Exact Solution for General Torsion Problems Using Boundary Singularities

Abstract

An exact and closed-form solution for general torsion problems of a rod having a simply connected cross sections is presented. Unlike the classical solution, which addresses the associated Dirichlet problem, the present formulation is applied to the torsion problem, which is given using Neumann boundary conditions, and thus serves as a fundamental solution that complements the classical one. The present solution, which is accomplished using the distribution of boundary-singularities, is demonstrated for an illustrative example.