Improving quality of torsional analysis of prismatic beams by using an interpolated warping function

Abstract

This paper examines the torsion of beams with undeformable cross-sections. A novel approach is proposed, in which an interpolated warping function is defined as a continuously differentiable function across the entire cross-sectional area. This formulation enables methods that require the warping value to be accessible as a continuous function at any point within the section. The approach facilitates deformation analysis within the framework of three-dimensional elasticity, employing continuum-based beam elements governed by general continuum mechanics material laws. The primary objective of this study is to establish a general method for determining warping functions for complex cross-sections, intended for future applications in the absolute nodal coordinate formulation. The approach does not replace earlier methods, which have proven highly efficient and even suitable for hand calculations. Instead, it provides a general-purpose framework that can yield improved accuracy in certain cases. Whereas traditional treatments distinguished primarily between open and closed profiles, the present formulation emphasizes the importance of recognizing the nature of each profile and selecting interpolation methods accordingly.