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

摘要

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. (C) 2019 Elsevier Ltd. All rights reserved.