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Three-dimensional buckling analysis of variable angle tow composite laminated plates

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Abstract

This paper presents three-dimensional solutions for the buckling of variable angle tow (VAT) composite laminated plates. The p-version finite element with hierarchical basis functions is adopted to determine the buckling of VAT composite laminates with different parameters. Inter-element compatibility is achieved by matching the generalized displacements at the vertices, edges, and faces shared by neighboring elements. The buckling loads of symmetrical and anti-symmetrical laminates with various boundary conditions are obtained. A convergence study is performed and the accuracy of the method is confirmed by comparing the numerical results with those in the literatures. The verified results indicate that the present 3D p-FEM method is accurate for the buckling analysis of VAT composite laminated plates, and that these three-dimensional results may serve as a benchmark for future studies.

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References

  • Bullock, F., Kowalski, S., Young, R.: Automated prepreg tow-placement for composite structures. In: 35th International SAMPE Symposium, Anaheim, CA, pp. 734–743 (1990)

  • Chen, X.D., Wu, Z.M., Nie, G.J., et al.: Buckling analysis of variable angle tow composite plates with a through-the-width or an embedded rectangular delamination. Int. J. Solids Struct. 138, 166–180 (2018)

    Article  Google Scholar 

  • Enders, M.L., Hopkins, P.C.: Developments in the fiber placement process. In: 36th International SAMPE Symposium, San Diego, CA, pp. 778–790 (1991)

  • Evans, D.O., Vaniglia, M.M., Hopkins, P.C.: Fiber placement process study. In: 34th International SAMPE Symposium, Covina, CA, pp. 1822–1833 (1989)

  • Groh, R.M.J., Weaver, P.M.: Buckling analysis of variable angle tow, variable thickness panels with transverse shear effects. Compos. Struct. 107, 482–493 (2014)

    Article  Google Scholar 

  • Gu, H.Z., Chattopadhyay, A.: Three-dimensional elasticity solution for buckling of composite laminates. Compos. Struct. 50(1), 29–35 (2000)

    Article  Google Scholar 

  • Guo, J.H., Sun, T.Y., Pan, E.: Three-dimensional buckling of embedded multilayered magneto-electro-elastic nanoplates/graphene sheets with nonlocal effect. J. Intell. Mater. Syst. Struct. 30(18–19), 2870–2893 (2019)

    Article  Google Scholar 

  • Gürdal, Z., Olmedo, R.: In-plane response of laminates with spatially varying fiber orientations: variable stiffness concept. AIAA J. 31(4), 751–758 (1993)

    Article  Google Scholar 

  • Gürdal, Z., Tatting, B.F., Wu, C.K.: Variable stiffness composite panels: effects of stiffness variation on the in-plane and buckling response. Compos. Part A Appl. Sci. Manuf. 39(5), 911–922 (2008)

    Article  Google Scholar 

  • Hao, P., Yuan, X.J., Liu, H.L., et al.: Isogeometric buckling analysis of composite variable-stiffness panels. Compos. Struct. 165, 192–208 (2017)

    Article  Google Scholar 

  • Houmat, A.: Three-dimensional free vibration analysis of plates using the h-p version of the finite element method. J. Sound Vibr. 290(3–5), 690–704 (2006)

    Article  Google Scholar 

  • Houmat, A.: Three-dimensional free vibration analysis of variable stiffness laminated composite rectangular plates. Compos. Struct. 194, 398–412 (2018)

    Article  Google Scholar 

  • Hyer, M.W., Lee, H.H.: The use of curvilinear fiber format to improve buckling resistance of composite plates with central circular holes. Compos. Struct. 18(3), 239–261 (1991)

    Article  Google Scholar 

  • Love, A.E.H.: On the small free vibrations and deformations of thin elastic shells. Philos. Trans. R. Soc. Lond. (A.) 179, 125–137(1888)

    Google Scholar 

  • Lu, C.F., Chen, W.Q., Shao, J.W.: Semi-analytical three-dimensional elasticity solutions for generally laminated composite plates. Euro. J. Mech. A. Solids 27(5), 737–958 (2008)

    Article  Google Scholar 

  • Mindlin, R.D.: Influence of rotatory inertia and shear on flexural motions of isotropic elastic plates. J. Appl. Mech. 18(1), 31–38 (1951)

    MATH  Google Scholar 

  • Noor, A.K., Burton, W.S.: Assessment of shear deformation theories for multilayered composite plate. Appl. Mech. Rev. 42(1), 1–13 (1989)

    Article  Google Scholar 

  • Noor, A.K., Burton, W.S.: Three-dimensional solutions for anti-symmetrically laminated anisotropic plates. J. Appl. Mech. 57(1), 182–188 (1990)

    Article  Google Scholar 

  • Olmedo, R., Gürdal, Z.: Buckling response of laminates with spatially varying fiber orientations. In: Proceedings of the 34th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials (SDM) Conference (1993)

  • Pagano, N.J.: Exact solutions for rectangular bidirectional composites and sandwich plates. J. Compos. Mater. 4(1), 20–34 (1970)

    Article  Google Scholar 

  • Pagano, N.J., Hatfield, S.J.: Elastic behavior of multilayered bidirectional composites. AIAA J. 10(7), 931–933 (1972)

    Article  Google Scholar 

  • Patni, M., Minera, S., Groh, R.M.J., et al.: Three-dimensional stress analysis for laminated composite and sandwich structures. Compos. Part B Eng. 155, 299–328 (2018)

    Article  Google Scholar 

  • Raju, G., Wu, Z.M., Weaver, P.M.: Prebuckling and buckling analysis of variable angle tow plates with general boundary conditions. Compos. Struct. 94(9), 2961–2970 (2012)

    Article  Google Scholar 

  • Raju, G., Wu, Z.M., Weaver, P.M.: Buckling and postbuckling of variable angle tow composite plates under in-plane shear loading. Int. J. Solids Struct. 58, 270–287 (2015)

    Article  Google Scholar 

  • Reddy, J.N.: A simple higher-order theory for laminated composite plates. J. Appl. Mech. 51(4), 745–752 (1984)

    Article  Google Scholar 

  • Reddy, J.N.: Mechanics of laminated composite plates and shells, theory and analysis. CRC Press, Boca Raton (2004)

    MATH  Google Scholar 

  • Reddy, J.N.: Theory and analysis of elastic plates and shells. CRC Press, Boca Raton (2007)

    Google Scholar 

  • Reissner, E.: The effect of transverse shear deformation on the bending of elastic plates. J. Appl. Mech. 12(1), 69–77 (1945)

    MathSciNet  MATH  Google Scholar 

  • Sciuva, M.D.: Development of an anisotropic, multilayered, shear deformable rectangular plate element. Comput. Struct. 21(4), 789–796 (1985)

    Article  Google Scholar 

  • Szabo, B., Duster, A., Rank, E.: The p-version of the finite element method. Wiley, New York (2004)

    Google Scholar 

  • Tatting, B. F., Gürdal Z.: Design and manufacture of elastically tailored tow placed plates. NASA/CR-2003-212679 (2003)

  • Waksmanski, N., Pan, E.: An analytical three-dimensional solution for free vibration of a magneto-electro-elastic plate considering the nonlocal effect. J. Intell. Mater. Syst. Struct. 28(11), 1501–1513 (2017)

    Article  Google Scholar 

  • Waldhart, C., Gürdal, Z., Ribbens, C.: Analysis of tow placed, parallel fiber, variable stiffness laminates. In: Proceedings of the 37th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials (SDM) Conference (1996)

  • Wu, C.P., Li, W.C.: Asymptotic nonlocal elasticity theory for the buckling analysis of embedded single-layered nanoplates/graphene sheets under biaxial compression. Phys. E 2(4), 851–856 (2017)

    Google Scholar 

  • Wu, Z.M., Raju, G., Weaver, P. M.: Buckling of VAT plates using energy methods. In: Proceedings of the 53th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials (SDM) Conference (2012a)

  • Wu, Z.M., Weaver, P.M., Raju, G., et al.: Buckling analysis and optimization of variable angle tow composite plates. Thin-Walled Struct. 60, 163–172 (2012)

    Article  Google Scholar 

  • Zhou, X.Y., Gosling, P.D.: Towards an understanding of variations in the buckling of tailored variable angle tow composite plates. Compos. Struct. 203, 797–809 (2018)

    Article  Google Scholar 

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Authors and Affiliations

  1. Nanjing University of Aeronautics and Astronautics, Nanjing, China

    Kun Nie

  2. Tongji University, Shanghai, China

    Yi Liu

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  1. Kun Nie
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  2. Yi Liu
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Correspondence to Yi Liu.

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Nie, K., Liu, Y. Three-dimensional buckling analysis of variable angle tow composite laminated plates. Int J Mech Mater Des 17, 89–98 (2021). https://doi.org/10.1007/s10999-020-09511-z

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  • DOI: https://doi.org/10.1007/s10999-020-09511-z

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