On the Access to Transverse Shear Stiffnesses and to Stiffness Quantities for Non-Uniform Warping Torsion in FGM Beam Structures

The application of first order shear beam theory in the analysis of beam structures made of functionally graded materials requires the access to homogenized stiffness quantities. These quantities depend on the cross-sectional shape and on the spatial variation of constitutive parameters. Some of these stiffness quantities can be evaluated easily by simple integration, however, the access to transverse shear stiffnesses and to stiffness quantities regarding warping torsion is typically cumbersome. In this contribution a novel approach for their evaluation is proposed, which is based on a reference beam problem. Here, we restrict ourselves to double symmetric cross-sections, however, a generalization of the proposed method to the arbitrary case is obvious. Besides that, a novel approach to cover non-uniform warping torsion is included. The proposed method is efficient, since the discretization of the cross-section suffices, and accurate as can be shown in challenging bench mark problems.