Improvement of 2D finite element analysis stress results by radial basis functions and balance equations

This paper presents a method able to upscale finite element (FE) results obtained for coarse meshes of 2D models at a higher resolution, using both radial basis functions (RBF) and balance equations. RBF supply a smooth function from nodal displacements. In addition to FE nodes, RBF interpolation embeds a certain number of additional points, for which displacements satisfy a minimization procedure of the error on balance equations. Derived fields (strain, stress) yield analytically from the constructed interpolator. We tested the method with two 2D structural cases where strong stress concentrations were included. As regards the stress field, an error reduction with respect to validated test benches was observed in all cases.