Element formulation and numerical techniques for stability problems in shells

Authors: Eriksson,  , Pacoste, C
Document Type: Article
Pubstate: Published
Journal: Comput Methods Appl Mech Engrg
Volume: 191   3775-3810
Year: 2002


In the context of instability problems in shells or shell like structures, the objective of the present paper is twofold. Primarily, the paper describes how quasi-static, conservative instability problems can be considered in a multi-parametric context, where generalised path-following procedures for augmented equilibrium problems are used as computational tools. These allow systematic treatment of the higher-dimensional solution sets generated under the variations of certain parameters deemed relevant for the given problem. The efficient implementation of the above mentioned procedures requires however, as an essential ingredient, a non-linear finite element which is not only accurate but also inexpensive. To this end, a systematic view on a co-rotational Total Lagrangean formulation is described. The TRIC element of Argyris and co-workers is slightly modified, and introduced as core element formulation. Special emphasis is given to the alternative methods for treatment of finite 3D rotations, with reference to both the element definition and solution algorithms. Numerical examples verify the element capabilities, and the possibility to completely describe instability phenomena of large, discretised models.