Torsion and flexure of a prismatic isotropic beam using the boundary element method

A boundary element solution procedure is developed for studying the coupled torsion and flexure problem of an isotropic beam having an arbitrary cross section. The torsion and flexure problems are formulated using the St. Venant semi-inverse method. The development of the boundary element procedure for the solution of the coupled flexure–torsion problem is presented. A three-node isoparametric boundary element is used to allow an accurate geometric representation of cross-sections having curved boundaries. A formulation for calculation of the cross-sectional geometrical properties (centroid, area, moments of inertia, etc.) and the elastic properties (shear center location, shear correction factor, torsional rigidity) is shown. A formulation is developed for shear stress calculation at any point in the cross section. Numerical results for cross-sectional geometric and elastic properties of six different cross-sectional shapes and shear stress calculations are presented to demonstrate the efficiency and accuracy of the method.