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# Monte Carlo Simulation of Fractures Using Isogeometric Boundary Element Methods Based on POD-RBF

Haojie Lian1, Zhongwang Wang2,3,*, Haowen Hu3, Shengze Li4, Xuan Peng5, Leilei Chen2,3
1 Key Laboratory of In-Situ Property-Improving Mining of Ministry of Education, Taiyuan University of Technology, Taiyuan, 030024, China
2 School of Architecture and Civil Engineering, Huanghuai University, Zhumadian, 463003, China
3 College of Architecture and Civil Engineering, Xinyang Normal University, Xinyang, 464000, China
4 Artificial Intelligence Research Center, National Innovation Institute of Defense Technology, Beijing, 100071, China
5 Department of Mechanical Engineering, Suzhou University of Science and Technology, Suzhou, 215009, China
* Corresponding Author: Zhongwang Wang. Email:
(This article belongs to this Special Issue: Recent Advance of the Isogeometric Boundary Element Method and its Applications)

Computer Modeling in Engineering & Sciences 2021, 128(1), 1-20. https://doi.org/10.32604/cmes.2021.016775

Received 25 March 2021; Accepted 22 April 2021; Issue published 28 June 2021

### Abstract

This paper presents a novel framework for stochastic analysis of linear elastic fracture problems. Monte Carlo simulation (MCs) is adopted to address the multi-dimensional uncertainties, whose computation cost is reduced by combination of Proper Orthogonal Decomposition (POD) and the Radial Basis Function (RBF). In order to avoid re-meshing and retain the geometric exactness, isogeometric boundary element method (IGABEM) is employed for simulation, in which the Non-Uniform Rational B-splines (NURBS) are employed for representing the crack surfaces and discretizing dual boundary integral equations. The stress intensity factors (SIFs) are extracted by M integral method. The numerical examples simulate several cracked structures with various uncertain parameters such as load effects, materials, geometric dimensions, and the results are verified by comparison with the analytical solutions.

### Keywords

Monte Carlo simulation; POD; RBF; isogeometric boundary element method; fracture

Lian, H., Wang, Z., Hu, H., Li, S., Peng, X. et al. (2021). Monte Carlo Simulation of Fractures Using Isogeometric Boundary Element Methods Based on POD-RBF. CMES-Computer Modeling in Engineering & Sciences, 128(1), 1–20.

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