Adaptive space frame analysis Part I: A plastic hinge approach

This is one of two companion papers presenting new procedures for the efficient large-displacement analysis of steel frames in the elasto-plastic range. In this Paper, emphasis is given to the development and improvement of a plastic hinge approach using the concept of adaptive mesh refinement. In the companion paper, such a concept is discussed in the context of a more accurate approach accounting for the spread of plasticity. The proposed plastic hinge approach is formulated through the extension of an earlier 3D elastic quartic element into the inelastic domain, where a general surface is suggested for representing plastic interaction between the axial force and the biaxial moments. The numerical problems associated with the formation of adjacent plastic hinges as well as the case of pure axial plasticity are highlighted, and methods for dealing with such problems are discussed. The efficiency of the proposed approach derives partly from the ability of the quartic formulation to represent beam-columns using only one element per member, but more significantly from the use of adaptive mesh refinement. The latter consideration is shown to have particular advantages in elasto-plastic analysis of braced structures. The methodology presented in this Paper and implemented in the non-linear analysis program adaptic is verified in terms of robustness, accuracy and efficiency, using a number of examples including geometric as well as material non-linearity effects.