Mixed Dimensional Coupling in Finite Element Stress Analysis

In many finite element analysis models, there are usually regions that are ideal candidates for dimensional reduction. In order to capture stress concentrations at local details, it would be desirable to combine the reduced dimensional element types with higher dimensional elements in the whole global model. Therefore, it is important in such cases to integrate into the analyses some scheme for coupling the element types that conforms to the governing equations of the problem. In this paper, a novel method that can correctly couple beams to solids, beams to shells and shells to solids for elastic problems is presented. The approach adopted is to equate the work done on either side of the mixed dimensional interface and this leads to multi-point constraint equations, providing compatible relationships of the nodal degrees of freedom between the differing element types. Example results show that the proposed technique does not introduce any spurious stresses at the dimensional interface