Generalized Beam Theory formulation for thin-walled pipes with circular axis

Abstract

In this paper, the linear Generalized Beam Theory (GBT) is formulated for stress and deformation analysis of curved thin-walled circular pipes. In comparison to the analysis of straight pipes, the analysis of pipe bends is a complex problem due to the strong coupling effect of the longitudinal bending, warping and the cross-sectional ovalization. GBT is a beam theory especially formulated for thin-walled sections with the capacity of determining the cross-sectional deformation through the combination of a set of predetermined cross-sectional deformation modes. This nature of GBT makes it suitable to precisely identify and determine possible couplings between the considered GBT deformation modes and to analyze the behavior of pipe bends with high accuracy and computational efficiency. The formulation presented in this paper is based on Kirchhoff’s thin-plate assumption with consideration of additional shear deformation modes to overcome null transverse extension and shear membrane strain assumptions of classical GBT formulations. Here, to illustrate the application and capabilities of the developed GBT formulation, a set of numerical examples with in-plane, out-of-plane and pressure loading conditions involving a combination and coupling of bending, warping, torsional, axisymmetric and local deformations are presented. For the purpose of validation, these examples are compared with refined shell finite element models in both displacement and stress fields.