The Effect of FEM Mesh Density on the Failure Probability Analysis of Structures

In the analysis of finite elements, mesh density can highly influence the accuracy of the results. Hence, researchers consider the determination and refinement of mesh an attractive issue. However, the subject has not been suitably investigated for the reliability evaluation of structures. This paper investigates the effects of mesh density on the reliability evaluation and the reliability-based sensitivity of structures. For this purpose, two common engineering problems modeled by Finite Element Method (FEM), with different mesh densities and their reliability results determined by Monte Carlo simulation and polynomial Response Surface Methodology (RSM). The analytical solutions to the proposed problems were present in the literature. Hence, the effects of the FEM mesh densities on the reliability results could be compared with the theoretical results. The outcomes based on the FEM results showed that RSM can very accurately evaluate the performance of these structures. However, the main achievement of the study was the finding that though a determined mesh density can be considered acceptable from the deterministic analysis viewpoint, its employment in reliability analysis could produce 100% error in estimating the failure probability of a structure.