تحلیل دینامیکی ضربه‌های غیرهم‌زمان سرعت پایین روی ورق چندلایه کامپوزیتی

نوع مقاله : مقاله پژوهشی

نویسندگان

دانشکده مهندسی مکانیک، دانشگاه صنعتی امیرکبیر، تهران، ایران

چکیده

یکی از مسائل کاربردی در پدیده برخورد، بررسی ضربه‌های غیر هم‌زمان به سازه است. در این پژوهش، تحلیل دینامیکی ضربه‌های سرعت پایین در زمان‌ها و محل‌های دلخواه روی ورق‌های چندلایه کامپوزیتی ارتوتروپ صورت گرفته است. ابتدا معادلات دینامیکی ورق با استفاده از اصل همیلتون و با فرض تئوری کلاسیک و تغییر شکل‌های کوچک و در نظر گرفتن قانون تماس هرتز در مدلسازی برخورد ضربه‌زننده با هدف بدست آمده است. در ادامه، حل دقیق مسئله با بسط میدان جابجایی و بارگذاری به صورت توابع فوریه دوبعدی ارائه شده است. صحت‌سنجی نتایج بدست آمده در قیاس با مقالات به همراه تحلیل همگرایی پاسخ دینامیکی، نشان‌دهنده اعتبار آن‌هاست. نتایج بدست آمده حاکی از آن است که زمان و محل ضربه‌ها نقش موثری در برهم نهی امواج ایجاد شده و در نتیجه مقدار حداکثر نیروی تماس، کمینه و بیشینه جابجایی عرضی ایجاد شده در سازه و همچنین مقدار انرژی جذب شده توسط آن را دارد. مدلسازی ضربه‌های غیرهم‌زمان سرعت پایین در آزمایش سقوط آزاد، یکی دیگر از نتایج قابل توجه بدست آمده در این پژوهش است که می‌تواند جایگزین آزمایش‌های متعدد شده و هزینه‌های آزمایش را کاهش دهد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Dynamic Analysis of Asynchronous Low-Velocity Impacts on Laminated Composite Plate

نویسندگان [English]

  • M. Kavousi Sisi
  • M. Shakeri
  • M. Sadighi
Mechanical Engineering Department, Amirkabir University of Technology, Tehran, Iran
چکیده [English]

ABSTRACT: Studying asynchronous low-velocity impacts on the structure is one of the applicable problems in this field. In this research, the dynamic analysis of asynchronous low-velocity impacts with arbitrary times and locations on the orthotropic laminated composite plates has been investigated. The dynamic equations of motion are obtained using Hamilton’s principle with the assumptions of small deformations and the Hertzian contact law is used for modeling the contact between target and impactors. Then, the closed form solution of the governing equations is obtained using double Fourier expansion of displacement and loading fields. The accuracy of the results has been checked by comparing them to those in the literature in conjunction with the example considering the convergence of the results. Several numerical examples showed that the times and locations of the impacts play an important role
on the superposition of induced waves which affect maximum contact forces, minimum and maximum of the plate transverse displacements, as well as the plate, absorbed energy. Modeling asynchronous low-velocity impacts of drop test could be mentioned as one of the significant results of this study. This modeling can substitute for experimental tests and decrease the costs.

کلیدواژه‌ها [English]

  • Laminated composite plates
  • Asynchronous low-velocity impacts
  • Arbitrary locations
  • Hamilton’s principle
[1] J.R. Vinson, R.L. Sierakowski, The behavior of structures composed of composite materials, M. Nijhoff, 1986.
[2] J.N. Reddy, A generalization of two- dimensional theories of laminated composite plates, Communications in Applied Numerical Methods, 3(3) (1987) 173-180.
[3] R.K. Kapania, S. Raciti, Recent advances in analysis of laminated beams and plates. Part I - Shear effects and buckling, AIAA Journal, 27(7) (1989) 923-935.
[4] Y. Ghugal, R. Shimpi, A review of refined shear deformation theories of isotropic and anisotropic laminated plates, Journal of Reinforced Plastics and Composites, 21(9) (2002) 775-813.
[5] C.T. Sun, S. Chattopadhyay, Dynamic Response of Anisotropic Laminated Plates Under Initial Stress to Impact of a Mass, Journal of Applied Mechanics, 42(3)(1975) 693-698.
[6] Y. Qian, S.R. Swanson, Experimental measurement of impact response in carbon/epoxy plates, AIAA Journal, 28(6) (1990) 1069-1074.
[7] A. Christoforou, S. Swanson, Analysis of impact response Structures, 27(2) (1991) 161-170.
[8] C.T. Sun, J.K. Chen, On the Impact of Initially Stressed Composite Laminates, Journal of Composite Materials, 19(6) (1985) 490-504.
[9] H.-Y.T. Wu, C. Fu-Kuo, Transient dynamic analysis of laminated composite plates subjected to transverse impact, Computers & structures, 31(3) (1989) 453-466.
[10] Y. Qian, S.R. Swanson, A comparison of solution techniques for impact response of composite plates, Composite Structures, 14(3) (1990) 177-192.
[11] T.M. Tan, C.T. Sun, Use of Statical Indentation Laws in the Impact Analysis of Laminated Composite Plates, Journal of Applied Mechanics, 52(1) (1985) 6-12.
[12] A. Nosier, R.K. Kapania, J.N. Reddy, Low-velocity impact of laminated composites using a layerwise theory, Computational Mechanics, 13(5) (1994) 360-379.
[13] N. Naik, S. Meduri, Polymer-matrix composites subjected to low-velocity impact: effect of laminate configuration, Composites science and technology, 61(10) (2001) 1429-1436. [14] D. Wyrick, D. Adams, Damage sustained by a carbon/epoxy composite material subjected to repeated impact,Composites, 19(1) (1988) 19-27.
[15] D.A. Wyrick, D.F. Adams, Residual strength of a carbon/epoxy composite material subjected to repeated impact, Journal of Composite Materials, 22(8) (1988)749-765.
[16] M. Hosur, M. Karim, S. Jeelani, Experimental investigations on the response of stitched/unstitched woven S2-glass/SC15 epoxy composites under single and repeated low velocity impact loading, Composite structures, 61(1) (2003) 89-102.
[17] J. Baucom, M. Zikry, A. Rajendran, Low-velocity impact damage accumulation in woven S2-glass composite systems, omposites science and technology, 66(10) (2006) 1229-1238.
[18] O. David-West, D. Nash, W. Banks, An experimental study of damage accumulation in balanced CFRP laminates due to repeated impact, Composite structures, 83(3) (2008) 247-258.
[19] G. Belingardi, M.P. Cavatorta, D.S. Paolino, A new damage index to monitor the range of the penetration process in thick laminates, Composites Science and Technology, 68(13) (2008) 2646-2652.
[20] G. Belingardi, M.P. Cavatorta, D.S. Paolino, On the rate of growth and extent of the steady damage accumulation phase in repeated impact tests, Composites Science and Technology, 69(11) (2009) 1693-1698.
[21] F. Morinière, R. Alderliesten, M. Tooski, R. Benedictus, Damage evolution in GLARE fibre-metal laminate under repeated low-velocity impact tests, Open Engineering, 2(4) (2012) 603-611.
[22] M.Y. Tooski, R. Alderliesten, R. Ghajar, S. Khalili, Experimental investigation on distance effects in repeated low velocity impact on fiber–metal laminates, Composite Structures, 99 (2013) 31-40.
[23] C. Atas, B.M. Icten, M. Küçük, Thickness effect on repeated impact response of woven fabric composite plates, Composites Part B: Engineering, 49 (2013) 80-85.
[24] V. Arikan, O. Sayman, Comparative study on repeated impact response of E-glass fiber reinforced polypropylene & epoxy matrix composites, Composites Part B: Engineering, 83 (2015) 1-6.
[25] R. Balan, V. Arumugam, K.A. Rauf, A.A.P. Sidharth, C. Santulli, Estimation of residual flexural strength of unidirectional glass fiber reinforced plastic composite laminates under repeated impact load, Journal of Composite Materials, 49(6) (2015) 713-722.
[26] M. Cohen, J. Achenbach, Probabilistic considerations of the growth and detection of delaminations for repeated impact on composites, Journal of Composite Materials, 48(25) (2014) 3179-3187.
[27] B.M. Icten, Low temperature effect on single and repeated impact behavior of woven glass-epoxy composite plates, Journal of Composite Materials, 49(10) (2015) 1171-1178.
[28] C. Atas, A. Dogan, An experimental investigation on the repeated impact response of glass/epoxy composites subjected to thermal ageing, Composites Part B:Engineering, 75 (2015) 127-134.
[29] A. Amaro, P. Reis, M. Neto, Experimental study of temperature effects on composite laminates subjected to multi-impacts, Composites Part B: Engineering, 98 (2016) 23-29.
[30] E. Wu, J.-C. Yeh, C.S. Yen, Identification of impact forces at multiple locations on laminated plates, AIAA journal, 32(12) (1994) 2433-2439.
[31] K.Y. Lam, T.S. Sathiyamoorthy, Response of composite beam under low-velocity impact of multiple masses, Composite Structures, 44(2) (1999) 205-220.
[32] D. Chakraborty, M. Kumar, Response of Laminated FRP Composites under Multiple Impact Loading, Journal of Reinforced Plastics and Composites, 24(14) (2005) 1457-1477.
[33] K. Malekzadeh, M.R. Khalili, R. Olsson, A. Jafari, Higher-order dynamic response of composite sandwich panels with flexible core under simultaneous low-velocity impacts of multiple small masses, International Journal of Solids and Structures, 43(22–23) (2006) 6667-6687.
[34] A. Veysi Gorgabad, Low velocity impact analysis of sandwich beam and plate with FGM core under single and multiple impacts, MSc Thesis, Amirkabir University of Technology, Tehran, Iran, 2011. (In Persian)
[35] A.R. Damanpack, M. Shakeri, M.M. Aghdam, A new finite element model for low-velocity impact analysis of sandwich beams subjected to multiple projectiles, Composite Structures, 104 (2013) 21-33.
[36] D. Li, Y. Liu, X. Zhang, Low-velocity impact responses of the stiffened composite laminated plates based on the progressive failure model and the layerwise/solidelements method, Composite Structures, 110 (2014) 249- 275.
[37] S.-R. Cho, D.D. Truong, H.K. Shin, Repeated lateral impacts on steel beams at room and sub-zero temperatures, International Journal of Impact Engineering, 72 (2014)75-84.
[38] M. Kavousi Sisi, M. Shakeri, M. Sadighi, Dynamic response of composite laminated beams under asynchronous/repeated low-velocity impacts of multiple masses, Composite Structures, 132 (2015) 960-973.
[39] K. Malekzadeh Fard, A. Veysi Gorgabad, Low Velocity Impact Response of the Thick Curved Sandwich Shells with Flexible Cores, Aerospace Mechanics Journal, 13(2) (2016) 23-34. (In Persian)
[40] S. Abrate, Impact on Composite Structures, Cambridge University Press, 1998.
[41] J.N. Reddy, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, Second Edition, Taylor & Francis, 2003.
[42] E. Süli, D.F. Mayers, An Introduction to Numerical Analysis, Cambridge University Press, 2003.
[43] A.R. Setoodeh, P. Malekzadeh, K. Nikbin, Low velocity impact analysis of laminated composite plates using a 3D elasticity based layerwise FEM, Materials & Design, 30(9) (2009) 3795-3801.
[44] N. Phan, J. Reddy, Analysis of laminated composite plates using a higher‐order shear deformation theory, International Journal for Numerical Methods in Engineering, 21(12) (1985) 2201-2219.
[45] R.L. Sierakowski, S.K. Chaturvedi, Dynamic loading and characterization of fiber-reinforced composites, John Wiley and Sons, University of Michigan, New York, 1997.
[46] R. Olsson, Closed form prediction of peak load and delamination onset under small mass impact, Composite Structures, 59(3) (2003) 341-349.