Elasticity/Warping of circular cylinder

Example 1: Circular Cylinder

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Choose warping function

 

Equilibrium ( ) is trivially satisfied.

The traction free BC is

 

Integrating,

 

where   is a constant.

Hence, a circle satisfies traction-free BCs.

  • There is no warping of cross sections for circular cylinders

The torsion constant is

 

The twist per unit length is

 

The non-zero stresses are

 

The projected shear traction is

 

Compare results from Mechanics of Materials solution

 

and