Effect of Boundary Conditions on Finite Element Submodeling

When a built-up structure such as a turbine or compressor is modeled with finite elements, a submodeling procedure can be used to assess critical features such as holes, fillets, or contact interfaces. To employ the method, one builds and solves a coarse-mesh finite element model of the whole structure. Then, a fine-mesh finite element submodel of the critical feature is built and solved by using boundary conditions that were estimated from the global model solution. This procedure reduces computational expense, but the predicted results from the submodel can be inaccurate if the global model produces inaccurate boundary conditions for the submodel. While a number of studies have considered the best methods to extract boundary conditions, little work has been done to assess how the submodel boundary location affects the results. This paper presents a case study to assess how the submodel boundary location affects the predicted results of the submodel. Specifically, a cantilever beam with stress concentration hole was analyzed. Numerous global models and submodels were generated and solved with the submodeling method. The maximum stress at the hole was reviewed as a metric. The results suggest that the location of the submodel boundary has a strong influence on the maximum stress predicted by the submodel. In particular, submodels with boundaries placed very close to the edge of the hole underpredicted the global model converged stress by up to 20%. The error in the submodels decreased as the submodel boundary was placed farther from the hole. The error also decreased as the mesh of the initial global model is refined. The results provided could inform analysts who employ this method in applications but do not investigate convergence of the global model or optimize the location of the submodel boundary.