##### From Elasticity with Mathematica: An Introduction to Continuum Mechanics and Linear Elasticity

## 5.5 AIRY STRESS FUNCTION OF THE FORM A _{0}(r, ?)

The change of coordinates from cartesian *(x, y, z)* to cylindrical polar *(r, ?* preserves all of the properties introduced in the previous sections. In fact, any coordinate transformation within the plane perpendicular to the *z* axis can be performed with the help of the **TensorAnalysis** package, provided the resulting coordinate system remains orthogonal.

For cylindrical polar coordinates the result has the form

Using MATHEMATICA, the derivation is performed in a few lines.

<b class="bold"><< Tensor2Analysis.m</b><b class="bold">SetCoordinates[Cylindrical[r, t, z]]</b><b class="bold">B = {{0, 0, 0}, {0, 0, 0}, {0, 0, Psi[r, t]}}</b><b class="bold">(Stress1 = Inc [B]) // MatrixForm</b>

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B := {{0, 0, 0}, {0, 0, 0}, {0, 0, A0 [x, y]}} | Airy stress function form of the Beltrami-Maxwell tensor potential |

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