# Introduction to Elasticity/Warping functions

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## Warping Function and Torsion of Non-Circular Cylinders[edit | edit source]

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

or,

The twist per unit length is given by

where the torsion constant