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Elasticity solutions for functionally graded plates in cylindrical bending

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Abstract

The plate theory of functionally graded materials suggested by Mian and Spencer is extended to analyze the cylindrical bending problem of a functionally graded rectangular plate subject to uniform load. The expansion formula for displacements is adopted. While keeping the assumption that the material parameters can vary along the thickness direction in an arbitrary fashion, this paper considers orthotropic materials rather than isotropic materials. In addition, the traction-free condition on the top surface is replaced with the condition of uniform load applied on the top surface. The plate theory for the particular case of cylindrical bending is presented by considering an infinite extent in the y-direction. Effects of boundary conditions and material inhomogeneity on the static response of functionally graded plates are investigated through a numerical example.

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References

  1. Reddy J N, Wang C M, Kitipornchai S. Axisymmetric bending of functionally graded circular and annular plates[J]. European Journal of Mechanics A-Solids, 1999, 18(1):185–199.

    Article  MATH  Google Scholar 

  2. Cheng Z G, Batra R C. Three-dimensional thermoelastic deformations of a functionally graded elliptic plate[J]. Composites B, 2000, 31(2):97–106.

    Article  Google Scholar 

  3. Bian Z G, Chen W Q, Lim C W, Zhang N. Analytical solutions for single-and multi-span functionally graded plates in cylindrical bending[J]. International Journal of Solids and Structures, 2005, 42(24/25):6433–6456.

    Article  MATH  Google Scholar 

  4. Chi S H, Chung Y L. Mechanical behavior of functionally graded material plates under transverse load-Part I: Analysis[J]. International Journal of Solids and Structures, 2006, 43(13):3657–3674.

    Article  MATH  Google Scholar 

  5. Chi S H, Chung Y L. Mechanical behavior of functionally graded material plates under transverse load-Part II: Numerical results[J]. International Journal of Solids and Structures, 2006, 43(13):3675–3691.

    Article  MATH  Google Scholar 

  6. Li X Y, Ding H J, Chen W Q. Pure bending of simply supported circular plate of transversely isotropic functionally graded material[J]. Journal of Zhejiang University, Science A, 2006, 7(8):1324–1328.

    Article  MATH  Google Scholar 

  7. Li X Y, Ding H J, Chen W Q. Elasticity solutions for a transversely isotropic functionally graded circular plate subject to an axisymmetric transverse load qr k[J]. International Journal of Solids and Structures, 2008, 45(1):191–210.

    Google Scholar 

  8. Mian A M, Spencer A J M. Exact solutions for functionally graded and laminated elastic materials[J]. Journal of the Mechanics and Physics of Solids, 1998, 46(12):2283–2295.

    Article  MATH  MathSciNet  Google Scholar 

  9. England A H. Bending solution for inhomogeneous and laminated elastic plates[J]. Journal of Elasticity, 2006, 82(2):129–173.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Civil Engineering, Zhejiang University, Hangzhou, 310027, P. R. China

    Bo Yang  (杨博), Hao-jiang Ding  (丁皓江) & Wei-qiu Chen  (陈伟球)

  2. Department of Civil Engineering, Zhejiang Forestry College, Lin’an, 311300, Zhejiang Province, P. R. China

    Bo Yang  (杨博)

Authors
  1. Bo Yang  (杨博)
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  2. Hao-jiang Ding  (丁皓江)
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  3. Wei-qiu Chen  (陈伟球)
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Corresponding author

Correspondence to Wei-qiu Chen  (陈伟球).

Additional information

Contributed by DING Hao-jiang

Project supported by the National Natural Science Foundation of China (Nos. 10472102, 10725210 and 10432030)

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Yang, B., Ding, Hj. & Chen, Wq. Elasticity solutions for functionally graded plates in cylindrical bending. Appl. Math. Mech.-Engl. Ed. 29, 999–1004 (2008). https://doi.org/10.1007/s10483-008-0803-9

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  • DOI: https://doi.org/10.1007/s10483-008-0803-9

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2000 Mathematics Subject Classification

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