The purpose of this paper is to present a homogenization approach to model mechanical structures with multiple scales and periodicity, as they occur, e.g. in power transformer windings, subjected to magnetic forces.
The idea is based on the framework of generalized finite element methods (GFEM), where the normal polynomial finite element basis functions are enriched by problem dependent basis functions, which are, in this case, the eigenmodes of a quasi‐periodic unit cell setup. These eigenmodes are used to enrich the standard polynomial basis functions of higher order on a coarse grid modeling the whole periodic structure.
It is shown that heterogeneous magnetomechanical structures can be homogenized with the developed method, as demonstrated by homogenization of a transformer coil setup.
An efficient homogenization procedure is proposed on the basis of the GFEM, which is extended using a special set of enrichment functions, i.e. the mechanic eigenmodes of a generalized eigenvalue problem.
