ON THE MECHANICAL RESPONSE OF A PRESSURIZED FUNCTIONALLY-GRADED CYLINDER
DOI:
https://doi.org/10.7251/COMEN1401026LAbstract
A pressurized functionally-graded cylinder is considered made of the material whose elastic moduli vary with the radial distance according to the power-law relation. Some peculiar features of the mechanical response are noted for an incompressible functionally-graded material with the power of radial inhomogeneity equal to two. In particular, it is shown that the maximum shear stress is constant throughout the cylinder, while the displacement changes proportional to 1/r along the radial distance. No displacement takes place at all under equal pressures applied at both boundaries.
References
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[2] R. M. Christensen, Properties of carbon fibers, J. Mech. Phys. Solids, Vol. 42 (1994) 681−695.
[3] C. O. Horgan, A. M. Chan, The pressurized hollow cylinder or disk problem for function¬ally graded isotropic linearly elastic materials, J. Elasticity, Vol. 55 (1999) 43−59.
[4] R. L. Fosdick, G. Royer-Carfagni, The constraint of local injectivity in linear elasticity theory, Proc. R. Soc. Lond. A, Vol. 457 (2001) 2167−2187.
[5] N. Tutanku, Stresses in thick-walled FGM cylinders with exponentially-varying proper¬ties, Eng. Structures, Vol. 29 (2007) 2032−2035.
[6] R. C. Batra, G. L. Iaccarino, Exact solutions for radial deformations of a functionally graded isotropic and incompressible second-order elastic cylinder, Int. J. Nonlin. Me¬chanics, Vol. 43 (2008) 383−398.
[7] E. Erdogan, Fracture mechanics of functionally graded materials, Composites Engineer¬ing, Vol. 5 (1995) 753−770.
[8] Z. H. Jin, R. C. Batra, Some basic fracture mechanics concepts in functionally graded materials, J. Mech. Phys. Solids, Vol. 44 (1996) 1221−1235.
[9] V. A. Lubarda, On pressurized curvilinearly orthotropic circular disk, cylinder and sphere made of radially nonuniform material, J. Elasticity, Vol. 109 (2012) 103−113.
[10] V. A. Lubarda, Elastic response of radially nonuniform, curvilinearly anisotropic solid and hollow disks, cylinders and spheres, Proc. Monten. Acad. Sci. Arts, Vol. 20 (2013).
[11] S. P. Timoshenko, J. N. Goodier, Theory of Elasticity, 3rd ed., McGraw-Hill, New York, 1970.
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2014-09-24
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