Elastic buckling analysis of thin-walled structural members with rectangular holes using generalized beam theory

• The GBT formulation for thin-walled members with holes is presented.
• A member is viewed as an assembly of sub-members linked by compatibility constraints.
• Geometric stiffness for members with holes essential for elastic buckling is derived.
• GBT buckling solutions are verified with finite element analysis in three examples.
• The method can be used in identifying elastic buckling modes for members with holes.

This paper presents a method to perform generalized beam theory buckling analysis on thin-walled structural members with holes. Generalized beam theory (GBT) is an ideal tool for analyzing thin-walled structures because it can directly compute buckling mode participation in an eigen-buckling analysis. The GBT extension to members with holes is made by treating a thin-walled structural member as an assembly of prismatic sub-members, and compatibility constraints on the GBT modal amplitudes are introduced to connect these sub-members. GBT shear modes with nonlinear warping deformation are included in both first order and buckling analyses to account for the nonlinear normal stress distribution in the vicinity of a hole. GBT buckling mode shapes are verified with shell finite element analysis (SFEA) in three examples that highlight the potential for quantitatively documenting buckling modes initiated by the presence of holes.