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Dynamic stress analysis of a functionally graded material plate with a circular hole

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Abstract

This paper is to study the two-dimensional dynamic stress of a functionally graded material (FGM) plate with a circular hole under plane compressional waves at infinity. With using the method of piece-wise homogeneous layers, the dynamic stress distribution of the FGM plate having radial arbitrary material parameters is derived based on the complex variable method. As examples, numerical results are presented for the FGM plate having given radial shear modulus, density and Poisson’s ratio. It is found that the dynamic stress around the circular hole in the FGM plate can be effectively reduced by choosing the proper change ways of the radial material parameters for different frequency incident wave.

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References

  1. Ma L, Wu LZ, Guo LC (2002) Dynamic behavior of two collinear anti-plane shear cracks in a functionally graded layer bonded to dissimilar half planes. Mech Res Commun 29:207–215

    Article  MATH  Google Scholar 

  2. Meguid SA, Wang XD, Jiang LY (2002) On the dynamic propagation of a finite crack in functionally graded materials. Eng Fract Mech 69:1753–1768

    Article  Google Scholar 

  3. Chen J, Liu ZX, Zou ZZ (2003) Electromechanical impact of a crack in a functionally graded piezoelectric medium. Theor Appl Fract Mech 39:47–60

    Article  Google Scholar 

  4. Song SH, Paulino GH (2006) Dynamic stress intensity factors for homogeneous and smoothly heterogeneous materials using the interaction integral method. Int J Solids Struct 43:4830–4866

    Article  MATH  Google Scholar 

  5. Feng WJ, Su RKL (2006) Dynamic internal crack problem of a functionally graded magneto-electro-elastic strip. Int J Solids Struct 43:5196–5216

    Article  MATH  Google Scholar 

  6. Li YD, Lee KY (2008) Fracture analysis of a weak-discontinuous interface in a symmetrical functionally gradient composite strip loaded by anti-plane impact. Arch Appl Mech 78:855–866

    Article  MATH  Google Scholar 

  7. Peng XL, Li XF (2009) Transient response of the crack-tip field in a magnetoelectroelastic half-space with a functionally graded coating under impacts. Arch Appl Mech 79:1099–1113

    Article  MATH  Google Scholar 

  8. Han X, Liu GR, Xi ZC, Lam KY (2002) Characteristics of waves in a functionally graded cylinder. Int J Numer Methods Eng 53:653–676

    Article  MATH  Google Scholar 

  9. Chen WQ, Bian ZG, Lv CF, Ding HJ (2004) 3D free vibration analysis of a functionally graded piezoelectric hollow cylinder filled with compressible fluid. Int J Solids Struct 41:947–964

    Article  MATH  Google Scholar 

  10. Elmaimouni L, Lefebvre JE, Zhang V, Gryba T (2005) Guided waves in radially graded cylinders: a polynomial approach. NDT E Int 38:344–353

    Article  Google Scholar 

  11. Bagri A, Eslami MR (2007) Analysis of thermoelastic waves in functionally graded hollow spheres based on the Green-Lindsay theory. J Therm Stresses 30:1175–1193

    Article  Google Scholar 

  12. Asgari M, Akhlaghi M, Hoseini SM (2009) Dynamic analysis of two-dimensional functionally graded thick hollow cylinder with finite length under impact loading. Acta Mech 208:163–180

    Article  MATH  Google Scholar 

  13. Shariyat M, Khaghani M, Lavasani SMH (2010) Nonlinear thermoelasticity, vibration, and stress wave propagation analyses of thick FGM cylinders with temperature-dependent material properties. Eur J Mech A, Solids 29:378–391

    Article  Google Scholar 

  14. Pao YH (1962) Dynamical stress concentration in an elastic plate. J Appl Mech 29:299–305

    Article  MATH  Google Scholar 

  15. Mow CC, McCabe WL (1963) Dynamic stresses in an elastic cylinder. Proceedings of the American Society of Civil Engineers, J Eng Mech Div 89:21–41

    Google Scholar 

  16. Liu DK, Gai BZ, Tao GY (1982) Applications of the method of complex function to dynamic stress concentration. Wave Motion 4:293–304

    Article  MathSciNet  MATH  Google Scholar 

  17. Shankar K (1998) A study of the dynamic stress concentration factors of a flat plate for sea applications. J Sound Vib 217:97–111

    Article  ADS  Google Scholar 

  18. Altenhof W, Zamani N, North W, Arnold B (2004) Dynamic stress concentrations for an axially loaded strut at discontinuities due to an elliptical hole or double circular notches. Int J Impact Eng 30:255–274

    Article  Google Scholar 

  19. Zirka AI, Malezhik MP, Chernyshenko IS (2004) Stress concentration in an orthotropic plate with a circular hole under dynamic loading. Int Appl Mech 40:226–230

    Article  Google Scholar 

  20. Gao SW, Wang YS, Zhang ZM, Ma XR (2005) Dual reciprocity boundary element method for flexural waves in thin plate with cutout. Appl Math Mech 26:1564–1573

    Article  MATH  Google Scholar 

  21. Wang JH, Zhou XL, Lu JF (2005) Dynamic stress concentration around elliptic cavities in saturated poroelastic soil under harmonic plane waves. Int J Solids Struct 42:4295–4310

    Article  MATH  Google Scholar 

  22. Wang GF, Wang TJ, Feng XQ (2006) Surface effects on the diffraction of plane compressional waves by a nanosized circular hole. Appl Phys Lett 89:231923

    Article  ADS  Google Scholar 

  23. Fang XQ, Hu C, Du SY (2006) Strain energy density of a circular cavity buried in semi-infinite functionally graded materials subjected to shear waves. Theor Appl Fract Mech 46:166–174

    Article  Google Scholar 

  24. Fang XQ, Hu C, Du SY (2007) Dynamic stress of a circular cavity buried in a semi-infinite functionally graded material subjected to shear waves. J Appl Mech 74:916–922

    Article  Google Scholar 

  25. Fang XQ, Hu C, Huang WH (2007) Strain energy density of a circular cavity buried in a semi-infinite slab of functionally graded materials subjected to anti-plane shear waves. Int J Solids Struct 44:6987–6998

    Article  MATH  Google Scholar 

  26. Dineva P, Gross D, Muller R, Rangelov T (2011) Dynamic stress and electric field concentration in a functionally graded piezoelectric solid with a circular hole. Z Angew Math Mech 91:110–124

    Article  MathSciNet  MATH  Google Scholar 

  27. Pao YH, Mow CC (1973) Diffraction of elastic waves and dynamic stress concentrations. Crane and Russak, New York

    Google Scholar 

  28. Yang QQ, Gao CF, Chen WT (2010) Stress analysis of a functional graded material plate with a circular hole. Arch Appl Mech 80:895–907

    Article  Google Scholar 

Download references

Acknowledgements

The authors thank the financial support from the National Natural Science Foundation of China (10972103) and the Ph.D. Programs Foundation of Ministry of Education of China (20093218110004). QQY is also grateful to the support of Funding of Jiangsu Innovation Program for Graduate Education (CXZZ11_0191) and Funding for Outstanding Doctoral Dissertation in NUAA (BCXJ11-03).

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Authors and Affiliations

  1. State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics & Astronautics, Nanjing, 210016, China

    Quanquan Yang & Cun-Fa Gao

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  1. Quanquan Yang
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  2. Cun-Fa Gao
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Correspondence to Cun-Fa Gao.

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Yang, Q., Gao, CF. Dynamic stress analysis of a functionally graded material plate with a circular hole. Meccanica 48, 91–101 (2013). https://doi.org/10.1007/s11012-012-9586-6

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  • DOI: https://doi.org/10.1007/s11012-012-9586-6

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