This note describes how the displacements and shear stresses of an axisymmetric elastic component, when loaded in torsion, can be computed by modelling the component with torsional axisymmetric finite elements. The model developed represents only minor modifications of the well-known plane stress or plane strain finite element technique.In the analysis, the model is split into a mesh of triangular annuli. Each node of each element has only one degree of freedom, the tangential displacement. The state of strain in each element is represented by a three-term displacement function, one representing a rigid body rotation, the second representing the state of torsion, and the third representing the state of strain in a hollow thin disc.The model has been applied satisfactorily to three torsional problems with known theoretical solutions. The first problem involves the computation of torsional shear stresses of a uniform shaft subjected to pure torsion. In the second problem, the solution is obtained for a conical shaft. In the third problem, known as the Reissner–Sagoci problem, an elastic semi-infinite medium is subjected to a torsional displacement on a small area of the surface.A typical application of the model to the problem of a shrink-fitted assembly subjected to torsion is discussed. Key words: torsion, finite element, elasticity, axisymmetry.
