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.

具有任意横截面的结构部件在多个工程领域中发挥着关键作用。许多工程结构都承受扭转力矩，因此设计和分析这类关键工程问题非常重要。首先，该研究为基于特征函数展开的均匀扭转力矩下任意环形楔形杆的Prandtl应力分布提供了一种新颖的解析解。接下来，通过将Cauchy-Riemann型关系集成到极坐标系中来得出翘曲函数。该解决方案包括将标准楔形钢筋作为子集的现有解决方案。最后，通过文献中提供的一些基准充分证明了所提出的分析方法的准确性。