The theory of buckling strength of compression members in the plastic range has been extensively studied, and numerical methods already exist which deal with such behaviour. However, there is a significant research interest in developing analytical models for the plastic buckling, largely driven by the need for simplified mechanics based design tools, but also by the desire for enhanced understanding of this complex phenomenon.
A thorough investigation into the inelastic buckling of columns and plates reveals the existence of two well-known inconsistencies recognised as the “Column Paradox” and the “Plate Plastic Buckling Paradox”. In the current research, addressing the conceptual issues related to the plastic buckling of columns and plates, including the two associated paradoxes, has been achieved by means of development and application of analytical models that are verified against nonlinear finite element analysis. These models are based on sound principles of structural mechanics and are intended to illustrate the mechanics of the plastic buckling response of stocky columns/plates by means of a simplified analytical approach, from the point of buckling initiation and considering the post-buckling response. In these models, the Rotational Spring Analogy is used for formulating the geometric stiffness matrix, whereas the material stiffness matrix is obtained with due consideration for the spread of material plasticity.
It is shown that the buckling of stocky perfect columns starts at the Engesser load while the von Karman upper limit is typically not realised due to tensile yielding at the outer fibre of the column cross-section. Furthermore, it is established that beyond a threshold level of imperfection, as evaluated directly from the developed model,
the plastic post-buckling response of columns is barely affected by a further increase
in the out-of-straightness.
Besides identifying previous misconceptions in the research literature, the proposed
analytical models for the plastic buckling of plates have proven to offer valuable insight into factors that influence the plastic buckling of stocky plates, and hence succeeded in resolving the long-standing paradox. It is the major contention of this thesis, verified through extensive studies, that the “Plate Plastic Buckling Paradox” is
resolved with the correct application of plasticity theory, considering not only the
influence of initial imperfections but also the interaction between flexural and planar
actions.