Plastic buckling of thin and moderately thin plates and shells: classic problems and new perspectives

Elastic-plastic instability of structures is an extensive field which encompasses a broad category of civil and mechanical engineering problems and involves several topics such as the physical and mechanical characterization of materials, yield criteria, different theories of plasticity and phenomena related to geometric nonlinearities, especially for thin and moderately thin plates and shells. The aim of this work is to investigate the plastic buckling of plates and shells subjected to different loading conditions with respect to the phenomenon of the plastic buckling paradox. Following the proposal of a new analytical approach to the problem, which throws light on the fundamental differences in the use of the flow theory and of the deformation theory of plasticity, by means of an extensive numerical investigation on cylindrical shells with different geometrical and material properties, some fundamental limitations of the modern numerical nonlinear analyses conducted by the use of the Finite Elements are highlighted and discussed in detail.