Finite difference displacement integration for linear buckling analysis of non-uniform columns

This paper proposes the use of the Finite Difference Displacement Integration (FDDI) technique for the numerical analysis of columns subjected to flexural buckling. The proposed method for buckling analysis is based on the approach suggested by other researchers, who have used the Curvature Based Displacement Interpolation (CBDI) technique. The CBDI technique, formulated within the realm of geometrically nonlinear force-based frame elements, employs a Lagrange interpolation of the cross-section bending curvature. However, this has shown numerical instability when numerous quadrature cross-sections are placed along the element length. Consequently, the proposed buckling analysis method is revisited with the incorporation of the FDDI technique, which employs a finite difference approximation of the cross-section compatibility conditions, yielding a more robust, yet computationally equivalent numerical method. Numerical tests are conducted to evaluate the efficacy of the proposed method, demonstrating that the FDDI effectively eliminates numerical difficulties and reliably converges to the exact solution.