of delaminated composite stiffened shell. Procedia Engineering, 173, 306-313.doi: 10.1016/j.proeng.2016.12.021 [20] Serge, A. (2005). Impact on composite structures. Cambridge University Press, Cambridge.. [21] Bellman, R., Casti, J. (1971). Differential quadrature and long-term integration. Journal of Mathematical Analysis and Applications, 34(2), 235-238. doi: 10.1016/0022-247X(71)90110-7 [22] Bellman, R., Kashef, B. G., Casti, J. (1972). Differential quadrature: A technique for the rapid solution of nonlinear partial differential equations. Journal of Computational Physics, 10(1), 40-52. doi: 10.1016/0021-9991(72)90089-7 [23] Shu, C. (2000). Differential quadrature and its applications in engineering, Springer-Verlag, Great Britain. [24] Bert, C. W., Malik, M. (1996). Differential quadrature method in computational mechanics: A review. Applied Mechanics Reviews, 49(1), 1-28. doi: 10.1115/1.3101882 [25] Chen, C.N. (2006). Discrete element analysis methods of generic differential quadratures. Springer, The Netherlands. [26] Tornabene, F., Fantuzzi, N., Ubertini, F., Viola, E. (2015). Strong formulation finite element method based on differential quadrature: A survey. Applied Mechanics Reviews, 67(2), 020801. doi: 10.1115/1.4028859 [27] Zong, Z., Zhang, Y. (2009). Advanced differential quadrature methods. CRC Press. [28] Hong, C. C. (2010). Transient responses of magnetostrictive plates by using the GDQ method. European Journal of Mechanics - A/Solids, 29(6), 1015-1021. doi: 10.1016/j.euromechsol.2010.07.007 [29] Kurtaran, H. (2015). Large displacement static and transient analysis of functionally graded deep curved beams with generalized differential quadrature method. Composite Structures, 131, 821-831. doi: 10.1016/j.compstruct.2015.06.024 [30] Kurtaran, H. (2015). Geometrically nonlinear transient analysis of thick deep composite curved beams with generalized differential quadrature method. Composite Structures, 128, 241-250. doi: 10.1016/j.compstruct.2015.03.060 [31] Kurtaran, H. (2015). Geometrically nonlinear transient analysis of moderately thick laminated composite shallow shells with generalized differential quadrature method. Composite Structures, 125, 605-614. doi: 10.1016/j.compstruct.2015.02.045 [32] Civalek, Ö. (2005). Geometrically nonlinear dynamic analysis of doubly curved ısotropic shells resting on elastic foundation by a combination of harmonic differential quadrature-finite difference methods. International Journal of Pressure Vessels and Piping, 82(6), 470-479. doi: 10.1016/j.ijpvp.2004.12.003 [33] Civalek, Ö. (2007). Nonlinear analysis of thin rectangular plates on winkler–pasternak elastic foundations by DSC–HDQ methods. Applied Mathematical Modelling, 31(3), 606-624. doi: 10.1016/j.apm.2005.11.023 [34] Viola, E., Miniaci, M., Fantuzzi, N., Marzani, A. (2014). Vibration analysis of multi-stepped and multi-damaged parabolic arches using GDQ. Curved and Layered Structures, 2(1), 28-49. doi: 10.1515/cls-2015-0003 [35] Xing, Y., Liu, B. (2009). High-accuracy differential quadrature finite element method and its application to free vibrations of thin plate with curvilinear domain. International Journal for Numerical Methods in Engineering, 80(13), 1718-1742. doi: 10.1002/nme.2685 [36] Reddy, J. N. (2003). Mechanics of laminated composite plates and shells: theory and analysis, CRC Press.
There are 1 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Articles
Authors

Hasan Kurtaran

Publication Date June 30, 2020
Published in Issue Year 2020 Volume: 3 Issue: 1

Cite

APA Kurtaran, H. (2020). Low-velocity impact analysis of laminated composite plates and shells with generalized differential quadrature method. Artıbilim: Adana Alparslan Türkeş Bilim Ve Teknoloji Üniversitesi Fen Bilimleri Dergisi, 3(1), 1-24.
AMA Kurtaran H. Low-velocity impact analysis of laminated composite plates and shells with generalized differential quadrature method. Artıbilim: Adana Alparslan Türkeş Bilim ve Teknoloji Üniversitesi Fen Bilimleri Dergisi. June 2020;3(1):1-24.
Chicago Kurtaran, Hasan. “Low-Velocity Impact Analysis of Laminated Composite Plates and Shells With Generalized Differential Quadrature Method”. Artıbilim: Adana Alparslan Türkeş Bilim Ve Teknoloji Üniversitesi Fen Bilimleri Dergisi 3, no. 1 (June 2020): 1-24.
EndNote Kurtaran H (June 1, 2020) Low-velocity impact analysis of laminated composite plates and shells with generalized differential quadrature method. Artıbilim: Adana Alparslan Türkeş Bilim ve Teknoloji Üniversitesi Fen Bilimleri Dergisi 3 1 1–24.
IEEE H. Kurtaran, “Low-velocity impact analysis of laminated composite plates and shells with generalized differential quadrature method”, Artıbilim: Adana Alparslan Türkeş Bilim ve Teknoloji Üniversitesi Fen Bilimleri Dergisi, vol. 3, no. 1, pp. 1–24, 2020.
ISNAD Kurtaran, Hasan. “Low-Velocity Impact Analysis of Laminated Composite Plates and Shells With Generalized Differential Quadrature Method”. Artıbilim: Adana Alparslan Türkeş Bilim ve Teknoloji Üniversitesi Fen Bilimleri Dergisi 3/1 (June 2020), 1-24.
JAMA Kurtaran H. Low-velocity impact analysis of laminated composite plates and shells with generalized differential quadrature method. Artıbilim: Adana Alparslan Türkeş Bilim ve Teknoloji Üniversitesi Fen Bilimleri Dergisi. 2020;3:1–24.
MLA Kurtaran, Hasan. “Low-Velocity Impact Analysis of Laminated Composite Plates and Shells With Generalized Differential Quadrature Method”. Artıbilim: Adana Alparslan Türkeş Bilim Ve Teknoloji Üniversitesi Fen Bilimleri Dergisi, vol. 3, no. 1, 2020, pp. 1-24.
Vancouver Kurtaran H. Low-velocity impact analysis of laminated composite plates and shells with generalized differential quadrature method. Artıbilim: Adana Alparslan Türkeş Bilim ve Teknoloji Üniversitesi Fen Bilimleri Dergisi. 2020;3(1):1-24.