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Material tailoring and moduli homogenization for finite twisting deformations of functionally graded Mooney-Rivlin hollow cylinders

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Abstract

We analytically analyze finite plane strain twisting deformations of a hollow cylinder made of an isotropic and inhomogeneous Mooney-Rivlin material with material moduli varying in the radial direction. The cylinder is deformed by applying either tangential tractions on the inner surface and tangential displacements on the outer surface or vice versa. The radial variation of the moduli is found that will minimize the tangential displacement of the bounding surface where tangential traction is specified. Furthermore, the modulus of a homogeneous neo-Hookean cylinder is found that is energetically equivalent to the inhomogeneous cylinder.

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References

  1. Leissa A.W., Vagins M.: The design of orthotropic materials for stress optimization. Int. J. Solids Struct. 14, 517–526 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bert, C.W., Niedenfuhr, F.W.: Stretching of a polar-orthotropic disk of varying thickness under arbitrary body forces. AIAA J. 1, 1385–90 (1963)

    Google Scholar 

  3. Batra R.C.: Optimal design of functionally graded incompressible linear elastic cylinders and spheres. AIAA J. 46, 2050–2057 (2008)

    Article  Google Scholar 

  4. Batra R.C.: Material tailoring and universal relations for axisymmetric deformations of functionally graded rubberlike cylinders and spheres. Math. Mech. Solids. 16(7), 729–738 (2011)

    Article  MathSciNet  Google Scholar 

  5. Tanaka K., Watanabe H., Sugano Y., Poterasu Y.F.: A multicriteria material tailoring of a hollow cylinder in functionally gradient materials: scheme to global reduction of thermoelastic stresses. Comput. Methods Appl. Mech. Eng. 135, 369–380 (1996)

    Article  MATH  Google Scholar 

  6. Sun M., Hyer M.W.: Use of material tailoring to improve buckling capacity of elliptical composite cylinders. AIAA J. 46, 770–782 (2008)

    Article  Google Scholar 

  7. Batra R.C., Jin J.: Natural frequencies of a functionally graded anisotropic rectangular plate. J. Sound Vib. 282, 509–516 (2005)

    Article  Google Scholar 

  8. Karandikar K., Mistree F.: Tailoring composite materials through optimal selection of their constituents. J. Mech. Des. 114, 451–458 (1992)

    Article  Google Scholar 

  9. Naghshineh, K. :Strategies for the optimum design of quiet structures: use of material tailoring and/or active vibration control. Thesis (PhD)—The Pennsylvania State University (1991)

  10. Qian L.F., Batra R.C.: Design of bidirectional functionally graded plate for optimal natural frequencies. J. Sound Vib. 280, 415–424 (2005)

    Article  Google Scholar 

  11. Nie G.J., Batra R.C.: Material tailoring and analysis of functionally graded isotropic and incompressible linear elastic hollow cylinders. Compos. Struct. 92, 265–274 (2010)

    Article  Google Scholar 

  12. Nie G.J., Batra R.C.: Stress analysis and material tailoring in isotropic linear thermoelastic incompressible functionally graded rotating disks of variable thickness. Compos. Struct. 92, 720–729 (2010)

    Article  Google Scholar 

  13. Batra R.C.: Torsion of a functionally graded cylinder. AIAA J. 44(6), 1363–1365 (2006)

    Article  Google Scholar 

  14. Truesdell C.A., Noll W.: The nonlinear field theory of mechanics. Handbuch der Physik, III/3. Springer, Berlin (1965)

    Google Scholar 

  15. Ericksen J.L.: Deformations possible in every isotropic incompressible perfectly elastic body. Z. Angew. Math. Phys. 5, 466–486 (1954)

    Article  MathSciNet  MATH  Google Scholar 

  16. Dryden, J., Batra, RC.: Optimum Young’s modulus of a homogeneous cylinder energetically equivalent to a functionally graded cylinder. J. Elast. (2012) doi:10.1007/s10659-012-9383-4

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Authors and Affiliations

  1. Department of Mechanical and Materials Engineering, The University of Western Ontario, London, ON, N6A 5B9, Canada

    J. R. Dryden

  2. Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, VA, 24061, USA

    R. C. Batra

Authors
  1. J. R. Dryden
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  2. R. C. Batra
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Correspondence to R. C. Batra.

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Dryden, J.R., Batra, R.C. Material tailoring and moduli homogenization for finite twisting deformations of functionally graded Mooney-Rivlin hollow cylinders. Acta Mech 224, 811–818 (2013). https://doi.org/10.1007/s00707-012-0784-z

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  • DOI: https://doi.org/10.1007/s00707-012-0784-z

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