Practical Convergence-Divergence Checks for Stresses from FEA

In practice in finite-element stress analysis, the engineer first needs to know if key stresses are converging, and second if they have converged to a reasonable level of accuracy. Then these stresses can be reliably used in design. The engineer further needs to know if, instead, key stresses are diverging because of singularities present. Then these stresses can be of no direct use in design. This paper describes some straightforward checks for assessing convergence or divergence of stresses from FEA. The performance of the convergence-divergence checks suggested here is evaluated analytically with a simple error model, and with series analogues. These checks are also evaluated on an extensive set of diverging trial problems and converging test problems. Some alternative checks put forward elsewhere are likewise evaluated. The evaluation of the suggested convergence-divergence checks shows that they can fairly consistently discern correctly whether stresses from FEA are converging or diverging. In addition, if converging, the evaluation shows that these checks can reasonably accurately and typically conservatively gauge the degree to which stresses have actually converged. In contrast, the evaluation shows that the alternative checks can conclude stresses are converging when, in fact, they are diverging. Thus these alternative checks can be seriously misleading.
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