Abstract
This chapter is devoted to the consideration of isotropic disk structures in Cartesian coordinates. After a short definition of what constitutes a disk, the two basic analytical approaches, namely the displacement method and the force method, are motivated and, for the force method, all basic equations necessary for the description of a disk are compiled. This is followed by an energetic consideration of the disk problem, before the solutions of the disk equation and elementary disk problems are discussed in detail.
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Notes
- 1.
George Bidell Airy, 1801–1892, English mathematician.
- 2.
Note that F is in the unit of a force in the case of considering the disk stresses, whereas F must be calculated with the unit of a force multiplied by a unit of length when using the internal force flows \(N_{xx}^0\), \(N_{yy}^0\), \(\tau _{xy}^0\). We will speak of the Airy stress function F in both cases in the following, and the unit to be used results from the respective context.
- 3.
Girkmann (1974) adds the volume forces to the definition of the shear stress in the form of \(\tau _{xy}=-\frac{{\partial ^2 F}}{{\partial x \partial y }}-yf_x-xf_y\).
- 4.
Adhémar Jean Claude Barré de Saint-Venant, 1797–1886, French mathematician and engineer.
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Mittelstedt, C. (2023). Isotropic Disks in Cartesian Coordinates. In: Theory of Plates and Shells. Springer Vieweg, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-66805-4_3
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DOI: https://doi.org/10.1007/978-3-662-66805-4_3
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