A mesh-geometry-based solution to mixed-dimensional coupling

When conducting a finite element analysis, the total number of degrees of freedom can be dramatically decreased using finite elements such as beams and shells. Because of geometric complexities, entire models (or portions of models) must be meshed using volume elements in order to obtain accurate simulation results. If however some parts of these models fit the description of shells or beams, then a mixed dimensional model containing shell, beam and volume elements side by side can be used. This approach, referred to as a mixed-dimensional analysis (MDA) can significantly reduce the time needed to mesh and solve the system. Unfortunately, problems arise when trying to connect the different types of element in part due to incompatibilities between the degrees of freedom, and due to the discontinuities between meshes generated independently. This paper presents a solution to these problems based on the generation of a compatible mesh composed solely of standard finite elements and without requiring the use of constraint equations. This mesh can then be exported to a standard FE solver without using specific connection elements.