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Mechanics of Solids and Materials by Vlado Lubarda, Robert Asaro

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10 Solutions in Polar Coordinates

10.1 Polar Components of Stress and Strain

We introduce a polar coordinate system as illustrated in Fig. 10.1. The polar coordinates r, θ are related to the cartesian coordinates x, y by

(10.1)

or, through their inverse,

(10.2)

Thus, derivatives can be formed via

(10.3)

For second derivatives we obtain

Another need is to express the components of stress, strain, and displacement in terms of ...

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