Distortional Analysis of Beams of Arbitrary Cross Section Using BEM

Abstract

This paper presents a general formulation for the distortional analysis of beams of arbitrary cross section under arbitrary external loading and general boundary conditions. The nonuniform distortional/warping distributions along the beam length are taken into account by employing independent parameters multiplying suitable deformation modes accounting for in-plane and out-of-plane cross-sectional deformation (distortional/warping functions). The paper proposes a novel procedure for cross-sectional analysis which results in the solution of separate boundary value problems for each resisting mechanism (flexure, torsion) on the cross-sectional domain instead of relying on eigenvalue analysis procedures encountered in the literature. These distortional and warping functions are computed employing a boundary element method (BEM) procedure. Subsequently, sixteen boundary value problems are formulated with respect to displacement and rotation components as well as to independent distortional/warping parameters along the beam length and solved using the analog equation method (AEM), a BEM-based technique. After the establishment of kinematical components, stress components on any arbitrary point of each cross section of the beam can be evaluated, yielding a prediction in good agreement with three-dimensional finite-element method (FEM) solutions, in contrast to conventional beam models.