Nonlinear Post-Buckling Analysis of Variable Cross-Section Beams Using the Carrera Unified Formulation

Variable cross-section beams are highly susceptible to instability phenomena, and traditional 3D Finite Element (FE) methods are often computationally demanding for slender members. This work proposes a refined, fully nonlinear one-dimensional (1D) beam model for tapered and twist geometries, developed within the Carrera Unified Formulation (CUF) framework. The element directly accounts for cross-sectional variation by performing a three-dimensional integration of of approximating function in the Jacobian matrix. The nonlinear governing equations, derived via the Principle of Virtual Work, are solved using a Newton-Raphson linearization scheme coupled with an arc-length path-following method. The formulation’s effectiveness is validated through numerical applications, including the buckling of a tapered steel C-section beam.