Distinguishing Physical Stress Concentration from Numerical Singularity in Large-Scale Structural FEM Analyses
DOI:
https://doi.org/10.5281/zenodo.21357202Keywords:
Finite Element Analysis, Numerical Singularity, Stress Concentration, Structural Analysis, Welded Steel StructuresAbstract
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.
References
J. R. Rice, "A path independent integral and the approximate analysis of strain concentration by notches and cracks," J. Appl. Mech., vol. 35, no. 2, pp. 379–386, 1968.
A. Carpinteri and M. Paggi, "Asymptotic analysis of stress singularities in composite laminates," Compos. Struct., vol. 71, pp. 210–219, 2005.
J. Bulling, H. Gravenkamp, and C. Birk, "A high-order finite element technique with automatic treatment of stress singularities by semi-analytical enrichment," Comput. Methods Appl. Mech. Eng., vol. 355, pp. 135–156, 2019, doi: 10.1016/j.cma.2019.06.013.
S. H. Ebrahimi, S. Mohammadi, and I. Mahmoudzadeh Kani, "A local PUFEM modeling of stress singularity in sliding contact with minimal enrichment for direct evaluation of generalized stress intensity factors," Eng. Fract. Mech., vol. 105, pp. 16–40, 2013.
Y. Qian and B. Teng, "A finite element–scaled boundary finite element coupled method for corner singularities in 2D second-order radiation problems," Ocean Eng., vol. 281, art. 114910, 2023, doi: 10.1016/j.oceaneng.2023.114910.
C. Wang, X. Ping, and X. Wang, "An adaptive finite element method for crack propagation based on a multifunctional super singular element," Int. J. Mech. Sci., vol. 247, art. 108191, 2023, doi: 10.1016/j.ijmecsci.2023.108191.
P. Dong, "A structural stress definition and numerical implementation for fatigue analysis of welded joints," Int. J. Fatigue, vol. 23, no. 10, pp. 865–876, 2001, doi: 10.1016/S0142-1123(01)00055-X.
A. Montanino and A. Iannuzzo, "A quadrilateral plate-type finite element to model stress singularities in no-tension materials," Comput. Methods Appl. Mech. Eng., vol. 432, art. 117433, 2024, doi: 10.1016/j.cma.2024.117433.
L. Jing, M. Feng, Y. Li, F. Teng, and Z. Luo, "A reduced-dimension method for unknown Crank–Nicolson finite element solution coefficient vectors of elastic wave equation with singular source term," J. Math. Anal. Appl., vol. 540, art. 128629, 2024, doi: 10.1016/j.jmaa.2024.128629.
G. B. Sinclair and B. P. Epps, "On the logarithmic stress singularities induced by the use of displacement shape functions in boundary conditions in submodelling," Commun. Numer. Methods Eng., vol. 18, pp. 121–130, 2002, doi: 10.1002/cnm.473.
M. A. Herrera-Garrido, L. Távara, M. Muñoz-Reja, A. Vázquez-Sánchez, and V. Mantič, "Enriched crack-tip element for logarithmic stress singularities of Mode I and II cracks in spring interfaces," Eng. Fract. Mech., vol. 336, art. 111941, 2026.
T. Yue and M. Abdel Wahab, "Finite element analysis of stress singularity in partial slip and gross sliding regimes in fretting wear," Wear, vol. 321, pp. 53–63, 2014, doi: 10.1016/j.wear.2014.09.008.
X.-C. Ping, M.-C. Chen, and J.-L. Xie, "Singular stress analyses of V-notched anisotropic plates based on a novel finite element method," Eng. Fract. Mech., vol. 75, pp. 3819–3838, 2008, doi: 10.1016/j.engfracmech.2008.01.003.
S. S. Pageau, P. F. Joseph, and S. B. Biggers Jr., "Finite element analysis of anisotropic materials with singular in-plane stress fields," Int. J. Solids Struct., vol. 32, no. 5, pp. 571–591, 1995, doi: 10.1016/0020-7683(94)00152-9.
W. Pan, C. Cheng, F. Wang, Z. Hu, and J. Li, "Determination of singular and higher order non-singular stress for angularly heterogeneous material notch," Eng. Fract. Mech., vol. 292, art. 109592, 2023, doi: 10.1016/j.engfracmech.2023.109592.
I. Poutiainen, P. Tanskanen, and G. Marquis, "Finite element methods for structural hot spot stress determination — a comparison of procedures," Int. J. Fatigue, vol. 26, pp. 1147–1157, 2004, doi: 10.1016/j.ijfatigue.2004.04.004.
A. Visentini, A. Campagnolo, V. Babini, and G. Meneghetti, "Automated implementation of the Peak Stress Method for the fatigue assessment of complex welded structures," Forces Mech., vol. 6, art. 100072, 2022, doi: 10.1016/j.finmec.2021.100072.
Q. Lei and D. Sornette, "Oscillatory finite-time singularities in rockbursts," Int. J. Rock Mech. Min. Sci., vol. 192, art. 106156, 2025, doi: 10.1016/j.ijrmms.2024.106156.
M. L. Williams, "Stress singularities resulting from various boundary conditions in angular corners of plates in extension," J. Appl. Mech., vol. 19, pp. 526–528, 1952, doi: 10.1115/1.4010550.
G. B. Sinclair, "Stress singularities in classical elasticity—I: Removal, interpretation, and analysis," Int. J. Numer. Methods Eng., vol. 60, no. 5, pp. 993–1018, 2004, doi: 10.1002/nme.1002.
G. B. Sinclair, "Stress singularities in classical elasticity—II: Asymptotic identification," Int. J. Numer. Methods Eng., vol. 60, no. 6, pp. 1019–1045, 2004, doi: 10.1002/nme.1003.
Y. Huang, C. Cheng, Z. Hu, D. Kondo, and R. Das, "Stress singularity analysis for the V-notch with a novel semi-analytical boundary element," Eng. Anal. Bound. Elem., vol. 163, pp. 84–93, 2024, doi: 10.1016/j.enganabound.2024.03.006.
T. Meshii and K. Watanabe, "Stress intensity factor error index for finite element analysis with singular elements," Eng. Fract. Mech., vol. 70, pp. 657–669, 2003, doi: 10.1016/S0013-7944(02)00083-9.
D. Radaj, "State-of-the-art review on the local strain energy density concept and its relation to the J-integral and peak stress method," Fatigue Fract. Eng. Mater. Struct., vol. 37, no. 10, pp. 1091–1112, 2014, doi: 10.1111/ffe.12231.
A. Visentini, A. Campagnolo, V. Babini, and G. Meneghetti, "Automated implementation of the Peak Stress Method for the fatigue assessment of complex welded structures," Forces Mech., vol. 6, art. 100072, 2022, doi: 10.1016/j.finmec.2021.100072.
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