Torsion

Using triangular elements, we shall now examine torsion of noncircular prismatic shafts. One basic difference from our previous undertakings will first be noted. Previously, we used the total potential energy as the quadratic functional to develop the key matrix equation for the finite element process. For torsion, we could still do the same by working with the warping function κ described in Section 5.2. Instead, we will find it easier to work with the stress function ψ, as discussed in Section 5.3. The total complementary potential energy in terms of ψ will then be the quadratic functional, the extremization of which will lead to the basic finite element matrix equation. This step will be the first that we shall take in broadening the finite element process; in Chapter 17 we shall use still other quadratic functionals.