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Thermal-induced snap-through buckling of simply-supported functionally graded beams

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Abstract

The instability of functionally graded material (FGM) structures is one of major threats to their service safety in widely engineering applications. This paper aims to clarify a long-standing controversy on the type of thermal instability of simply-supported FGM beams. Firstbased on the Euler-Bernoulli beam theory and von Kármán geometric nonlinearitya nonlinear governing equation of simply-supported FGM beams under uniform thermal loads by Zhang’s two-variable method is formulated. Secondan approximate analytic solution to the nonlinear integro-differential boundary value problem with a thermal-induced inhomogeneous force boundary condition is obtained by using a semi-inverse method when the coordinate axis is relocated to the bending axis (physical neutral plane), and then the analytical predictions are verified by the differential quadrature method (DQM). Finallybased on the free energy theoremit is revealed that the symmetry breaking caused by the material inhomogeneity can make the simply-supported FGM beam under uniform thermal loads occur snap-through postbuckling only in odd modes; furthermorethe nonlinear critical load of thermal buckling varies non-monotonically with the functional gradient index due to the stretching-bending coupling effect. These results are expected to provide new ideas and references for the design and regulation of FGM structures.

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Author information

Authors and Affiliations

  1. School of Mechanics and Engineering Science, Shanghai University, Shanghai, 200444, China

    Yongyong Xi, Qiang Lyu, Nenghui Zhang & Junzheng Wu

  2. Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai, 200072, China

    Nenghui Zhang

Authors
  1. Yongyong Xi
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  2. Qiang Lyu
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  3. Nenghui Zhang
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  4. Junzheng Wu
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Correspondence to Nenghui Zhang.

Additional information

Citation: XI, Y. Y., LYU, Q., ZHANG, N. H., andWU, J. Z. Thermal-induced snap-through buckling of simply-supported functionally graded beams. Applied Mathematics and Mechanics (English Edition), 41(12), 1821–1832 (2020) https://doi.org/10.1007/s10483-020-2691-7

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Xi, Y., Lyu, Q., Zhang, N. et al. Thermal-induced snap-through buckling of simply-supported functionally graded beams. Appl. Math. Mech.-Engl. Ed. 41, 1821–1832 (2020). https://doi.org/10.1007/s10483-020-2691-7

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  • DOI: https://doi.org/10.1007/s10483-020-2691-7

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Chinese Library Classification

2010 Mathematics Subject Classification

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