An extended first-order generalized beam theory for perforated thin-walled members

Abstract

This paper presents an extended first-order generalized beam theory (GBT) formulation for prismatic thin-walled members with arbitrary cross-section perforations. The classic GBT kinematic relationships are extended by explicitly adding several enrichment functions which approximate the discontinuities of displacement fields due to the presence of holes. The geometrical profiles of holes are described by a set of zero level set functions, which are also used to construct the enrichment functions. First, all the cross-section holes are filled with another kind of much ‘softer’ material, so that a perforated bar can be seen as a bi-material non-perforated member. Second, the displacement-strain relationships in terms of the GBT modal displacement coordinates and the set of cross-section nodal displacement coordinates corresponding to the enrichment functions are derived and it is shown how the regularities of strain field at bi-material interfaces are incorporated. Third, the equilibrium equations are obtained with the principle of virtual work. Finally, a standard displacement-based extended finite element is proposed to solve the governing equations, and a set of illustrative examples are presented to show its potential and validity for analyses of perforated members undergoing complex local-global deformations. It is shown that the presented GBT formulation can lead to modal results, e.g., retrieving the pure modes of the deformed configurations of perforated members, and preserve the high computational efficiency the same as the classic GBT for non-perforated members.