Space-fractional finite element method for scale sensitive truss structures: theory and implementation

The paper has two primary aims, both related to the description and analysis of scale sensitive truss structures. The first considers the elaboration of the space-fractional (non-local) truss model (s-FTM) based on the principle of virtual work within the framework of space-fractional continuum mechanics (s-FCM)—the model which enables the prediction of strong scale effect. The second encompasses the development of a space-fractional finite element method (s-FFEM) for s-FTM—the numerical method allowing the analysis of arbitrary topological complexity of the truss and arbitrary boundary conditions. It is important that elaborated s-FTM allows to model spatially variable the scale effect, which in phenomenological sense maps non-homogeneous microstructure. Comprehensive numerical study enables understanding of the convergence of s-FFEM, and moreover, it is shown that smooth passage to classical (local) truss theory is obtained as a special case of s-FTM (from both the theoretical and approximated points of view).