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Buckling Analysis of Symmetrically Laminated Rectangular Thin Plates under Biaxial Compression

Yıl 2021, Cilt: 32 Sayı: 6, 11287 - 11314, 01.11.2021
https://doi.org/10.18400/tekderg.606620

Öz

In this parametric study, the buckling analysis of symmetrically laminated rectangular thin plates subjected to biaxial compression is presented. The simply supported boundary condition is considered at the edges of the symmetrically laminated quasi-isotropic, cross-ply and angle-ply plates. The Rayleigh-Ritz Method is used to specify the critical buckling load of the plates based on the Classical Laminated Plate Theory (CLPT). A convergence study is achieved by increasing the number of parameters of assumed shape function. Validation of isotropic case is verified. The effects of the lamination types, plate aspect ratios (a/b, b/a) and thickness on the critical buckling load of the laminated plates under bi-axial compression were then investigated. The results were compared with Finite Element Method (FEM) solutions performed by ANSYS software package and fairly good agreement is obtained. Non-dimensional results were tabulated and presented for practical use for designers.

Kaynakça

  • Lekhnitskii, S. G., Anisotropic plates, second ed, translated from the Russian by S. W. Tsai and T. Cheron, Gordon and Breach, New York.,1968.
  • Ambartsumyan, S. A.,Theory of anisotropic plates, Technomic Publishing, Stamford CT., 1970.
  • Ashton, J. E. and Whitney, J. M., Theory of laminated plates, Technomic [43 Publishing, Stamford CT. 1970.
  • Szilard R., Theory and analysis of plates: classical and numerical methods. Englewood Cliffs, New Jersey: Prentice-Hall, 1974.
  • Jones, R. M., Mechanics of composite materials, Scripta, Washington DC, 1975.
  • Chia, C.Y, Nonlinear analysis of plates, McGraw-Hill, New York, 1980.
  • Leissa, A. W., A review of laminated composite plate buckling, Appl Mech Rev vol 40, no 5, May, 575-591, 1987.
  • Tung, T. K. and Surdenas, J., Buckling of Rectangular Orthotropic Plates Under Biaxial Loading, Journal of Composite Materials, Vol. 21-February, 124-128, 1987.
  • Nagendra, S., Haftka, R.T. and Gurdal, Z., Stacking sequence optimization of simply supported laminates with stability and strain constraints, AIAA-92-2310-CP-2526-2535, 1992.
  • Zhang, J.W., Buckling and Postbuckling of Unsymmetrically Laminated Angle-ply Plates in Uniaxial and Biaxial Compression, Thin- Walled Structures 15, 271-290, 1993.
  • Kim Y.S. and Hoa S.V., Bi-axial buckling behavior of composite rectangular plates, Composite Structures 31, 247-252, 1995.
  • Nair, S., Singh, G.L. and G. Rao, V., Stability of Laminated Composite Plates Subjected To Various Types of In-Plane Loadings, Int. J. Mech. Sci., Vol. 38. No. 2, pp. 191-202, 1996.
  • Sundaresan,P., Singh, G. and Rao,G.V., Buckling and post-buckling analysis of moderately thick laminated rectangular plates, Computers & Structures Vol. 61, No. I, pp.79-86, 1996.
  • Walker,M., Adali, S. and Verijenko,V., Optimization of symmetric laminates for maximum buckling load including the effects of bending-twisting coupling, Computers&Structures, Vol.58, No.2, pp.313-319, 1996a.
  • Walker, M., Adali, S. and Verijenko, V. E., Optimal design of symmetric angle-ply laminates subject to nonuniform buckling loads and in-plane restraints, Thin-Walled Structures Vol.26, No. I, pp. 45 60, 1996b.
  • Adali,S., Richter,A. and Verijenko, K.E., Optimization of shear-deformable laminated plates under buckling and strength criteria, Composite Structures Vol. 39, No.3-4, pp. 167-178, 1997.
  • Durban, D. and Zuckerman, Z., Elastoplastic buckling of rectangular plates in biaxial compression/tension, International Journal of Mechanical Sciences 41, 751—765, 1999.
  • Sarma, M.A., Singh, G. and Rao,G.V., Stability behaviour of angle ply plates subjected to various types of inplane loadings, Indian Journal of Engineering& Materials Sciences, Vol.6, August, pp.173-181, 1999.
  • Tuttle, M., Singhatanadgid, P. and Hinds, G., Buckling of Composite Panels Subjected to Biaxial Loading, Experimental Mechanics, VoI. 39, No. 3, September, pp.191-201, 1999.
  • Kollar, L.P. and Veres, I.A., Buckling of Rectangular Orthotropic Plates Subjected to Biaxial Normal Forces, Journal of Composite Materials, Vol. 35, No. 07, 625-635, 2001.
  • Romeo, G. and Ferrero, G., Analytical/Experimental Behavior of Anisotropic Rectangular Panels Under Linearly Varying Combined Loads, AIAA Journal, Vol. 39, No. 5, May, 932-941, 2001.
  • Narita, Y. and Turvey, G. J., Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Maximizing the buckling loads of symmetrically laminated composite rectangular plates using a layerwise optimization approach, 218: 681-691, 2004.
  • Ni,Q., Xie, J. and Iwamoto, M., Buckling analysis of laminated composite plates with arbitrary edge supports, Composite Structures, 69, 209–217, 2005.
  • Shukla, K. K., Nath, Y., Kreuzer, E. and Kumar, K.V.S., Buckling of Laminated Composite Rectangular Plates, J. Aerosp. Eng.18, 215-223, 2005.
  • Timarci, T. and Aydogdu, M., Buckling of symmetric cross-ply square plates with various boundary conditions, Composite Structures 68, 381–389, 2005.
  • Bert, C.W. and Malik,M., On the buckling characteristics of symmetrically laminated cross-ply plates, Mechanics of Composite Materials and Structures, 4:1, 39-67, 2007.
  • Qiao, P. and Shan,L., Explicit local buckling analysis of rotationally restrained composite plates under biaxial loading, International Journal of Structural Stability and Dynamics, Vol. 7, No. 3, 487–517, 2007
  • Aktaş,M., Buckling Behaviour Of Carbon/Epoxy Laminated Composite Plates Under Biaxial Loading, Advanced Composites Letters, Vol. 18, Iss. 3, 85-93, 2009.
  • Latalski, J., Ply Thickness Tolerances In Stacking Sequence Optimization Of Multilayered Laminate Plates, Journal Of Theoretical And Applied Mechanics, 51, 4, pp. 1039-1052, Warsaw, 2013.
  • Sayyad, A.S. and Ghugal,Y.M., On the Buckling of Isotropic, Transversely Isotropic and Laminated Composite Rectangular Plates, International Journal of Structural Stability and Dynamics, Vol. 14, No. 6, 1450020, 2014.
  • Bourada,F., Amara, K. and Tounsi, A., Buckling analysis of isotropic and orthotropic plates using a novel four variable refined plate theory, Steel and Composite Structures, Vol. 21, No. 6, 1287-1306, 2016.
  • Becheri,T. Amara,K., Bouazza, M. and Benseddiq,N., Buckling of symmetrically laminated plates using nth-order shear deformation theory with curvature effects, Steel and Composite Structures, Vol. 21, No. 6, 1347-1368, 2016.
  • Rajanna, T. , Banerjee,S., Desai, Y.M. and Prabhakara, D.L., Vibration and buckling analyses of laminated panels with and without cutouts under compressive and tensile edge loads, Steel and Composite Structures, Vol. 21, No. 1, 37-55, 2016.
  • Belkacem, A., Tahar,H.D., Abderrezak,R., Amine,B.M., Mohamed,Z. and Boussad,A., Mechanical buckling analysis of hybrid laminated composite plates under different boundary conditions, Structural Engineering and Mechanics, Vol. 66, No. 6, 761-769, 2018.
  • Topal,U., Vo-Duy,T., Dede,T. and Nazarimofrad,E., Buckling load optimization of laminated plates resting on Pasternak foundation using TLBO, Structural Engineering and Mechanics, Vol. 67, No. 6, 617-628, 2018.
  • Bourada, M., Bouadi,A., Bousahla,A.A., Senouci,A., Bourada,F., Tounsi,A. and Mahmoud, S.R., Buckling behavior of rectangular plates under uniaxial and biaxial compression, Structural Engineering and Mechanics, Vol. 70, No. 1, 113-123, 2019.
  • Fellah, M., Draiche,K., Houari,M.S.A., Tounsi,A., Saeed,T., Alhodaly, M.Sh. and Benguediab,M., A novel refined shear deformation theory for the buckling analysis of thick isotropic plates, Structural Engineering and Mechanics, Vol. 69, No. 3, 335-345, 2019.
  • Altekin, M., Bending of super-elliptical Mindlin plates by finite element method, Teknik Dergi, 29, No:4, 8469-8496, 2018.
  • Altekin, M., Free linear vibration and buckling of super-elliptical plates resting on symmetrically distributed point-supports on the diagonals, Thin-Walled Structures, Vol.46, 10, 1066-1086, 2008.
  • Altunsaray, E. and Bayer,İ., Buckling of symmetrically laminated quasi-isotropic thin rectangular plates, Steel and Composite Structures, Vol. 17, No. 3, 305-320, 2014.
  • Tsai, S.W., Composites design, (4th Edition), Think Composites, 1988.
  • Köksal, E. and Köksal, T.Çubuk Plak Kabuk Stabilitesi, Yıldız Teknik Üniversitesi Yayını, Yayın No:309, Yıldız Teknik Üniversitesi Matbaası, İstanbul ,1996 (In Turkish).
  • Köksal, T., Sonlu Elemanlar Metodu, Yıldız Teknik Üniversitesi Yayını, Yayın No:304, Yıldız Teknik Üniversitesi Matbaası İstanbul ,1996 (In Turkish)
  • Fish, J. and Belytschko, T., A first cours in Finite Elements, John Wiley&Sons,Ltd, 2007.
  • ANSYS 2019.1, Academic version, Dokuz Eylul University, 2019.
  • Iyengar,N.G.R., Structural stability of columns and plates, John Wiley&Sons,Ltd, 1988
  • Reddy, J.N., Mechanics of laminated composite plates and shells: Theory and Analysis (2nd Ed.), Boca Raton, FL: CRC Press, 2004.
  • Ventsel,E and Krauthammer,T., Thin plates and shells, theory, analysis, and applications, Marcel Dekker Inc., 2001
  • Wolfram Mathematica 11.3.0, Dokuz Eylul University, 2019.
  • Matlab R2018a, Dokuz Eylul University, 2019.
  • Jones, R.M., Mechanics of composite materials, 2nd ed., Taylor&Francis, 1999.

Buckling Analysis of Symmetrically Laminated Rectangular Thin Plates under Biaxial Compression

Yıl 2021, Cilt: 32 Sayı: 6, 11287 - 11314, 01.11.2021
https://doi.org/10.18400/tekderg.606620

Öz

In this parametric study, the buckling analysis of symmetrically laminated rectangular thin plates assumed to be subjected to biaxial compression was presented. The simply supported boundary condition was considered at the edges of the symmetrically laminated quasi-isotropic, cross-ply and angle-ply plates. The Rayleigh-Ritz Method was used to specify the critical buckling load of the plates based on the Classical Laminated Plate Theory (CLPT). A convergence study was achieved by increasing the number of parameters of assumed shape function. Validation of isotropic case was verified. The effects of the lamination types, plate aspect ratios (a/b, b/a) and thickness on the critical buckling load of the laminated plates under bi-axial compression were then investigated. The results were compared with Finite Element Method (FEM) solutions performed by ANSYS software package and fairly good agreement was obtained. Non-dimensional results were tabulated and presented for practical use for designers.

Kaynakça

  • Lekhnitskii, S. G., Anisotropic plates, second ed, translated from the Russian by S. W. Tsai and T. Cheron, Gordon and Breach, New York.,1968.
  • Ambartsumyan, S. A.,Theory of anisotropic plates, Technomic Publishing, Stamford CT., 1970.
  • Ashton, J. E. and Whitney, J. M., Theory of laminated plates, Technomic [43 Publishing, Stamford CT. 1970.
  • Szilard R., Theory and analysis of plates: classical and numerical methods. Englewood Cliffs, New Jersey: Prentice-Hall, 1974.
  • Jones, R. M., Mechanics of composite materials, Scripta, Washington DC, 1975.
  • Chia, C.Y, Nonlinear analysis of plates, McGraw-Hill, New York, 1980.
  • Leissa, A. W., A review of laminated composite plate buckling, Appl Mech Rev vol 40, no 5, May, 575-591, 1987.
  • Tung, T. K. and Surdenas, J., Buckling of Rectangular Orthotropic Plates Under Biaxial Loading, Journal of Composite Materials, Vol. 21-February, 124-128, 1987.
  • Nagendra, S., Haftka, R.T. and Gurdal, Z., Stacking sequence optimization of simply supported laminates with stability and strain constraints, AIAA-92-2310-CP-2526-2535, 1992.
  • Zhang, J.W., Buckling and Postbuckling of Unsymmetrically Laminated Angle-ply Plates in Uniaxial and Biaxial Compression, Thin- Walled Structures 15, 271-290, 1993.
  • Kim Y.S. and Hoa S.V., Bi-axial buckling behavior of composite rectangular plates, Composite Structures 31, 247-252, 1995.
  • Nair, S., Singh, G.L. and G. Rao, V., Stability of Laminated Composite Plates Subjected To Various Types of In-Plane Loadings, Int. J. Mech. Sci., Vol. 38. No. 2, pp. 191-202, 1996.
  • Sundaresan,P., Singh, G. and Rao,G.V., Buckling and post-buckling analysis of moderately thick laminated rectangular plates, Computers & Structures Vol. 61, No. I, pp.79-86, 1996.
  • Walker,M., Adali, S. and Verijenko,V., Optimization of symmetric laminates for maximum buckling load including the effects of bending-twisting coupling, Computers&Structures, Vol.58, No.2, pp.313-319, 1996a.
  • Walker, M., Adali, S. and Verijenko, V. E., Optimal design of symmetric angle-ply laminates subject to nonuniform buckling loads and in-plane restraints, Thin-Walled Structures Vol.26, No. I, pp. 45 60, 1996b.
  • Adali,S., Richter,A. and Verijenko, K.E., Optimization of shear-deformable laminated plates under buckling and strength criteria, Composite Structures Vol. 39, No.3-4, pp. 167-178, 1997.
  • Durban, D. and Zuckerman, Z., Elastoplastic buckling of rectangular plates in biaxial compression/tension, International Journal of Mechanical Sciences 41, 751—765, 1999.
  • Sarma, M.A., Singh, G. and Rao,G.V., Stability behaviour of angle ply plates subjected to various types of inplane loadings, Indian Journal of Engineering& Materials Sciences, Vol.6, August, pp.173-181, 1999.
  • Tuttle, M., Singhatanadgid, P. and Hinds, G., Buckling of Composite Panels Subjected to Biaxial Loading, Experimental Mechanics, VoI. 39, No. 3, September, pp.191-201, 1999.
  • Kollar, L.P. and Veres, I.A., Buckling of Rectangular Orthotropic Plates Subjected to Biaxial Normal Forces, Journal of Composite Materials, Vol. 35, No. 07, 625-635, 2001.
  • Romeo, G. and Ferrero, G., Analytical/Experimental Behavior of Anisotropic Rectangular Panels Under Linearly Varying Combined Loads, AIAA Journal, Vol. 39, No. 5, May, 932-941, 2001.
  • Narita, Y. and Turvey, G. J., Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Maximizing the buckling loads of symmetrically laminated composite rectangular plates using a layerwise optimization approach, 218: 681-691, 2004.
  • Ni,Q., Xie, J. and Iwamoto, M., Buckling analysis of laminated composite plates with arbitrary edge supports, Composite Structures, 69, 209–217, 2005.
  • Shukla, K. K., Nath, Y., Kreuzer, E. and Kumar, K.V.S., Buckling of Laminated Composite Rectangular Plates, J. Aerosp. Eng.18, 215-223, 2005.
  • Timarci, T. and Aydogdu, M., Buckling of symmetric cross-ply square plates with various boundary conditions, Composite Structures 68, 381–389, 2005.
  • Bert, C.W. and Malik,M., On the buckling characteristics of symmetrically laminated cross-ply plates, Mechanics of Composite Materials and Structures, 4:1, 39-67, 2007.
  • Qiao, P. and Shan,L., Explicit local buckling analysis of rotationally restrained composite plates under biaxial loading, International Journal of Structural Stability and Dynamics, Vol. 7, No. 3, 487–517, 2007
  • Aktaş,M., Buckling Behaviour Of Carbon/Epoxy Laminated Composite Plates Under Biaxial Loading, Advanced Composites Letters, Vol. 18, Iss. 3, 85-93, 2009.
  • Latalski, J., Ply Thickness Tolerances In Stacking Sequence Optimization Of Multilayered Laminate Plates, Journal Of Theoretical And Applied Mechanics, 51, 4, pp. 1039-1052, Warsaw, 2013.
  • Sayyad, A.S. and Ghugal,Y.M., On the Buckling of Isotropic, Transversely Isotropic and Laminated Composite Rectangular Plates, International Journal of Structural Stability and Dynamics, Vol. 14, No. 6, 1450020, 2014.
  • Bourada,F., Amara, K. and Tounsi, A., Buckling analysis of isotropic and orthotropic plates using a novel four variable refined plate theory, Steel and Composite Structures, Vol. 21, No. 6, 1287-1306, 2016.
  • Becheri,T. Amara,K., Bouazza, M. and Benseddiq,N., Buckling of symmetrically laminated plates using nth-order shear deformation theory with curvature effects, Steel and Composite Structures, Vol. 21, No. 6, 1347-1368, 2016.
  • Rajanna, T. , Banerjee,S., Desai, Y.M. and Prabhakara, D.L., Vibration and buckling analyses of laminated panels with and without cutouts under compressive and tensile edge loads, Steel and Composite Structures, Vol. 21, No. 1, 37-55, 2016.
  • Belkacem, A., Tahar,H.D., Abderrezak,R., Amine,B.M., Mohamed,Z. and Boussad,A., Mechanical buckling analysis of hybrid laminated composite plates under different boundary conditions, Structural Engineering and Mechanics, Vol. 66, No. 6, 761-769, 2018.
  • Topal,U., Vo-Duy,T., Dede,T. and Nazarimofrad,E., Buckling load optimization of laminated plates resting on Pasternak foundation using TLBO, Structural Engineering and Mechanics, Vol. 67, No. 6, 617-628, 2018.
  • Bourada, M., Bouadi,A., Bousahla,A.A., Senouci,A., Bourada,F., Tounsi,A. and Mahmoud, S.R., Buckling behavior of rectangular plates under uniaxial and biaxial compression, Structural Engineering and Mechanics, Vol. 70, No. 1, 113-123, 2019.
  • Fellah, M., Draiche,K., Houari,M.S.A., Tounsi,A., Saeed,T., Alhodaly, M.Sh. and Benguediab,M., A novel refined shear deformation theory for the buckling analysis of thick isotropic plates, Structural Engineering and Mechanics, Vol. 69, No. 3, 335-345, 2019.
  • Altekin, M., Bending of super-elliptical Mindlin plates by finite element method, Teknik Dergi, 29, No:4, 8469-8496, 2018.
  • Altekin, M., Free linear vibration and buckling of super-elliptical plates resting on symmetrically distributed point-supports on the diagonals, Thin-Walled Structures, Vol.46, 10, 1066-1086, 2008.
  • Altunsaray, E. and Bayer,İ., Buckling of symmetrically laminated quasi-isotropic thin rectangular plates, Steel and Composite Structures, Vol. 17, No. 3, 305-320, 2014.
  • Tsai, S.W., Composites design, (4th Edition), Think Composites, 1988.
  • Köksal, E. and Köksal, T.Çubuk Plak Kabuk Stabilitesi, Yıldız Teknik Üniversitesi Yayını, Yayın No:309, Yıldız Teknik Üniversitesi Matbaası, İstanbul ,1996 (In Turkish).
  • Köksal, T., Sonlu Elemanlar Metodu, Yıldız Teknik Üniversitesi Yayını, Yayın No:304, Yıldız Teknik Üniversitesi Matbaası İstanbul ,1996 (In Turkish)
  • Fish, J. and Belytschko, T., A first cours in Finite Elements, John Wiley&Sons,Ltd, 2007.
  • ANSYS 2019.1, Academic version, Dokuz Eylul University, 2019.
  • Iyengar,N.G.R., Structural stability of columns and plates, John Wiley&Sons,Ltd, 1988
  • Reddy, J.N., Mechanics of laminated composite plates and shells: Theory and Analysis (2nd Ed.), Boca Raton, FL: CRC Press, 2004.
  • Ventsel,E and Krauthammer,T., Thin plates and shells, theory, analysis, and applications, Marcel Dekker Inc., 2001
  • Wolfram Mathematica 11.3.0, Dokuz Eylul University, 2019.
  • Matlab R2018a, Dokuz Eylul University, 2019.
  • Jones, R.M., Mechanics of composite materials, 2nd ed., Taylor&Francis, 1999.
Toplam 51 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makale
Yazarlar

Erkin Altunsaray 0000-0003-3099-6059

İsmail Bayer 0000-0002-8589-671X

Yayımlanma Tarihi 1 Kasım 2021
Gönderilme Tarihi 19 Ağustos 2019
Yayımlandığı Sayı Yıl 2021 Cilt: 32 Sayı: 6

Kaynak Göster

APA Altunsaray, E., & Bayer, İ. (2021). Buckling Analysis of Symmetrically Laminated Rectangular Thin Plates under Biaxial Compression. Teknik Dergi, 32(6), 11287-11314. https://doi.org/10.18400/tekderg.606620
AMA Altunsaray E, Bayer İ. Buckling Analysis of Symmetrically Laminated Rectangular Thin Plates under Biaxial Compression. Teknik Dergi. Kasım 2021;32(6):11287-11314. doi:10.18400/tekderg.606620
Chicago Altunsaray, Erkin, ve İsmail Bayer. “Buckling Analysis of Symmetrically Laminated Rectangular Thin Plates under Biaxial Compression”. Teknik Dergi 32, sy. 6 (Kasım 2021): 11287-314. https://doi.org/10.18400/tekderg.606620.
EndNote Altunsaray E, Bayer İ (01 Kasım 2021) Buckling Analysis of Symmetrically Laminated Rectangular Thin Plates under Biaxial Compression. Teknik Dergi 32 6 11287–11314.
IEEE E. Altunsaray ve İ. Bayer, “Buckling Analysis of Symmetrically Laminated Rectangular Thin Plates under Biaxial Compression”, Teknik Dergi, c. 32, sy. 6, ss. 11287–11314, 2021, doi: 10.18400/tekderg.606620.
ISNAD Altunsaray, Erkin - Bayer, İsmail. “Buckling Analysis of Symmetrically Laminated Rectangular Thin Plates under Biaxial Compression”. Teknik Dergi 32/6 (Kasım 2021), 11287-11314. https://doi.org/10.18400/tekderg.606620.
JAMA Altunsaray E, Bayer İ. Buckling Analysis of Symmetrically Laminated Rectangular Thin Plates under Biaxial Compression. Teknik Dergi. 2021;32:11287–11314.
MLA Altunsaray, Erkin ve İsmail Bayer. “Buckling Analysis of Symmetrically Laminated Rectangular Thin Plates under Biaxial Compression”. Teknik Dergi, c. 32, sy. 6, 2021, ss. 11287-14, doi:10.18400/tekderg.606620.
Vancouver Altunsaray E, Bayer İ. Buckling Analysis of Symmetrically Laminated Rectangular Thin Plates under Biaxial Compression. Teknik Dergi. 2021;32(6):11287-314.