Submodeling approach to adaptive mesh refinement

A submodeling approach for adaptively refining stress concentrations has been developed. The stress concentrations are separated from the remainder of the problem one at time by defining internal boundaries in terms of elemental error measures. The fact that the effects of the remainder of the problem are satisfactorily included in the subproblem by interpolating the displacements across the internal boundary is indicated by the accuracy of the results. The adaptive refinement is terminated when the maximum elemental error reaches a predetermined value. This contrasts to some approaches where a global error measure is used to terminate the analysis. The use of the elemental error measure to stop the analysis removes the effect of the far-field elements from the assessment of the accuracy of the results at the stress concentration. The accuracy of the analysis in the region of interest is used to terminate the analysis. The adaptive refinement of a submodel containing a stress concentration allows the computational resources to be focused on the regions of the problem where they can best be utilized. For instance, if a problem has several high-stress regions, each one can be treated separately and in detail. The 5% elemental error criterion used here to define both the internal boundary and to terminate the analysis was chosen arbitrarily. Previous experience had shown that this value would produce well-converged results for the example problems solved here. Thus, a valuable area of future resarch would be to determine a process for identifying the criteria that would produce the desired mix between accuracy and efficiency for general problems.