GBT-based computational approach to analyse the geometrically non-linear behaviour of steel and composite thin-walled members

The numerical implementation of a geometrically non-linear Generalised Beam Theory (GBT) is presented, discussed and illustrated. This GBT-based computational approach is intended to (i) perform buckling analyses in thin-walled members made of isotropic or orthotropic materials (e.g. cold formed steel, composite or laminated plate profiles) and to (ii) analyse the post-buckling behaviour of initially imperfect isotropic members (mostly cold-formed steel profiles). A non-linear beam finite element formulation is specifically developed and numerically implemented to solve the GBT system of (linearised or non-linear) differential equilibrium equations. It employs Hermitean polynomials to approximate the mode amplitude functions and leads to a system of algebraic equations which either (i) defines a linear eigenvalue problem (buckling analysis) or (ii) is non-linear and must be solved by resorting to incremental iterative techniques (post-buckling analysis). In order to validate and illustrate the application and capabilities of the proposed GBT-based computational approach, several numerical results are presented and thoroughly discussed. They concern (i) the buckling behaviour of composite lipped channel columns and beams and (ii) the post-buckling behaviour of cold-formed steel lipped channel columns. Some of these results are compared with values yielded by fully numerical (finite element or finite strip) analyses. A few words are also devoted to the computational efficiency of the GBT-based approach, mostly because it takes advantage of the unique mode decomposition nature of the theory.