Distinguishing Physical Stress Concentration from Numerical Singularity in Large-Scale Structural FEM Analyses (Aintelia Science Notes, 2026)
In large-scale structural finite element analyses (FEA), extreme stress peaks frequently occur at geometric discontinuities, boundary conditions, and perfectly bonded interfaces. These values are often directly compared with the material yield strength, which may lead to overly conservative or misleading safety assessments. However, such stress peaks may originate from mathematical singularities inherent to linear elastic formulations rather than physically admissible stress states. This study investigates the distinction between physical stress concentration and numerical singularity in an industrial-scale structural steel model subjected to end loading. A three-dimensional finite element model containing approximately one million elements was analyzed under service loading conditions. The simulation results indicated that the maximum von Mises stresses reached nearly three times the yield strength of S355JR steel. Through theoretical evaluation of asymptotic stress behavior, plastic deformation theory, mesh characteristics, and contact modeling effects, it is demonstrated that these stress peaks represent numerical artifacts rather than actual structural failure conditions. A systematic engineering interpretation framework is proposed to prevent the misclassification of singular stresses in industrial FEM applications.