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Stress field of a radially functionally graded panel with a circular elastic inclusion under static anti-plane shear loading

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Abstract

The elastic stress field around a circular elastic inclusion in an infinite functionally graded material (FGM) panel that is subjected to a uniform static anti-plane shear loading at infinity is considered. Assuming the rigidity modulus of the FGM panel to be exponential, the analytical solutions of stress and strain distribution around the circular elastic inclusion are obtained by using the variable separation method. Due the generality of the elastic inclusion, other geometrical discontinuities, such as hole and rigid inclusion, can be seen as special cases of circular elastic inclusion when the inclusion rigidity modulus takes a suitable value. Therefore, the present solutions analytically reduce to some classical solution in some special cases. The present analytical solutions are compared with the existing exact solutions to verify them. Finally, the effects of the relative inclusion rigidity modulus ratio and the inhomogeneous rigidity modulus ratio on the stress distribution and the concentration factor are systematically investigated.

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References

  1. N. Cherradi, A. Kawasaki and M. Gasik, Worldwide trends in functional gradient materials research and development, Composites Engineering, 4 (8) (1994) 883–894.

    Article  Google Scholar 

  2. R. M. Mahamood et al., Functionally graded material: An overview, Proc. of the World Congress on Engineering, London, U.K. (2012).

    Google Scholar 

  3. V. Birman and L. W. Byrd, Modeling and analysis of functionally graded materials and structures, Applied Mechanics Reviews, 60 (5) (2007) 195–216.

    Article  Google Scholar 

  4. D. K. Jha, T. Kant and R. K. Singh, A critical review of recent research on functionally graded plates, Composite Structures, 96 (2013) 833–849.

    Article  Google Scholar 

  5. P. Shanmugavel et al., An overview of fracture analysis in functionally graded materials, European Journal of Scientific Research, 68 (3) (2012) 412–439.

    Google Scholar 

  6. Q. Q. Yang, C. F. Gao and W. Chen, Stress analysis of a functional graded material plate with a circular hole, Archive of Applied Mechanics, 80 (8) (2010) 895–907.

    Article  MATH  Google Scholar 

  7. P. Dineva et al., Dynamic stress and electric field concentration in a functionally graded piezoelectric solid with a circular hole, ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 91 (2) (2011) 110–124.

    Article  MATH  MathSciNet  Google Scholar 

  8. M. Batista, On the stress concentration around a hole in an infinite plate subject to a uniform load at infinity, International Journal of Mechanical Sciences, 53 (4) (2011) 254–261.

    Article  Google Scholar 

  9. M. Mohammadi, J. R. Dryden and L. Y. Jiang, Stress concentration around a hole in a radially inhomogeneous plate, International Journal of Solids and Structures, 48 (3) (2011) 483–491.

    Article  MATH  Google Scholar 

  10. R. Müller et al., Anti-plane dynamic hole-crack interaction in a functionally graded piezoelectric media, Archive of Applied Mechanics, 82 (1) (2012) 97–110.

    Article  MATH  Google Scholar 

  11. R. Sburlati, Analytical elastic solutions for pressurized hollow cylinders with internal functionally graded coatings, Composite Structures, 94 (12) (2012) 3592–3600.

    Article  Google Scholar 

  12. Q. Q. Yang and C. F. Gao, Dynamic stress analysis of a functionally graded material plate with a circular hole, Meccanica, 48 (1) (2013) 91–101.

    Article  MATH  MathSciNet  Google Scholar 

  13. R. Sburlati, Stress concentration factor due to a functionally graded ring around a hole in an isotropic plate, International Journal of Solids and Structures, 50 (22) (2013) 3649–3658.

    Article  Google Scholar 

  14. R. Sburlati, S. Atashipour and S. Atashipour, Reduction of the stress concentration factor in a homogeneous panel with hole by using a functionally graded layer, Composites Part B: Engineering, 61 (2014) 99–109.

    Article  Google Scholar 

  15. D. Kubair, Stress concentration factors and stress-gradients due to circular holes in radially functionally graded panels subjected to anti-plane shear loading, Acta Mechanica, 224 (11) (2013) 2845–2862.

    Article  MATH  Google Scholar 

  16. D. Kubair, Stress concentration factor in functionally graded plates with circular holes subjected to anti-plane shear loading, Journal of Elasticity, 114 (2) (2014) 179–196.

    Article  MATH  MathSciNet  Google Scholar 

  17. I. V. Singh, B. K. Mishra and S. Bhattacharya, XFEM simulation of cracks, holes and inclusions in functionally graded materials, International Journal of Mechanics and Materials in Design, 7 (3) (2011) 199–218.

    Article  Google Scholar 

  18. S. Bhattacharya, I. V. Singh and B. K. Mishra, Mixedmode fatigue crack growth analysis of functionally graded materials by XFEM, International Journal of Fracture, 183 (1) (2013) 81–97.

    Article  Google Scholar 

  19. G. Bhardwaj, I. V. Singh and B. K. Mishra, Stochastic fatigue crack growth simulation of interfacial crack in bilayered FGMs using XIGA, Computer Methods in Applied Mechanics and Engineering, 284 (2015) 186–229.

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. School of Mechano-Electronic Engineering, Xidian University, Xi’an, 710071, China

    Peng-peng Shi

  2. Key Laboratory of Mechanics on Disaster and Environment in Western China, Lanzhou University, Ministry of Education, Lanzhou, 730000, China

    Peng-peng Shi

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  1. Peng-peng Shi
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Correspondence to Peng-peng Shi.

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Recommended by Associate Editor Heung Soo Kim

Shi Peng-peng received the M.S. degree in mathematics and computer science from the Ningxia Univesity, Ningxia, China, 2013. He is currently working toward the Ph.D. in Mechano-Electronic Engineering at Xidian University, Shaanxi, China. His research interests include elasticity and fracture mechanics of multi-field coupling materials, weak magnetic nondestructive testing technique for ferromagnetic materials, and mathematical physics methods involved in mechanic analysis.

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Shi, Pp. Stress field of a radially functionally graded panel with a circular elastic inclusion under static anti-plane shear loading. J Mech Sci Technol 29, 1163–1173 (2015). https://doi.org/10.1007/s12206-015-0228-5

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  • DOI: https://doi.org/10.1007/s12206-015-0228-5

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