A spatially curved beam element with warping and wagner effects

This paper presents a new spatially curved-beam element with warping and Wagner effects that can be used for the non-linear large displacement analysis of members that are curved in space. The non-linear behaviour of members curved in space shows that the Wagner effects are substantial in the large twist rotation analysis. Most existing finite beam element models, such as ABAQUS and ANSYS cannot predict the non-linear large displacement response of members curved in space correctly because the Wagner effects, viz. the Wagner moment and the corresponding finite strain terms, have not been considered in these finite beam elements. As a consequence, these finite beam elements do not provide correct predictions for the out-of-plane buckling and postbuckling behaviour of arches as well. In this paper, the symmetric tangent stiffness matrix has been derived based on the finite rotations parameterized by the conventional displacements. The warping and Wagner effects: both the Wagner moment and the corresponding finite strain terms and their constitutive relationship, are included in the spatially curved-beam element. Two components of the initial curvature, the initial twist and their interactions with the displacements are also considered in the spatially curved-beam element. This ensures that the large twist rotation analysis for the members curved in space is accurate. Comparisons with existing experimental, analytical and numerical results show that the spatially curved-beam element is accurate and efficient for the non-linear elastic analysis of curved members, buckling and postbuckling analysis of arches, and in its ability to predict large deflections and twist rotations in more arbitrarily curved members.