On the plane strain and plane stress solutions of functionally graded rotating solid shaft and solid disk problems

By Ahmet N. Eraslan, Tolga Akış. 2006

128 citations recorded by the source corpus.

SummaryClosed form solutions to functionally graded rotating solid shaft and rotating solid disk problems are obtained under generalized plane strain and plane stress assumptions, respectively. The nonhomogeneity in the material arises from the fact that the modulus of elasticity of the material varies radially according to two different continuously nonlinear forms: exponential and parabolic. Both forms contain two material parameters and lead to finite values of the modulus of elasticity at the center. Analytical expressions for the stresses at the center are determined. These limiting expressions indicate that at the center of shaft/disk: (i) the stresses are finite, (ii) the radial and the circumferential stress components are equal, and (iii) the values of the stresses are independent of the variation of the modulus of elasticity. It is also shown mathematically that the nonhomogeneous solutions presented here reduce to those of homogeneous ones by an appropriate choice of the material parameters describing the variation of the modulus of elasticity.

Subfields: Civil and Structural Engineering, Control and Systems Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/dbbf053447af3608615b623ea12e44553c722f6d

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In Civil and Structural Engineering

In Control and Systems Engineering

In Mechanics of Materials

Citations in the corpus

Stress analysis in functionally graded rotating disks with non-uniform thickness and variable angular velocity (2016, unknown): “In order to validate the numerical method presented in this paper, we compare our results with analytical results presented by Eraslan and Akis [25] for the case of an FG rotating disk with constant angular velocity.”
Investigation of mechanical behavior for a rotating FGM circular disk with a variable angular speed (2015, background): “[5], that is, in this example the modulus of elasticity 0 ( ) [1 ( / ) ] k E r E n r b = and both the mass density r and the Poisson’s ratio n being constant.”
Three-dimensional free vibration of variable thickness thick circular and annular isotropic and functionally graded plates on Pasternak foundation (2011, background): “Eraslan and Akis [30] obtained the closed-form solution of FG rotating solid shaft and rotating solid disk under generalized plane strain and plane stress assumptions, respectively.”
Stress analysis and material tailoring in isotropic linear thermoelastic incompressible functionally graded rotating disks of variable thickness (2010, background): “Eraslan and Akis [13] obtained closed-form solutions for FG rotating solid shafts and disks by assuming that E is either an exponential or a parabolic function of r. Kordkheili and Naghdabadi [14] used a semi-analytical approach to analyze axisymmetric thermoelastic deformations of hollow and solid ”