GBT-based semi-analytical solutions for the plastic bifurcation of thin-walled members

This paper presents the development and illustrates the application of semi-analytical solutions for plastic buckling (bifurcation) problems involving perfectly straight and uniformly compressed thin-walled metal members. These solutions are derived on the basis of a non-linear Generalised Beam Theory (GBT) formulation, recently proposed by two of the authors, that resorts to a linearised buckling analysis that adopts Hill’s hypo-elastic comparison solid method to obtain the plastic bifurcation loads and associated buckling mode shapes. Moreover, both J2J2 small-strain incremental and deformation plasticity theories are employed. Several numerical illustrative examples are presented and discussed throughout the paper and closed-form analytical formulae are also derived. The accuracy of the GBT-based semi-analytical plastic bifurcation predictions is assessed through the comparison with (i) available theoretical solutions and/or (ii) results yielded by a special shell finite element model developed by one of the authors.