Evaluation of Nonlinear Frame Finite-Element Models

In recent years nonlinear dynamic analysis of three-dimensional structural models is used more and more in the assessment of existing structures in zones of high seismic risk and in the development of appropriate retrofit strategies. In this framework beam finite-element models of various degrees of sophistication are used in the description of the hysteretic behavior of structural components under a predominantly uniaxial state of strain and stress. These models are commonly derived with the displacement method of analysis, but recent studies have highlighted the benefits of frame models that are based on force interpolation functions (flexibility approach). These benefits derive from the fact that models with force interpolation functions that reproduce the variation of internal element forces in a strict sense yield the exact solution of the governing equations in the absence of geometric nonlinearity. While the numerical implementation of force-based models at first appears cumbersome, simple examples of nonlinear analysis in this paper offer conclusive proof of the numerical and computational superiority of these models on account of the smaller number of model degrees of freedom for the same degree of accuracy in the global and local response. A numerical implementation that bypasses the iterative nature of the element state determination in recent force-based elements is also introduced, thus further expanding the benefits of flexibility-based nonlinear frame models.