Elasticity/Warping functions

Warping Function and Torsion of Non-Circular Cylinders edit

Warping functions are quite useful in the solution of problems involving the torsion of cylinders with non-circular cross sections.

For such problems, the displacements are given by


where   is the twist per unit length, and   is the warping function.

The stresses are given by


where   is the shear modulus.

The projected shear traction is


Equilibrium is satisfied if


Traction-free lateral BCs are satisfied if




The twist per unit length is given by


where the torsion constant