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

Date

2006-01-01

Author

Eraslan, Ahmet Nedim

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

247
views

0
downloads

Closed 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.

Subject Keywords

Mechanical Engineering, Computational Mechanics

URI

https://hdl.handle.net/11511/46338

Journal

ACTA MECHANICA

DOI

https://doi.org/10.1007/s00707-005-0276-5

Collections

Department of Engineering Sciences, Article

Suggestions

OpenMETU
Core

On efficient use of simulated annealing in complex structural optimization problems Hasançebi, Oğuzhan (Springer Science and Business Media LLC, 2002-01-01) The paper is concerned with the efficient use of simulated annealing (SA) in structural optimization problems of high complexity. A reformulation of the working mechanism of the Boltzmann parameter is introduced to accelerate and enhance the general productivity of SA in terms of convergence reliability. Two general and complementary parameters, referred as "weighted Boltzmann parameter" and "critical Boltzmann parameter," are proposed, Several alternative methodologies are suggested for these two parameter...
Thermal convection in the presence of a vertical magnetic field Guray, E.; Tarman, H. I. (Springer Science and Business Media LLC, 2007-11-01) The interaction between thermal convection and an external uniform magnetic field in the vertical is numerically simulated within a computational domain of a horizontally periodic convective box between upper and lower rigid plates. The numerical technique is based on a spectral element method developed earlier to simulate natural thermal convection. In this work, it is extended to a magnetoconvection problem. Its main features are the use of rescaled Legendre-Lagrangian polynomial interpolants in expanding...
Computational and experimental study of high-speed impact of metallic Taylor cylinders Konokman, H. Emrah; Coruh, M. Murat; Kayran, Altan (Springer Science and Business Media LLC, 2011-08-01) High-speed impact of metallic Taylor cylinders is investigated computationally and experimentally. On the computational side, a modular explicit finite element hydrocode based on updated Lagrangian formulation is developed. A non-classical contour integration is employed to calculate the nodal forces in the constant strain axisymmetric triangular elements. Cell and nodal averaging of volumetric strain formulations are implemented on different mesh architectures to reduce the incompressibility constraints an...
The strain hardening rotating hollow shaft subject to a positive temperature gradient Eraslan, Ahmet Nedim; Mack, W. (Springer Science and Business Media LLC, 2007-11-01) Based on Tresca's yield criterion and the flow rule associated with it, the distribution of stress, strain and displacement in a linearly strain hardening elastic-plastic hollow shaft subject to a positive radial temperature gradient and monotonously increasing angular speed is investigated. Presupposing circular symmetry and plane strain conditions, the problem is accessible to an analytical treatment. It is found that - depending on the temperature difference between the outer and the inner surface - qual...
Analytical solution to the bending of a nonlinearly hardening wide curved bar Arslan, Eray; Eraslan, Ahmet Nedim (Springer Science and Business Media LLC, 2010-02-01) An analytical solution to the partially plastic deformation of a nonlinearly hardening wide curved bar is derived. The bar considered has a narrow rectangular cross-section and is under pure bending. The analytical treatment is based on Tresca's yield criterion, its associated flow rule and a Swift-type nonlinear hardening law. Taking numerical limits, the complete solution is verified in comparison to the linear hardening solution available in the literature.

Citation Formats

A. N. Eraslan, “On the plane strain and plane stress solutions of functionally graded rotating solid shaft and solid disk problems,” ACTA MECHANICA, pp. 43–63, 2006, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/46338.