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Part of the book series: Foundations of Engineering Mechanics ((FOUNDATIONS))

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Abstract

An annular disk of variable thickness h (r) and radii a and b, clamped at the inner edge, is subjected to steady rotation about the axis of symmetry with an angular velocity ω and uniform radial tension along the periphery. Plane stress state σ z = 0 and creep incompressibility ε cm = 0 assumed when the transient creep problem is solved in velocities by the use of cylindrical coordinate system r, ϑ, z. Hence, for a rotationally symmetric deformation, the equilibrium equation takes the following form:

$$\frac{1}{h}\,\frac{d}{{dr}}\left( {h{\sigma _r}} \right) + \frac{{{\sigma _r}{\sigma _\vartheta }}}{r} + \rho {\omega ^2}r = 0.$$
(12.1)

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© 1999 Springer-Verlag Berlin Heidelberg

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Skrzypek, J.J., Ganczarski, A. (1999). Optimal design of axisymmetric disks. In: Modeling of Material Damage and Failure of Structures. Foundations of Engineering Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69637-7_12

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  • DOI: https://doi.org/10.1007/978-3-540-69637-7_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-08353-2

  • Online ISBN: 978-3-540-69637-7

  • eBook Packages: Springer Book Archive

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