Shell instability phenomena studied by multiparametric non-linear analyses

The paper describes how quasi-static, conservative instability problems can be analysed in a multi-parametric context; using generalised path-following procedures for augmented equilibrium problems. The developed numerical algorithms are based on systematic manifold evaluations, aimed at finding the structural response and critical state solutions, under the variations of certain parameters (geometrical, mechanical, loading or imperfection) deemed relevant for the problem. A co-rotational flat facet triangular element is specially designed to fit the algorithms. The multi-parametric setting can be used for an improved phenomenological understanding and in the theoretical treatment of all relevant mechanical phenomena occurring in optimised shell structures. They can also be important parts in a practical design process. The results give interesting visualisations of catastrophe theoretical basic cases.