A Mesh-Geometry Based Approach for Mixed-Dimensional Analysis

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 can significantly reduce the time needed to mesh and solve the system. Unfortunately, problems arise when trying to connect elements of different dimensions in part due to the incompatible degrees of freedom and the independently created meshes. This paper presents a solution to these problems based on the generation of a compatible mesh composed solely of basic elements and without the requirement of constraint equations.