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Published in:
Basics of Elasticity Theory Read chapter Read first chapter

2023 | OriginalPaper | Chapter

3. Isotropic Disks in Cartesian Coordinates

Author : Christian Mittelstedt

Published in: Theory of Plates and Shells

Publisher: Springer Berlin Heidelberg

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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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previous chapter Energy Methods of Elastostatics
next chapter Isotropic Disks in Polar Coordinates
Footnotes
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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Metadata
Title
Isotropic Disks in Cartesian Coordinates
Author
Christian Mittelstedt
Copyright Year
2023
Publisher
Springer Berlin Heidelberg
Book
Theory of Plates and Shells

Print ISBN: 978-3-662-66804-7

Electronic ISBN: 978-3-662-66805-4

Copyright Year: 2023

DOI
https://doi.org/10.1007/978-3-662-66805-4_3

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