Progress in Collapse Analyses

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Abstract
In the field of finite element structural analysis, the computation of collapse states of structures prone to unstable behavior has long been considered a difficult if not intractable problem. Only recently have procedures that deal effectively with this difficulty found their way in general-purpose finite element codes. Although the explanation for the cause of the so-called limit point obstacle is actually simple—an inappropriate parameterization of the governing equations in the neighborhood of the limit point—this cause does not seem to have been widely understood in the period of development of the finite element technique. In this paper, some of the remedies that have been proposed to overcome the problems are reviewed, including the principle of adaptive parameterization which is now the basis of a new procedure for collapse analysis in the finite element code STAGS. The discussion also includes the treatment of simple bifurcation points because unstable bifurcation can be considered a special form of collapse. It can be concluded that collapse problems, in the sense discussed in this paper, no longer present difficulties that exceed those normally encountered during the solution of nonlinear deformation paths. Further developments, in particular those with respect to improved efficiency, are in progress. Some of the promising ventures in this direction are indicated.

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