Improved minimal augmentation procedure for the direct computation of critical points. (English) Zbl 1140.74547

Summary: This paper presents a new numerical procedure for the direct computation of critical points for elastic beam structures undergoing large displacements and rotations. Compared to the approach described by Wriggers et al., the condition of criticality is expressed by a scalar equation instead of a vectorial one. Next, the present procedure does not use exclusively the extended system obtained from the equilibrium equations and the criticality condition, but also introduces intermediate iterations based purely on equilibrium equations under load or displacement control. Eight numerical examples, presenting bifurcation and limit points, are used in order to compare the performances of this new method and the one presented earlier.


74S05 Finite element methods applied to problems in solid mechanics
74G60 Bifurcation and buckling
74K10 Rods (beams, columns, shafts, arches, rings, etc.)


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