Open Access

ARTICLE

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

Haojie Lian¹, Zhongwang Wang^2,3,*, Haowen Hu³, Shengze Li⁴, Xuan Peng⁵, Leilei Chen^2,3
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.

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Keywords

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

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