Chapter 16 Effect of Boundary Conditions on Finite Element Submodeling Michael W. Sracic and William J. Elke Abstract 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. Keywords Finite Element Submodeling · Boundary Interpolation · Error Convergence 16.1 Introduction Analysts can effectively model large, built-up structures with the finite element method when a submodeling routine is employed to reduce the computational burden. The critical features in a structure that define the operational life or maintenance schedule of a structure tend to be localized to small regions within a large assembly. Submodeling refers to the approach where one creates a global finite element model of the large structure as well as a submodel of the local region of interest. By enforcing a course mesh with a limited number of elements on the global model, the size and computational cost of the global model is controlled. The local submodel, however, is created with a very fine mesh that is capable of estimating accurate finite element analysis results in the region of interest. These two models are required to establish the submodeling procedure, which entails first solving the global model and using the result of the global model to establish the boundary conditions to apply to the submodel. The submodel is subsequently solved and then refined to the desired level of accuracy. Figure 16.1 shows a basic flowchart of this procedure. Submodeling is well established in research and has been effectively applied in numerous industrial finite element modeling applications. Since the technique requires the modeler to obtain boundary conditions from one model that are then applied to another model, studies employ one of two possible techniques: the application of boundary conditions as displacements or the application of boundary conditions as tractions. For example, Zienkiewicz and Zhu developed an efficient technique to recover the stress tractions on element boundaries [1, 2]. This procedure has been used effectively to produce traction boundary conditions from a global model to apply to a submodel. For example, Kitamura et al. have explored and enhanced the method for large deformation problems [3] and then applied the method effectively to the analysis of a M. W. Sracic ( ) · W. J. Elke Milwaukee School of Engineering, Milwaukee, WI, USA e-mail: sracic@msoe.edu © The Society for Experimental Mechanics, Inc. 2019 G. Kerschen (ed.), Nonlinear Dynamics, Volume 1, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-319-74280-9_16 163
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