A geometrically exact cross-section deformable thin-walled beam finite element based on generalized beam theory. (1st July 2019)

• Record Type: Journal Article
• Authors: Duan, Liping; Zhao, Jincheng
• Is Part Of: Computers & structures. Volume 218(2019)
• Page Start: 32
• Page End: 59
• Publication Date: 2019-07-01
• Subjects: Generalized beam theory -- Nonlinear analysis -- Geometrically exact beam elements -- Thin-walled members; Structural engineering -- Data processing -- Periodicals; Electronic data processing -- Structures, Theory of -- Periodicals; 624.171
• DOI: 10.1016/j.compstruc.2019.04.001
• Languages: English
• ISSNs: 0045-7949

Abstract

Highlights: New geometrically exact beam formulation for elastic/elastoplastic analyses of thin-walled members. New beam element involving the interaction between global and local deformations. Improved GBT-based approach for kinematic parameterization of the deformed configurations. Beam equations of equilibrium in terms of shell-type stress resultants and stress couples. Less computational cost for an equivalently accurate analysis compared to shell finite elements. 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.