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http://dx.doi.org/10.12989/scs.2020.34.2.227

Nonlinear and post-buckling responses of FGM plates with oblique elliptical cutouts using plate assembly technique  

Ghannadpour, S.A.M. (New Technologies and Engineering Department, Shahid Beheshti University)
Mehrparvar, M. (New Technologies and Engineering Department, Shahid Beheshti University)
Publication Information
Steel and Composite Structures / v.34, no.2, 2020 , pp. 227-239 More about this Journal
Abstract
The aim of this study is to obtain the nonlinear and post-buckling responses of relatively thick functionally graded plates with oblique elliptical cutouts using a new semi-analytical approach. To model the oblique elliptical hole in a FGM plate, six plate-elements are used and the connection between these elements is provided by the well-known Penalty method. Therefore, the semi-analytical technique used in this paper is known as the plate assembly technique. In order to take into account for functionality of the material in a perforated plate, the volume fraction of the material constituents follows a simple power law distribution. Since the FGM perforated plates are relatively thick in this research, the structural model is assumed to be the first order shear deformation theory and Von-Karman's assumptions are used to incorporate geometric nonlinearity. The equilibrium equations for FGM plates containing elliptical holes are obtained by the principle of minimum of total potential energy. The obtained nonlinear equilibrium equations are solved numerically using the quadratic extrapolation technique. Various sets of boundary conditions for FGM plates and different cutout sizes and orientations are assumed here and their effects on nonlinear response of plates under compressive loads are examined.
Keywords
post-buckling behavior; oblique elliptical cutouts; functionally graded plates; plate assembly technique; penalty method, Mapping;
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Times Cited By KSCI : 14  (Citation Analysis)
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1 Ghannadpour, S.A.M. and Shakeri, M. (2018), "Energy based collocation method to predict progressive damage behavior of imperfect composite plates under compression", Latin Am. J. Solids Struct., 15(4).
2 Ghannadpour, S.A.M., Karimi, M. and Tornabene, F. (2019), "Application of plate decomposition technique in nonlinear and post-buckling analysis of functionally graded plates containing crack", Compos. Struct., 220, 158-167. https://doi.org/10.1016/j.compstruct.2019.03.025.   DOI
3 Alinia, M.M. and Ghanndpour, S.A.M. (2009), "Nonlinear analysis of pressure loaded FGM plates", Compos. Struct., 88(3), 354-359. https://doi.org/10.1016/j.compstruct.2008.04.013.   DOI
4 Baba, B.O. and Baltaci, A. (2007), "Buckling characteristics of symmetrically and antisymmetrically laminated composite plates with central cutout", Appl. Compos. Mater., 14, 265-276. https://doi.org/10.1007/s10443-007-9045-z.   DOI
5 Bailey, R. and Wood, J. (1996), "Stability characteristics of composite panels with various cutout geometries", Compos. Struct., 35(1), 21-31. https://doi.org/10.1016/0263-8223(96)00021-9.   DOI
6 Britt, V.O. (1994), "Shear and compression buckling analysis for anisotropic panels with elliptical cutouts", AIAA J., 32(11) 2293-2299. https://doi.org/10.2514/3.12289.   DOI
7 Jain, P. and Kumar, A. (2004), "Postbuckling response of square laminates with a central circular/elliptical cutout", Compos. Struct., 65(2), 179-185. https://doi.org/10.1016/j.compstruct.2003.10.014.   DOI
8 Ghannadpour, S.A.M., Najafi, A. and Mohammadi, B. (2006), "On the buckling behavior of cross-ply laminated composite plates due to circular/elliptical cutouts", Compos. Struct., 75, 3-6. https://doi.org/10.1016/j.compstruct.2006.04.071.   DOI
9 Ghannadpour, S.A.M., Ovesy, H.R. and Nassirnia, M. (2012), "An investigation on buckling behavior of functionally graded plates using finite strip method", Appl. Mech. Mater., 152-154, 1470-1476. https://doi.org/10.4028/www.scientific.net/AMM.152-154.1470.   DOI
10 Heidari-Rarani, M. and Kharratzadeh, M. (2019), "Buckling behavior of composite cylindrical shells with cutout considering geometric imperfection", Steel Compos. Struct., 30(4), 305-313. https://doi.org/10.12989/scs.2019.30.4.305.   DOI
11 Javaheri, R. and Eslami, M.R. (2002), "Buckling of functionally graded plates under in-plane compressive load", J. Appl.Math. Mech., 82(4), 277-283. https://doi.org/10.1002/1521-4001(200204)82:4<277::AID-ZAMM277>3.0.CO;2-Y.
12 Kandasamya, R., Dimitrib, R. and Tornabene, F. (2016), "Numerical study on the free vibration a nd thermal buckling behavior of moderately thick functionally graded structures in thermal environment", Compos. Struct., 157, 207-221. https://doi.org/10.1016/j.compstruct.2016.08.037.   DOI
13 Kar, V.R. and Panda S.K., (2016), "Post-buckling behavior of shear deformable functionally graded curved shell panel under edge compression", Int. J. Mech. Sci., 115-116, 318-324. https://doi.org/10.1016/j.ijmecsci.2016.07.014.   DOI
14 Koizumi, M. (1997), "FGM activities in Japan", Compos. Part B, 28(1-2), 1-4. https://doi.org/10.1016/S1359-8368(96)00016-9.   DOI
15 Kumar, D. and Singh, S.B. (2010), "Effect of boundary conditions on buckling and postbuckling responses of composite laminate with various shaped cutouts", Compos. Struct., 92(3), 769-779. https://doi.org/10.1016/j.compstruct.2009.08.049.   DOI
16 Chen, Y., Jin, G. and Liu, Z. (2014), "Flexural and in-plane vibration analysis of elastically restrained thin rectangular plate with cutout using Chebyshev-Lagrangian method", Int. J. Mech. Sci., 89, 264-278. https://doi.org/10.1016/j.ijmecsci.2014.09.006.   DOI
17 Komur, M.A. and Sonmez, M. (2008), "Elastic buckling of rectangular plates under linearly varying in-plane normal load with a circular cutout", Mech. Res. Commun., 35(6), 361-371. https://doi.org/10.1016/j.mechrescom.2008.01.005.   DOI
18 Komur, M.A., Sen, F., Atas, A. and Arslan, N. (2010), "Buckling analysis of laminated composite plates with an elliptical/circular cutout using FEM", Adv. Eng. Softw., 41(2), 161-164. https://doi.org/10.1016/j.advengsoft.2009.09.005.   DOI
19 Kong, C.W., Hong, C.S. and Kim, C.G. (2001), "Postbuckling strength of composite plate with a hole", J. Reinforced Plastics Compos., 20(6), 466-481. https://doi.org/10.1177/073168401772678652.   DOI
20 Kopriva, D.A. (2009), Implementing spectral methods for partial differential equations: Algorithms for scientists and engineers, Springer Science & Business Media.
21 Kumar, D. and Singh, S.B. (2010), "Postbuckling strengths of composite laminate with various shaped cutouts under in-plane shear", Compos. Struct., 92(12), 2966-2978. https://doi.org/10.1016/j.compstruct.2010.05.008.   DOI
22 Lee, Y.Y., Zhao, X. and Reddy, J.N. (2010), "Postbuckling analysis of functionally graded plates subject to compressive and thermal loads", Computer. Method. Appl. M., 199(25-28), 1645-1653. https://doi.org/10.1016/j.cma.2010.01.008.   DOI
23 Ma, L.S. and Wang, T.J. (2003), "Nonlinear bending and post-buckling of a functionally graded circular plate under mechanical and thermal loadings", Int. J. Solids Struct., 40(13-14), 3311-3330. https://doi.org/10.1016/S0020-7683(03)00118-5.   DOI
24 Nemeth, M.P. (1990), "Buckling and postbuckling behavior of square compression-loaded graphite-epoxy plates with circular cutouts", NASA Technical Paper 3007.
25 Ma, Y., Cheng, X., Wang, Z., Guo, X., Zhang, J. and Xu, Y. (2018), "Buckling and post-buckling behaviors of 1/3 composite cylindrical shell with an opening", Steel Compos. Struct., 27(5), 555-566. https://doi.org/10.12989/scs.2018.27.5.555.   DOI
26 Mehrparvar, M. and Ghannadpour, S.A.M. (2018), "Plate assembly technique for nonlinear analysis of relatively thick functionally graded plates containing rectangular holes subjected to in-plane compressive load", Compos. Struct., 202, 867-880. https://doi.org/10.1016/j.compstruct.2018.04.053.   DOI
27 Mohammadi, B., Najafi, A. and Ghannadpour, S.A.M. (2006), "Effective widths of compression-loaded of perforated cross-ply laminated composites", Compos. Struct., 75(1-4), 7-13. https://doi.org/10.1016/j.compstruct.2006.04.025.   DOI
28 Noor, A.K. and Kim, Y.H. (1996), "Buckling and postbuckling of composite panels with cutouts subjected to combined edge shear and temperature change", Compos. Struct., 60(2), 203-222. https://doi.org/10.1016/0045-7949(95)00398-3.   DOI
29 Ovesy, H.R. and Ghannadpour, S.A.M. (2007), "Large deflection finite strip analysis of functionally graded plates under pressure loads", Int. J. Struct. Stab. Dynam., 7(2), 193-211. https://doi.org/10.1142/S0219455407002241.   DOI
30 Ovesy, H.R., Ghannadpour, S.A.M. and Nassirnia, M. (2015), "Post-buckling analysis of rectangular plates comprising functionally graded strips in thermal environment", Compos. Struct., 147, 209-215. https://doi.org/10.1016/j.compstruc.2014.09.011.   DOI
31 Pradhan, K.K. and Chakraverty, S. (2015), "Static analysis of functionally graded thin rectangular plates with various boundary supports", Arch. Civil Mech. Eng., 15(3), 721-734. https://doi.org/10.1016/j.acme.2014.09.008.   DOI
32 Ritchie, D. and Rhodes, J. (1975), "Buckling and postbuckling behaviour of plates with holes", The Aeronautical Quarterly, 26(4), 281-296. https://doi.org/10.1017/S0001925900007435.   DOI
33 Rajanna, T., Banerjee, S., Desai, Y.M. and Prabhakara, D.L. (2016), "Vibration and buckling analyses of laminated panels with and without cutouts under compressive and tensile edge loads", Steel Compos. Struct., 21(1), 37-55. http://dx.doi.org/10.12989/scs.2016.21.1.037.   DOI
34 Reddy, J.N. (1982), "Large amplitude flexural vibration of layered composite plates with cutouts", J. Sound Vib., 83(1), 1-10. https://doi.org/10.1016/S0022-460X(82)80071-0.   DOI
35 Reddy, J.N. (2004), Mechanics of laminated composite plates and shells: theory and analysis, CRC Press, Boca Raton, U.S.A.
36 Sherafat, M.H., Ovesy, H.R. and Ghannadpour, S.A.M. (2013), "Buckling analysis of functionally graded plates under mechanical loading using higher order functionally graded strip", Int. J. Struct. Stab. Dynam., 13(6) 1350033. https://doi.org/10.1142/S0219455413500338.   DOI
37 Srivatsa, K.S. and Krishna Murty, A.V. (1992), "Stability of laminated composite plates with cut-outs", Comput. Struct., 43(2), 273-279. https://doi.org/10.1016/0045-7949(92)90144-O.   DOI
38 Taheri-Behrooz, F. and Omidi, M. (2018), "Buckling of axially compressed composite cylinders with geometric imperfections", Steel Compos. Struct., 29(4), 557-567. https://doi.org/10.12989/scs.2018.29.4.557.   DOI
39 Vandenbrink, D.J. and Kamat, M.P. (1987), "Post-buckling response of isotropic and laminated composite square plates with circular holes", Finite Elem. Anal. Des., 3(3), 165-174. https://doi.org/10.1016/0168-874X(87)90021-7.   DOI
40 Wu, Tsung-Lin, Shukla, K.K. and Huang, Jin H. (2007), "Post-buckling analysis of fuctionally graded rectangular plates", Compos. Struct., 81(1), 1-10. https://doi.org/10.1016/j.compstruct.2005.08.026.   DOI
41 Ghannadpour, S.A.M. and Karimi, M. (2018), "Domain decomposition technique to simulate crack in nonlinear analysis of initially imperfect laminates", Struct. Eng. Mech., 68(5), 603-619. https://doi.org/10.12989/sem.2018.68.5.603.   DOI
42 Yang, J. and Shen, Hui-Shen (2003), "Non-linear analysis of functionally graded plates under transverse and in-plane loads", Int. J. Non-Linear Mech., 38(4), 467-482. https://doi.org/10.1016/S0020-7462(01)00070-1.   DOI
43 Yang, J., Liew, K.M. and Kitipornchai, S. (2006), "Imperfection sensitivity of the post-buckling behavior of higher-order shear deformable functionally graded plates", Int. J. Solids Struct., 43(17), 5247-5266. https://doi.org/10.1016/j.ijsolstr.2005.06.061.   DOI
44 Cheng, B. and Li, C. (2012), "Buckling behavior of strengthened perforated plates under shear loading", Steel Compos. Struct., 13(4), 367-382. https://doi.org/10.12989/scs.2012.13.4.367.   DOI
45 Choudhary, P.K. and Jana, P. (2018), "Position optimization of circular/elliptical cutout within an orthotropic rectangular plate for maximum buckling load", Steel Compos. Struct., 29(1), 39-51. https://doi.org/10.12989/scs.2018.29.1.39.   DOI
46 Ghannadpour, S.A.M. and Alinia, M.M. (2006), "Large deflection behavior of functionally graded plates under pressure loads", Compos. Struct., 75(1-4), 67-71. https://doi.org/10.1016/j.compstruct.2006.04.004.   DOI
47 Ghannadpour, S.A.M. and Kiani, P. (2018), "Nonlinear spectral collocation analysis of imperfect functionally graded plates under end-shortening", Struct. Eng. Mech., 66(5), 557-568. https://doi.org/10.12989/sem.2018.66.5.557.   DOI
48 Ghannadpour, S.A.M. and Mehrparvar, M. (2018), "Energy effect removal technique to model circular/elliptical holes in relatively thick composite plates under in-plane compressive load", Compos. Struct., 202, 1032-1041. https://doi.org/10.1016/j.compstruct.2018.05.026.   DOI