Geometrically nonlinear formulation of Generalized Beam Theory for the analysis of thin-walled circular pipes: Fid-Bau Portal

Geometrically nonlinear formulation of Generalized Beam Theory for the analysis of thin-walled circular pipes

Habtemariam, Abinet K. / Bianco, Marcelo J. / Könke, Carsten / Zabel, Volkmar

Abstract In this paper, the formulation of Generalized Beam Theory (GBT) for the geometrically nonlinear analysis of thin-walled circular pipes is presented. GBT is a computationally efficient numerical method which is especially formulated for thin-walled members with a capacity of determining the cross-sectional deformation through a combination of a set of pre-determined cross-sectional deformation modes. In this study, the current GBT analysis of circular pipes which is limited to buckling analysis is enhanced to a full geometrically nonlinear analysis. This new formulation considers the nonlinear membrane kinematic description based on the Green–Lagrange strain definition. The nonlinear tangent stiffness matrices and the internal force vectors are derived from the variation of the internal energy which results in third and fourth-order GBT deformation mode coupling tensors. These tensors can predetermine the type of GBT deformation modes needed for the nonlinear analysis based on the applied loading conditions. In addition to the classical GBT deformation modes, the non-conventional GBT deformations modes have a vital role since without these modes the coupling tensors and the nonlinear stiffness matrix related to the transverse and the shear membrane energy will be lost. Here, to illustrate the application and capabilities of the developed GBT formulation, two numerical examples involving transverse and longitudinal bending are presented to show the nonlinear relationship between bending, cross-sectional ovalization, and higher local deformation modes. For the purpose of validation, these examples are compared with refined shell finite element models in both displacement and stress fields.

Highlights • Geometrically nonlinear GBT formulation is presented and validated. • The third and fourth-order GBT deformation mode coupling tensors are identified. • Numerical examples involving transverse and longitudinal bending of thin-walled circular pipes are presented. • The GBT nonlinear stress resultants for the membrane forces are formulated. • The nonlinear cross-sectional ovalization of a thin-walled circular pipe is with high computational efficiency and accuracy determined.