An extended GBT formulation for elastoplastic analyses of perforated thin-walled members

Abstract

A physically and geometrically nonlinear beam finite element modelling of thin-walled members with arbitrarily complex holes is presented. The beam finite element approximation of the member configuration space is achieved by using the extended generalized beam theory kinematic description, which covers discontinuities in member cross-sections due to holes or cut-outs of various shapes. The proposed beam finite element deals with perforated members in a manner of treating them as non-perforated ones by filling the perforations with much softer materials. Then the level-set functions are used to represent the bi-material interfaces and also used to construct the enrichment functions which describe the discontinuities in the displacement fields. The enrichment functions are then integrated into the standard GBT-based beam finite element approximation by the Partition of Unity Method. The J2-plasticity model combined with isotropic hardening and associated flow rule for isotropic materials (e.g., soft steel) is used in the model. To show the potential of the proposed approach, four illustrative examples are provided, where results obtained by the presented model are compared with the shell finite element results. The proposed GBT model shows significant superiorities in the computational efficiency and structural clarity over the shell model.