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Analytical solution for buckling of VAT composite laminates with elastic restraints on two opposite edges

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Abstract

Based on classical laminated plate theory, an analytical solution for buckling of variable angle tow (VAT) composite laminates with elastic restraints on two opposite edges and simply supported conditions on the other edges is presented in this paper. It is assumed that the fiber orientation angle of each lamina varies linearly or nonlinearly along the x direction. The governing differential equation with variable coefficients for the buckling of VAT laminates is established. The coefficients of the governing equation are expanded into Taylor series with respect to x, and then Frobenius series is employed to solve the governing equation. The buckling behavior of VAT laminates under the action of a uniform end shortening is investigated by the presented analytical method. The accuracy and convergence of the present solutions are verified by comparing with existing solutions and the ABAQUS results. The influence of the variation of the fiber orientation angle, different fiber paths, and different elastically supported stiffness on the critical buckling load of VAT laminate is discussed in numerical examples. The analytical solution presented here can be used as a benchmark to evaluate numerical solutions for buckling of VAT laminates. Moreover, the combination of Taylor series and Frobenius series is an alternative and effective analytical method to investigate the mechanical behavior of in-plane variable stiffness laminates.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 12072239, 11772232, and 11372225). Xiaodong Chen would like to thank the financial support from the Special Fund for Doctoral Talents (Henan University of Urban Construction, China).

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Authors and Affiliations

  1. School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, 200092, China

    Guojun Nie

  2. School of Civil and Transportation Engineering, Henan University of Urban Construction, Pingdingshan, 467000, China

    Xiaodong Chen

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  1. Guojun Nie
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  2. Xiaodong Chen
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Correspondence to Guojun Nie.

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Nie, G., Chen, X. Analytical solution for buckling of VAT composite laminates with elastic restraints on two opposite edges. Meccanica 57, 2085–2099 (2022). https://doi.org/10.1007/s11012-022-01535-3

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