On numerical realization of the problem of torsion and bending of prismatic bars of arbitrary cross section

Abstract

We have developed software for computation of geometric characteristics and analysis of tangential stresses of prismatic bars with an arbitrary cross section in the stages of preprocessing, processing, and postprocessing of data in a finite-element analysis. Based on the principle of virtual works, we obtain variational functionals for the Saint-Venant problem of torsion of a prismatic bar and bending by a transverse force that does not cause torsion. These functionals are directly used to obtain resolving relations of the finite-element method. On the basis of the Betti reciprocal theorem, the coordinates of the center of bending are determined. We formulate all relations for the warping function, which enables us to avoid problems associated with ambiguity in the case of using the Prandtl function of stresses for a multiply connected domain.