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

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Xiaowei Shen ◽  
Haowen Hu ◽  
Zhongwang Wang ◽  
Xiuyun Chen ◽  
Chengbin Du
Keyword(s):  
Finite Element ◽  
Proper Orthogonal Decomposition ◽  
Radial Basis Functions ◽  
Orthogonal Decomposition ◽  
Basis Functions ◽  
Uncertain Variables ◽  
Computation Efficiency ◽  
Radial Basis ◽  
Proper Orthogonal ◽  
Scaled Boundary Finite Element

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.

scholarly journals Proper Orthogonal Decomposition–Radial Basis Function Surrogate Model-Based Inverse Analysis for Identifying Nonlinear Burgers Model Parameters From Nanoindentation Data

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Salah U. Hamim ◽  
Raman P. Singh
Keyword(s):  
Experimental Data ◽  
Finite Element ◽  
Radial Basis Function ◽  
Proper Orthogonal Decomposition ◽  
Basis Function ◽  
Surrogate Model ◽  
Orthogonal Decomposition ◽  
Model Parameters ◽  
Radial Basis ◽  
Proper Orthogonal

This study explores the application of a proper orthogonal decomposition (POD) and radial basis function (RBF)-based surrogate model to identify the parameters of a nonlinear viscoelastic material model using nanoindentation data. The inverse problem is solved by reducing the difference between finite element simulation-trained surrogate model approximation and experimental data through genetic algorithm (GA)-based optimization. The surrogate model, created using POD–RBF, is trained using finite element (FE) data obtained by varying model parameters within a parametric space. Sensitivity of the model parameters toward the load–displacement output is utilized to reduce the number of training points required for surrogate model training. The effect of friction on simulated load–displacement data is also analyzed. For the obtained model parameter set, the simulated output matches well with experimental data for various experimental conditions.

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