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
The twist per unit length is given by
where the torsion constant