The Stress Response of Functionally Graded Isotropic Linearly Elastic Rotating Disks |
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Authors: | CO Horgan AM Chan |
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Institution: | (1) Applied Mechanics Program, Department of Civil Engineering, University of Virginia, Charlottesville, VA, 22903, U.S.A. E-mail;(2) Remote Sensing Analysis Group, Lockheed Martin Corporation, King of Prussia, PA, 19406, U.S.A |
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Abstract: | The purpose of this research is to investigate the effects of material inhomogeneity on the response of linearly elastic isotropic solid circular disks or cylinders, rotating at constant angular velocity about
a central axis. The work is motivated by the recent research activity on functionally graded materials (FGMs), i.e., materials
with spatially varying properties tailored to satisfy particular engineering applications. The analog of the classic problem
for a homogeneous isotropic rotating solid disk or cylinder is considered. The special case of a body with Young"s modulus depending on the
radial coordinate only, and with constant Poisson"s ratio, is examined. For the case when the Young"s modulus has a power-law
dependence on the radial coordinate, explicit exact solutions are obtained. It is shown that the stress response of the inhomogeneous disk (or cylinder) is significantly different from that of the homogeneous body. For example, the maximum radial and hoop
stresses do not, in general, occur at the center as in the case for the homogeneous material. Furthermore, for the case where the Young"s
modulus increases with radial distance from the center, it is shown that radially symmetric solutions exist provided the rate of growth of
the Young"s modulus is, at most, cubic in the radial variable. It is also shown for the general inhomogeneous isotropic case how the material inhomogeneity may
be tailored so that the radial and hoop stress are identical throughout the disk.
This revised version was published online in August 2006 with corrections to the Cover Date. |
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Keywords: | uniformly rotating solid disks or cylinders linear isotropic inhomogeneous elasticity maximum radial and hoop stresses functionally graded materials |
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