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Scale effects on nonlocal buckling analysis of bilayer composite plates under non-uniform uniaxial loads

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Abstract

Scale effects are studied on the buckling behavior of bilayer composite plates under non-uniform uniaxial compression via the nonlocal theory. Each isotropic plate is composed of a material that is different from others, and the adhesive between the plates is modeled as the Winkler elastic medium. According to the symmetry, effects of the Winkler non-dimensional parameter, the thickness ratio, the ratio of Young’s moduli, and the aspect ratio are also considered on the buckling problem of bilayer plates, where only the top plate is under the uniaxial compression. Numerical examples show that the Winkler elastic coefficient, the thickness ratio, and the ratio of Young’s moduli play decisive roles in the buckling behavior. Nonlocal effect is significant when the high-order buckling mode occurs or the aspect ratio is small.

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References

  1. Iijima, S. Helical microtubules of graphitic carbon. nature, 354, 56–58 (1991)

    Article  Google Scholar 

  2. Lu, P., Lee, H. P., Lu, C., and Zhang, P. Q. Dynamic properties of flexural beams using a nonlocal elasticity model. Journal of Applied Physics, 99, 073510 (2006)

    Article  Google Scholar 

  3. Wang, C. M. and Duan, W. H. Free vibration of nanorings/arches based on nonlocal elasticity. Journal of Applied Physics, 104, 014303 (2008)

    Article  Google Scholar 

  4. Duan, W. H. and Wang, C. M. Exact solutions for axisymmetric bending of micro/nanoscale circular plates based on nonlocal plate theory. Nanotechnology, 18(38), 385704 (2007)

    Article  Google Scholar 

  5. Gupta, A., Akin, D., and Bashir, R. Detection of bacterial cells and antibodies using surface micromachined thin silicon cantilever resonators. Journal of Vacuum Science & Technology B, 22(6), 2785–2791 (2004)

    Article  Google Scholar 

  6. Li, C., Thostenson, E. T., and Chou, T. W. Sensors and actuators based on carbon nanotubes and their composites: a review. Composites Science and Technology, 68(6), 1227–1249 (2008)

    Article  Google Scholar 

  7. Timoshenko, S. P. and Goodier, J. N. Theory of Elasticity, McGraw-Hill Publishing Company, New York (1970)

    MATH  Google Scholar 

  8. Yakobson, B. I., Brabec, C. J., and Bernholc, J. Nanomechanics of carbon tubes: instabilities beyond linear response. Physcial Review Letters, 76, 2511–2514 (1996)

    Article  Google Scholar 

  9. Ru, C. Q. Axially compressed buckling of a double-walled carbon nanotube embedded in an elastic medium. Journal of the Mechanics and Physics of Solids, 49, 1265–1279 (2001)

    Article  MATH  Google Scholar 

  10. Ru, C. Q. Effect of van de Waals forces on axial buckling of a double-walled carbon nanotube. Journal of Applied Physics, 87, 7227–7231 (2000)

    Article  Google Scholar 

  11. Ansari, R., Rajabiehfard, R., and Arash, B. Nonlocal finite element model for vibrations of embedded multilayered graphene sheets. Computational Materials Science, 49, 831–838 (2010)

    Article  Google Scholar 

  12. Arash, B. and Wang, Q. A review on the application of nonlocal elastic models in modeling of carbon nanotubes and graphenes. Computational Materials Science, 51, 303–313 (2012)

    Article  Google Scholar 

  13. Wang, C. M., Zhang, Y. Y., Ramesh, S. S., and Kitipornchai, S. Buckling analysis of microand nano-rods/tubes based on nonlocal Timoshenko beam theory. Journal of Physics D: Applied Physics, 39(17), 3904–3909 (2006)

    Article  Google Scholar 

  14. Erigen, A. C. Nonlocal Continuum Field Theories, Springer, New York (2001)

    Google Scholar 

  15. Pradhan, S. C. and Murmu, T. Small scale effect on the buckling analysis of single-layered graphene sheet embedded in an elastic medium based on nonlocal plate theory. Physica E, 42, 1293–1301 (2010)

    Article  Google Scholar 

  16. Assadi, A. and Farshi, B. Stability analysis of graphene based laminated composite sheets under non-uniform inplane loading by nonlocal elasticity. Applied Mathematical Modelling, 35, 4541–4549 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  17. Murmu, T., Sienz, J., Adhikari, S., and Arnold, C. Nonlocal buckling of double nanoplate systems under biaxial compression. Composites Part B: Engineering, 44, 84–94 (2013)

    Article  Google Scholar 

  18. Erigen, A. C. Nonlocal polar elastic continua. International Journal of Engineering Science, 10, 1–16 (1972)

    Article  MathSciNet  Google Scholar 

  19. Eringen, A. C. On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. Journal of Applied Physics, 54, 4703–4710 (1983)

    Article  Google Scholar 

  20. Wu, L. Y. Stability Theory of Plates and Shells (in Chinese), Huazhong University of Science & Technology Press, Wuhan (1996)

    Google Scholar 

  21. Huang, Y. and He, F. S. Beams, Plates and Shells on Elastic Foundation (in Chinese), Science Press, Beijing (2005)

    Google Scholar 

  22. Reddy, J. N. Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates. International Journal of Engineering Science, 48, 1507–1518 (2010)

    Article  MathSciNet  MATH  Google Scholar 

Download references

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Authors and Affiliations

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

    Xiang-wu Peng, Xing-ming Guo, Liang Liu & Bing-jie Wu

Authors
  1. Xiang-wu Peng
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  2. Xing-ming Guo
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  3. Liang Liu
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  4. Bing-jie Wu
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Corresponding author

Correspondence to Xing-ming Guo.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 10632040 and 11472163), the National Key Basic Research Project of China (No. 2014CB04623), and the Shanghai Municipal Commission of Eduction (No. 13ZZ067)

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Peng, Xw., Guo, Xm., Liu, L. et al. Scale effects on nonlocal buckling analysis of bilayer composite plates under non-uniform uniaxial loads. Appl. Math. Mech.-Engl. Ed. 36, 1–10 (2015). https://doi.org/10.1007/s10483-015-1900-7

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  • DOI: https://doi.org/10.1007/s10483-015-1900-7

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Chinese Library Classification

2010 Mathematics Subject Classification

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