Stochastic Fracture Analysis Using Scaled Boundary Finite Element Methods Accelerated by Proper Orthogonal Decomposition and Radial Basis Functions

Xiaowei Shen,Xiuyun Chen,Zhongwang Wang,Chengbin Du,Haowen Hu,Jinze Xu

doi:10.1155/2021/9181415

Abstract

This paper presents a stochastic analysis method for linear elastic fracture mechanics using the Monte Carlo simulations (MCs) and the scaled boundary finite element method (SBFEM) based on proper orthogonal decomposition (POD) and radial basis functions (RBF). The semianalytical solutions obtained by the SBFEM enable us to capture the stress intensity factors (SIFs) easily and accurately. The adoption of POD and RBF significantly reduces the model order and increases computation efficiency, while maintaining the versatility and accuracy of MCs. Numerical examples of cracks in homogeneous and bimaterial plates are provided to demonstrate the effectiveness and reliability of the proposed method, where the crack inclination angles are set as uncertain variables. It is also found that the larger the scale of the problem, the more advantageous the proposed method is.

Highlights

Fracture mechanics is central to many engineering applications, but the simulation of fractures poses great challenges to finite element analysis
scaled boundary finite element method (SBFEM) is used for linear elastic fracture analysis and Monte Carlo simulation (MCs) for uncertainty qualification, which is accelerated by the combination of proper orthogonal decomposition (POD) and radial basis function (RBF)
It is shown that the combination of POD and RBF is effective in model reduction and accelerating MCs computation, which achieves the goal of reducing computing cost and improving computing efficiency

Summary

Introduction

Fracture mechanics is central to many engineering applications, but the simulation of fractures poses great challenges to finite element analysis To address this problem, a number of numerical algorithms were developed, such as meshfree methods [1, 2], extended finite element methods [3,4,5], phase field methods [6], boundary element methods [7] and peridynamics methods [8]. This paper proposes a novel procedure for stochastic analysis of linear fracture mechanics With this method, SBFEM is used for linear elastic fracture analysis and MCs for uncertainty qualification, which is accelerated by the combination of POD and RBF.

Monte Carlo Model

Proper Orthogonal Decomposition and Radial Basis Functions

Numerical Examples

Findings

Conclusions