Three-Dimensional Submodeling of Stress Concentrations

Stress concentrations are a concern in engineering because of their implications regarding structural integrity. Efficiently and accurately computing the associated stresses is therefore important. Unfortunately it is not always an easy task. This task becomes more challenging when the complex configurations encountered in practice require three-dimensional analysis. Submodeling with finite element analysis is one means available to meet this challenge. With submodeling, a subregion is broken out from the original global region and analyzed separately. This subregion requires boundary conditions taken from the finite element analysis of the global region. Accurately estimating the errors associated with these boundary conditions is critical to controlling them and thereby enabling efficient submodeling. In this paper, we outline a two-dimensional submodeling procedure that addresses this issue, then show how it can be extended for three-dimensional analyses. We check the procedure on a three-dimensional test problem with a known exact solution. The analysis of this problem illustrates the improved stress results that one can get with the submodeling procedure in return for moderate computational effort.
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