Isogeometric buckling analysis of planar beam structures

This study constructs a linear buckling analysis procedure for planar curved beams by adopting a total Lagrangian Timoshenko-Ehrenfest beam formulation. The present approach is based on isogeometric analysis (IGA). Because of the ability to accurately describe complex geometry, non-uniform rational B-spline (NURBS) curves are employed in the IGA context. The system of equations from the adopted nonlinear formulation is linearized for linear buckling analysis. The geometric stiffness matrix in this study considers the influence of membrane, bending, and shear actions. The B-bar method is also adopted to ensure the proposed formulation is locking-free and applicable to curved beam structures with arbitrary geometry. The outputs of the proposed formulation are compared to the existing exact or numerical solutions.