Mixed-dimensional modeling of structures with thin coatings using rotation-free elements

Abstract

This paper describes a new mixed-dimensional finite element model for structures that consist of thick substrates with thin coatings. For such structures, the difference in length scale between the substrate and the coating often makes meshing problematic, leading to severe solution inefficiencies for conventional finite element techniques. In the new approach presented here, rotation-free beam elements are used to model the thin coating, and solid elements to model the substrate. The new model employs a unique transition element to couple the rotation-free beam elements to biquadratic quadrilateral elements without using additional constraint equations. The 10-node transition element is created by modifying the shape functions of a biquadratic quadrilateral element to ensure that the displacement field on the coated surface is consistent with the displacement field of an overlaid rotation-free beam element. Convergence studies of thin-coated structures with both straight and curved geometries show excellent accuracy while using orders of magnitude fewer degrees of freedom than a conventional finite element model using only solid elements. Hence the new model enables efficient analysis of complicated coated structures.