Behaviour of steel portal frames in fire: Comparison of implicit and explicit finite element methods

The use of finite element methods to determine the collapse behavior of steel portal frames in fire requires temperature, large deformation, complex geometry, boundary conditions and degradation of material stiffness to be taken into account. For such analyses, the cost of computation is important as well as the accuracy, robustness and stability of the analyses. The implicit dynamic method is a rigorous technique that considers the equilibrium of every time step. However, convergence may become an issue, particularly if the frame undergoes structural instability while using a direct time incrementation scheme. In contrast, the explicit dynamic method does not require the equilibrium criteria to be met in every time step, and thus convergence problems are not encountered, although the cost of computation may be tremendous if the natural time scale is used. This paper presents a comparison between the efficiency, stability and accuracy of computations using the implicit and explicit dynamic methods, in determining the collapse behavior of portal frames at elevated temperatures; the models are quasi-static since inertia forces are ignored. It is found that similar results can be obtained using both the implicit and explicit dynamic methods, although the analysis times differ significantly. It is shown that, if the applied artificial inertia forces, in terms of residual forces, are magnified and an automatic time incrementation scheme is activated in the implicit dynamic method, then this method shows significant superiority over the explicit dynamic method both in terms of the cost of computation and the accuracy of results obtained for such structures.