Doctor of Philosophy (PhD)
Submodeling can enable stress analysts using finite elements to focus analysis on a subregion containing the stress concentration of interest, with consequent computational savings. Such benefits are only truly realized if the boundary conditions on the edges of the subregion that were originally contained within the global region are sufficiently accurate. These boundary conditions are drawn from initial global finite element analysis (FEA), and consequently themselves have errors that in turn lead to errors in the stresses sought. When these last boundary-condition errors are controlled, and the discretization errors incurred by the FEA of ensuing submodels are also controlled, submodeling is effective. Here we furnish improved estimations of boundary-condition and discretization errors. These estimates are used in conjunction with precautions against underestimating errors in the presence of nonmonotonic convergence. To access the efficacy of our procedure, we apply it to four 2D and nine 3D test problems. These test problems have a range of stress concentration factors that exceed those normally encountered in practice. These test problems have exact solutions so that there is no ambiguity whatsoever as to the actual errors occasioned by their FEA. The performance of our approach is assessed with free and structured meshes, for elements of different orders, and for shape functions and cubic splines or bicubic surfaces for interpolating displacements in boundary conditions. For all these problems, whenever estimates of the boundary-condition errors indicate that there is a need to enlarge the subregion, actual errors due to cut boundary conditions confirm this, in fact, to be the case. Thereafter, whenever subregions are enlarged and estimates indicate that errors due to cut boundary conditions are then low enough to proceed with the FEA of submodels, actual errors also confirm this to be the case. Ultimately for all thirteen test problems, accurate error estimates are made which are confirmed by actual error values, with significantly fewer degrees of freedom being used in submodel meshes. Finally, we implement our submodeling procedure on two practical problems. The error estimates indicate that excellent results are obtained for both the applications with significant computational savings.
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Kardak, Ajay Ashok, "On an Effective Submodeling Procedure for Stresses Determined with Finite Element Analysis" (2015). LSU Doctoral Dissertations. 306.