This paper presents a numerically efficient tool for linear buckling predictions of perforated thin-walled bars within the framework of generalized beam theory (GBT). GBT-based beam finite element methods (GBT-FEM) have been well developed for eigenvalue buckling analyses of non-perforated thin-walled bars. The novelty of this paper consists in an extension of the standard GBT to the scope of thin-walled members with arbitrarily shaped and placed holes. This is achieved by combining the standard GBT and the extended finite element method (X-FEM). More specifically, insert a set of locally supported enrichment functions, accounting for the discontinuities on displacement fields arising from the cross-section cut-outs/holes, into the GBT-based finite element approximations of the member configuration spaces, using the partition of unity method (PUM), where a set of level-set functions are used to describe the geometric profiles of hole edges, i.e., with the hole edges being the zero level sets, and also used to construct the enrichment functions. The proposed approach makes it possible to calculate the deformation mode participations for any perforated thin-walled members as the classic GBT for non-perforated ones. Finally, the proposed approach is calibrated against the shell/solid finite element analysis with four illustrative examples. It can be found that the presented approach is of higher computation efficiency than the shell model.

本文提出了一种在广义梁理论 (GBT) 框架内对穿孔薄壁钢筋进行线性屈曲预测的有效数值工具。基于 GBT 的梁有限元方法 (GBT-FEM) 已被很好地开发用于非穿孔薄壁钢筋的特征值屈曲分析。本文的新颖之处在于将标准 GBT 扩展到具有任意形状和放置孔的薄壁构件的范围。这是通过结合标准 GBT 和扩展有限元方法 (X-FEM) 来实现的。更具体地说，插入一组局部支持的富集函数，考虑由横截面切口/孔引起的位移场的不连续性，使用统一的划分，到基于 GBT 的成员配置空间的有限元近似中方法（PUM），其中一组水平集函数用于描述孔边缘的几何轮廓，即孔边缘为零水平集，也用于构造富集函数。所提出的方法使得计算任何穿孔薄壁构件的变形模式参与成为可能，作为非穿孔构件的经典 GBT。最后，所提出的方法针对壳/固体有限元分析与四个说明性示例进行校准。可以发现，所提出的方法比壳模型具有更高的计算效率。所提出的方法可以计算任何穿孔薄壁构件的变形模式参与度，作为非穿孔构件的经典 GBT。最后，所提出的方法针对壳/固体有限元分析与四个说明性示例进行校准。可以发现，所提出的方法比壳模型具有更高的计算效率。所提出的方法使得计算任何穿孔薄壁构件的变形模式参与成为可能，作为非穿孔构件的经典 GBT。最后，所提出的方法针对壳/固体有限元分析与四个说明性示例进行校准。可以发现，所提出的方法比壳模型具有更高的计算效率。