International Journal of Fracture

, Volume 195, Issue 1–2, pp 1–14

# Stochastic fracture analysis of cracked structures with random field property using the scaled boundary finite element method

• X. Y. Long
• C. Jiang
• X. Han
• W. Gao
• D. Q. Zhang
Original Paper

## Abstract

This paper presents a stochastic fracture analysis method for random non-homogenous cracked structures using the scaled boundary finite element method (SBFEM). The analyzed cracked domain is divided into polygon-based sub-domains such that the material property of each sub-domain can be modeled differently in the SBFEM. The spatial variability of the material property is represented as random field which is then incorporated directly into the coefficient matrices of the SBFEM. The stochastic global stiffness matrix and the stochastic equilibrium equation of the SBFEM through which the stochastic structural responses can be successfully calculated are further formulated. The stochastic stress intensity factors (SIFs) considering the spatial variability of the material property are then directly extracted from the stress solution of the cracked polygon. Numerical examples are given to demonstrate the validity of the proposed method and investigate the effect of the spatial distribution of the material property on the SIFs.

## Keywords

Scaled boundary finite element method Random field  Scaled boundary polygons Stochastic fracture

## Notes

### Acknowledgments

This work is supported by the State Key Program of National Science Foundation of China (11232004), the National Natural Science Foundation of China (51175160), and the National Excellent Doctoral Dissertation special fund (201235).

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## Authors and Affiliations

• X. Y. Long
• 1
• C. Jiang
• 1
• X. Han
• 1
• W. Gao
• 2
• D. Q. Zhang
• 1
1. 1.State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle EngineeringHunan UniversityChangsha CityPeople’s Republic of China
2. 2.School of Civil and Environmental EngineeringThe University of New South WalesSydneyAustralia