On computational shells with scale effects

The paper deals with the computations of so-called geometrically exact shells with scale effects. These type of computations are relevant to thin-walled structures at small scales (e.g. thin films, nanotubes etc.). The shell formulation exhibits higher order gradients and is developed following some author's recent work on generalised continua. The framework has been modified as to account for two-dimensional surfaces as well. The shell formulation reduces to a standard one upon disregarding the higher gradient terms. The classical part of the formulation is a well known 7-parameter model previously developed by one of the authors which takes thickness change into account. The numerical treatment is based on a meshfree formulation which provides the necessary C1 continuity. As possible applications, dynamic buckling of cylindrical and spherical shells is investigated and some results for various states of loading and scale parameters are presented. The examples include also nanotubes of different dimensions where scale effects matter. The influence of the extra gradients is well demonstrated resulting in different buckling behaviours.