A geometrically exact cross-section deformable thin-walled beam finite element based on generalized beam theory

Abstract

A new nonlinear cross-section deformable beam formulation based on generalized beam theory (GBT) is presented for elastic/elastoplastic analyses of thin-walled members undergoing arbitrary deformations, such as large deflections, finite rotations, distortional/local buckling, and out-of-plane warping. For rigorous numerical analyses of thin-walled structures, considering both the global and local deformation effects, shell finite elements are widely used. This paper aims at providing a more computationally efficient and structurally clarifying alternative to simulate prismatic and curved thin-walled members. Compared to the traditional beam elements and other beam formulations based on higher-order beam theories, we improved the kinematic description of member cross-section displacement field, where the kinematic parameterization is performed on two scales, i.e., global member scale and local wall scale; especially, the local wall deformations are described by means of the predetermined GBT modes which are structurally meaningful and allow for the cross-section deformations. Beam equations of equilibrium are built on the local wall scale in terms of shell-type stress resultants and stress couples; therefore, the present beam formulation owns the feature of a shell model. A Galerkin method based beam finite element is developed to solve the equilibrium equations. Finally, six illustrative examples are examined for the validity of the proposed beam formulation.