Hello,(adsbygoogle = window.adsbygoogle || []).push({});

I'm working with a problem in linear elasticity, and I have to calculate the strain energy function as follows:

2W = σ_{ij}ε_{ij}

Where σ and ε are symmetric rank 2 tensors.

For cartesian coordinates it is really easy because the metric is just the identity matrix, hence:

2W = σ_{xx}ε_{xx}+ σ_{yy}ε_{yy}+ σ_{zz}ε_{zz}+ 2 σ_{xy}ε_{xy}+ 2 σ_{xz}ε_{xz}+ 2 σ_{zy}ε_{zy}

My question is how the expression should be for cylindrical polar coordinates (r,θ,z)

Thanks!

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Double dot product in Cylindrical Polar coordinates

Loading...

Similar Threads for Double product Cylindrical |
---|

Air resistance: cylindrical rotor in stator with air gap |

Q: cantilevered cylindrical shell |

Automotive Interesting video of a car production line |

Pressure loss to double wall pipe (ventilation) |

**Physics Forums | Science Articles, Homework Help, Discussion**