Upscaling 2D finite element analysis stress results using radial basis functions

This paper presents a method of interpolation and regularisation of finite element (FE) results based on radial basis functions (RBF) capable to upscale at a finer resolution the displacement fields and, accordingly, the strains and the stresses obtained with a coarse mesh. RBF interpolation of nodal displacements supplies an analytical approximation of the field over the whole discretized domain, suitable for mathematical differentiation. The stress status can be retrieved starting from the given analytical expression of the strain. The introduced technique is tested on two-dimensional FE problems presenting stress raisers: a plate in traction with a central hole, a plate in traction with nine aligned holes and a compressed wing rib with three lightening holes. For all the investigated geometries we observe that numerical FE results obtained adopting coarse grids and treated with the proposed approach compares well to FE results obtained adopting finer grids.