Reliability analysis of the stress intensity factor using multilevel Monte Carlo methods

authored by: Khader M. Hamdia, Hamid Ghasemi
Abstract: This paper presents a reliability analysis for fracture toughness using a multilevel refinement on a hierarchy of computational models. A 2D finite element model discretized by quadrilateral elements is developed to analyze the stress intensity with the presence of an initial edge crack. The multilevel simulations are obtained considering a non-uniform sequence of mesh refinement in the vicinity of the crack tip. We set the probabilistic problem accounting for applied stress and crack size uncertainties. We analyze several error tolerances using the standard and multilevel Monte Carlo methods combined with the selective refinement procedure. The probability of failure is estimated by expanding it in a telescoping sum of an initial approximation at the coarsest mesh and a series of incremental corrections between the subsequent levels. In our analysis, we take on two common fracture problems; a single-edge notched tension to investigate the pure mode-I and an asymmetric four-points bending to consider the mixed mode-I/II. The results show significant savings in the computation cost.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Arak University of Technology
Ministry of Science, Research and Technology Islamic Republic of Iran
Type: Article
Journal: Probabilistic Engineering Mechanics
Volume: 74
ISSN: 0266-8920
Publication date: 10.2023
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Statistical and Nonlinear Physics, Civil and Structural Engineering, Nuclear Energy and Engineering, Condensed Matter Physics, Aerospace Engineering, Ocean Engineering, Mechanical Engineering
Electronic version(s): https://doi.org/10.1016/j.probengmech.2023.103497 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{1d71d0bb9ea345348224edd0d3669f55,
title = "Reliability analysis of the stress intensity factor using multilevel Monte Carlo methods",
abstract = "This paper presents a reliability analysis for fracture toughness using a multilevel refinement on a hierarchy of computational models. A 2D finite element model discretized by quadrilateral elements is developed to analyze the stress intensity with the presence of an initial edge crack. The multilevel simulations are obtained considering a non-uniform sequence of mesh refinement in the vicinity of the crack tip. We set the probabilistic problem accounting for applied stress and crack size uncertainties. We analyze several error tolerances using the standard and multilevel Monte Carlo methods combined with the selective refinement procedure. The probability of failure is estimated by expanding it in a telescoping sum of an initial approximation at the coarsest mesh and a series of incremental corrections between the subsequent levels. In our analysis, we take on two common fracture problems; a single-edge notched tension to investigate the pure mode-I and an asymmetric four-points bending to consider the mixed mode-I/II. The results show significant savings in the computation cost.",
keywords = "Fracture mechanics, Multilevel Monte Carlo, Probability of failure, Reliability analysis, Stress intensity factor",
author = "Hamdia, {Khader M.} and Hamid Ghasemi",
note = "Funding Information: Khader M. Hamdia, thanks the support of Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - Projektnummer 492535144. Hamid Ghasemi thanks the support provided by the Center for International Scientific Studies & Collaborations (CISSC), Ministry of Science, Research and Technology of Iran . ",
year = "2023",
month = oct,
doi = "10.1016/j.probengmech.2023.103497",
language = "English",
volume = "74",
journal = "Probabilistic Engineering Mechanics",
issn = "0266-8920",
publisher = "Elsevier Ltd.",
}