Abstract:
This paper addresses the shortcomings of the finite element method (FEM) as a deterministic tool by proposing a metrology-based uncertainty analysis approach for failure scenarios with incomplete data. The study treats each FEM simulation in a grid-convergence sequence as a "numerical experiment" to quantify uncertainty. The methodology is demonstrated on two benchmark problems, one of which involves a square plate resting on a grillage with a progressively weakening model. This model simulates load redistribution as individual columns fail, and it allows for the prediction of collapse time with confidence bounds. While the paper does not focus on shape optimization in the traditional sense, it highlights the importance of incorporating parametric variables such as mesh size and element type to quantify uncertainty in a systematic, non-deterministic way.
