Free Vibration Analysis of Delaminated Composite Plate Using 3D Degenerated Element
Publication: Journal of Aerospace Engineering
Volume 32, Issue 5
Abstract
In this study, a new model for analyzing delaminated plates was developed using three-dimensional (3D) degenerated elements. The elements were developed using the degenerated solid approach based on Reissner-Mindlin assumptions. Thus, the shear deformation and rotary inertia effect were considered, and the 3D field was reduced to a two-dimensional (2D) field in terms of midsurface nodal variables. The delamination was incorporated using Heaviside step functions. The proposed model was found to be very accurate and also faster in comparison with layerwise/higher-order theories. Results for natural frequencies of plates and beams with and without delamination were compared with theoretical and experimental results available in the literature and were in excellent agreement. New results were generated using the proposed method for different boundary conditions, ply orientations, size of delamination, and location of delamination; these will serve as benchmarks for future research.
Get full access to this article
View all available purchase options and get full access to this article.
References
Ahmad, S., B. M. Irons, and O. Zienkiewicz. 1970. “Analysis of thick and thin shell structures by curved finite elements.” Int. J. Numer. Methods Eng. 2 (3): 419–451. https://doi.org/10.1002/nme.1620020310.
Balamurugan, V., and S. Narayanan. 2008. “A piezolaminated composite degenerated shell finite element for active control of structures with distributed piezosensors and actuators.” Smart Mater. Struct. 17 (3): 035031. https://doi.org/10.1088/0964-1726/17/3/035031.
Barbero, E., and J. Reddy. 1991. “Modeling of delamination in composite laminates using a layer-wise plate theory.” Int. J. Numer. Methods Eng. 28 (3): 373–388. https://doi.org/10.1016/0020-7683(91)90200-Y.
Chattopadhyay, A., and H. Gu. 1994. “New higher order plate theory in modeling delamination buckling of composite laminates.” AIAA J. 32 (8): 1709–1716. https://doi.org/10.2514/3.1216310.2514/3.12163.
Cho, M., and J.-S. Kim. 2001. “Higher-order zig-zag theory for laminated composites with multiple delaminations.” J. Appl. Mech. 68 (6): 869–877. https://doi.org/10.1115/1.1406959.
Hirwani, C. K., S. Panda, T. Mahapatra, and S. Mahapatra. 2017. “Numerical study and experimental validation of dynamic characteristics of delaminated composite flat and curved shallow shell structure.” J. Aerosp. Eng. 30 (5): 04017045. https://doi.org/10.1061/(ASCE)AS.1943-5525.0000756.
Hirwani, C. K., R. K. Patil, S. K. Panda, S. S. Mahapatra, S. K. Mandal, L. Srivastava, and M. K. Buragohain. 2016a. “Experimental and numerical analysis of free vibration of delaminated curved panel.” Aerosp. Sci. Technol. 54 (Jul): 353–370. https://doi.org/10.1016/j.ast.2016.05.009.
Hirwani, C. K., S. Sahoo, and S. Panda. 2016b. “Effect of delamination on vibration behaviour of woven glass/epoxy composite plate—An experimental study.” In Vol. 115 of Proc., IOP Conf. Series: Materials Science and Engineering, 012010. Bristol, UK: IOP Publishing.
Huang, H., and E. Hinton. 1986. “A new nine node degenerated shell element with enhanced membrane and shear interpolation.” Int. J. Numer. Methods Eng. 22 (1): 73–92. https://doi.org/10.1002/nme.1620220107.
Jayasankar, S., S. Mahesh, S. Narayanan, and C. Padmanabhan. 2007. “Dynamic analysis of layered composite shells using nine node degenerate shell elements.” J. Sound Vib. 299 (1–2): 1–11. https://doi.org/10.1016/j.jsv.2006.06.058.
Ju, F., H. Lee, and K. Lee. 1995. “Finite element analysis of free vibration of delaminated composite plates.” Compos. Eng. 5 (2): 195–209. https://doi.org/10.1016/0961-9526(95)90713-L.
Kim, H. S., A. Chattopadhyay, and A. Ghoshal. 2003a. “Characterization of delamination effect on composite laminates using a new generalized layerwise approach.” Comput. Struct. 81 (15): 1555–1566. https://doi.org/10.1016/S0045-7949(03)00150-0.
Kim, H. S., A. Chattopadhyay, and A. Ghoshal. 2003b. “Dynamic analysis of composite laminates with multiple delamination using improved layerwise theory.” AIAA J. 41 (9): 1771–1779. https://doi.org/10.2514/2.729510.2514/2.7295.
Kim, J.-S., and M. Cho. 2002. “Buckling analysis for delaminated composites using plate bending elements based on higher-order zig-zag theory.” Int. J. Numer. Methods Eng. 55 (11): 1323–1343. https://doi.org/10.1002/nme.545.
Kumar, S. K., M. Cinefra, E. Carrera, R. Ganguli, and D. Harursampath. 2014. “Finite element analysis of free vibration of the delaminated composite plate with variable kinematic multilayered plate elements.” Compos. Part B: Eng. 66 (Nov): 453–465. https://doi.org/10.1016/j.compositesb.2014.05.031.
Lee, K., W. Lin, and S. Chow. 1994. “Bidirectional bending of laminated composite plates using an improved zig-zag model.” Compos. Struct. 28 (3): 283–294. https://doi.org/10.1016/0263-8223(94)90015-9.
Lee, K., N. Senthilnathan, S. Lim, and S. Chow. 1990. “An improved zig-zag model for the bending of laminated composite plates.” Compos. Struct. 15 (2): 137–148. https://doi.org/10.1016/0263-8223(90)90003-W.
Li, D., Y. Liu, and X. Zhang. 2015. “An extended layerwise method for composite laminated beams with multiple delaminations and matrix cracks.” Int. J. Numer. Methods Eng. 101 (6): 407–434. https://doi.org/10.1002/nme.4803.
Liang, K., and Q. Sun. 2017. “Buckling and post-buckling analysis of the delaminated composite plates using the Koiter-Newton method.” Compos. Struct. 168 (May): 266–276. https://doi.org/10.1016/j.compstruct.2017.01.038.
Lu, X., and D. Liu. 1992a. “An interlaminar shear stress continuity theory for both thin and thick composite laminates.” J. Appl. Mech. 59 (3): 502–509. https://doi.org/10.1115/1.2893752.
Lu, X., and D. Liu. 1992b. “Interlayer shear slip theory for cross-ply laminates with nonrigid interfaces.” AIAA J. 30 (4): 1063–1073. https://doi.org/10.2514/3.1102810.2514/3.11028.
Luo, H., and S. Hanagud. 1996. “Delamination modes in composite plates.” J. Aerosp. Eng. 9 (4): 106–113. https://doi.org/10.1061/(ASCE)0893-1321(1996)9:4(106).
Marjanović, M., and D. Vuksanović. 2014. “Layerwise solution of free vibrations and buckling of laminated composite and sandwich plates with embedded delaminations.” Compos. Struct. 108 (Feb): 9–20. https://doi.org/10.1016/j.compstruct.2013.09.006.
Reddy, J. 1985. “A review of the literature on finite-element modeling of laminated composite plates.” Int. J. Numer. Methods Eng. 17 (4): 3–8.
Reddy, J. 1987. “A generalization of two-dimensional theories of laminated composite plates.” Int. J. Numer. Methods Biomed. Eng. 3 (3): 173–180. https://doi.org/10.1002/cnm.1630030303.
Reddy, J. 1990. “A review of refined theories of laminated composite plates.” Shock Vib. Dig. 22 (7): 3–17. https://doi.org/10.1177/058310249002200703.
Reddy, J. N. 2004. Mechanics of laminated composite plates and shells: Theory and analysis. Boca Raton, FL: CRC Press.
Sahoo, S. S., S. K. Panda, and D. Sen. 2016. “Effect of delamination on static and dynamic behavior of laminated composite plate.” AIAA J. 54 (8): 2530–2544. https://doi.org/10.2514/1.J054908.
Shen, M.-H., and J. Grady. 1992. “Free vibrations of delaminated beams.” AIAA J. 30 (5): 1361–1370. https://doi.org/10.2514/3.1107210.2514/3.11072.
Vuksanović, D. 2000. “Linear analysis of laminated composite plates using single layer higher-order discrete models.” Compos. Struct. 48 (1–3): 205–211. https://doi.org/10.1016/S0263-8223(99)00096-3.
Whitney, J. 1969. “The effect of transverse shear deformation on the bending of laminated plates.” J. Compos. Mater. 3 (3): 534–547. https://doi.org/10.1177/002199836900300316.
Williams, T. O. 1999. “A generalized multilength scale nonlinear composite plate theory with delamination.” Int. J. Solids Struct. 36 (20): 3015–3050. https://doi.org/10.1016/S0020-7683(98)00138-3.
Williams, T. O., and F. L. Addessio. 1997. “A general theory for laminated plates with delaminations.” Int. J. Solids Struct. 34 (16): 2003–2024. https://doi.org/10.1016/S0020-7683(96)00131-X.
Zhen, W., C. Wanji, and R. Xiaohui. 2010. “An accurate higher-order theory and finite element for free vibration analysis of laminated composite and sandwich plates.” Compos. Struct. 92 (6): 1299–1307. https://doi.org/10.1016/j.compstruct.2009.11.011.
Zienkiewicz, O., R. Taylor, and J. Too. 1971. “Reduced integration technique in general analysis of plates and shells.” Int. J. Numer. Methods Eng. 3 (2): 275–290. https://doi.org/10.1002/nme.1620030211.
Information & Authors
Information
Published In
Copyright
©2019 American Society of Civil Engineers.
History
Received: Nov 28, 2018
Accepted: Mar 19, 2019
Published online: Jun 11, 2019
Published in print: Sep 1, 2019
Discussion open until: Nov 11, 2019
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.