A novel analytical solution for warping analysis of arbitrary annular wedge-shaped bars

Abstract

Structural components with arbitrary cross sections play a key role in several engineering fields. Many engineering structures are subjected to torsional moments, so it is important to design and analyze these type of crucial engineering issues. First, this study offers a novel analytical solution for Prandtl’s stress distribution of arbitrary annular wedge-shaped bars under uniform torsion moment based on eigenfunction expansion. Next, warping function is derived by integration of Cauchy-Riemann type relations in polar coordinate system. The solution encompasses existing solutions for standard wedge-shaped bars as subsets. Finally, accuracy of the proposed analytical method is fully demonstrated through some benchmarks which are available in the literature.