Verification of Submodeling for the Finite Element Analysis of Stress Concentrations

Submodeling enables finite element engineers to focus analysis on the subregion containing the stress concentrator of interest with consequent computational savings. Such benefits are only really gained if the boundary conditions on the edges of the subregion that are drawn from an initial global finite element analysis (FEA) are verified to have been captured sufficiently accurately. Here, we offer a two-pronged approach aimed at realizing such solution verification. The first element of this approach is an improved means of assessing the error induced by submodel boundary conditions. The second element is a systematic sizing of the submodel region so that boundary-condition errors become acceptable. The resulting submodel procedure is demonstrated on a series of two-dimensional (2D) configurations with significant stress concentrations: four test problems and one application. For the test problems, the assessment means are uniformly successful in determining when submodel boundary conditions are accurate and when they are not. When, at first, they are not, the sizing approach is also consistently successful in enlarging submodel regions until submodel boundary conditions do become sufficiently accurate.