Identification of a scatterer embedded in elastic heterogeneous media using dynamic XFEM

Struct Control Health Monit

Tapia

et al. 2020

Summary Identifying structural damage can usually be modeled as a problem with the use of linear equations. Due to measurement noise and spatial incompleteness of the measured mode shapes, these linear equations are usually ill conditioned, which will significantly reduce the accuracy of subsequent damage assessment. This study develops an iterative total least squares (TLS) based estimation method, which can effectively mitigate such ill conditioning and avoid propagating noise into estimates of structural damage severity. In particular, a procedure, called the δ–p curve method, is proposed to choose the effective rank of a TLS estimation. Further, an iterative approach of TLS‐based estimation is proposed to eliminate spurious damage estimates due to modal expansion and measurement noise. To investigate the effectiveness of the proposed iterative TLS‐based estimation method, detailed numerical studies of damage assessment are first conducted on a simulated 3D frame structure, in which both noise pollution and spatial incompleteness of the mode shapes are considered. Additionally, experimental tests with a laboratory structure are performed to validate the proposed method. Results indicate that the proposed iterative TLS‐based method can accurately identify the structural damage, even with noise‐polluted and spatially incomplete modes.

Section: Scenariomentioning

confidence: 99%

An iterative total least squares‐based estimation method for structural damage identification of 3D frame structures

Struct Control Health Monit

Tapia

et al. 2020

“…However, the applications of the 12‐fold bimaterial enrichment functions are somewhat limited since these enrichment functions require more degrees of freedom (DOFs) and most often yield worse conditioning of the algebraic system than the approximate 4‐fold ones, especially in 3‐dimensional cases. There is some confusion as to whether it is necessary to use the 12‐fold bimaterial enrichment for interface cracks: Some XFEM studies adopted the bimaterial enrichment functions whereas others stick with the approximate 4‐fold ones. Huynh and Belytschko studied interface fracture in composite materials using both types of enrichment functions and found that less but still good accuracy can be obtained with the 4‐fold homogeneous enrichment.…”

Section: Introductionmentioning

confidence: 99%

Material‐dependent crack‐tip enrichment functions in XFEM for modeling interfacial cracks in bimaterials

Numerical Meth Engineering

Waisman

2017

Summary A novel set of enrichment functions within the framework of the extended finite element method is proposed for linear elastic fracture analysis of interface cracks in bimaterials. The motivation for the new enrichment set stems from the revelation that the accuracy and conditioning of the widely accepted 12‐fold bimaterial enrichment functions significantly deteriorates with the increase in material mismatch. To this end, we propose an 8‐fold material‐dependent enrichment set, derived from the analytical asymptotic displacement field, that well captures the near‐tip oscillating singular fields of interface cracks, including the transition to weak discontinuities of bimaterials. The performance of the proposed material‐dependent enrichment functions is studied on 2 benchmark examples. Comparisons are made with the 12‐fold bimaterial enrichment as well as the classical 4‐fold homogeneous branch functions, which have also been used for bimaterials. The numerical studies clearly demonstrate the superiority of the new enrichment functions, which yield the most accurate results but with less number of degrees of freedom and significantly improved conditioning than the 12‐fold functions.

“…Compared with the standard FEM, the XFEM offers two superior capabilities: (i) a more accurate representation of fields in the vicinity of the crack tip singularity and (ii) alleviation of the need for costly re-meshing as the crack is propagating in the structure [25,26]. These favorable features have been exploited in [27,28,29,30,31] by combining XFEM and optimization algorithms for deterministic and probabilistic flaw detection in structures. In [31], the Bayesian approach [32,33,34,35] was used to quantify uncertainties from modeling errors and measurement noise, leading to the probability distributions of the flaw parameters.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic Model Updating for Sizing of Hole-Edge Crack Using Fiber Bragg Grating Sensors and the High-Order Extended Finite Element Method

Yang

et al. 2016

Sensors

This paper presents a novel framework for probabilistic crack size quantification using fiber Bragg grating (FBG) sensors. The key idea is to use a high-order extended finite element method (XFEM) together with a transfer (T)-matrix method to analyze the reflection intensity spectra of FBG sensors, for various crack sizes. Compared with the standard FEM, the XFEM offers two superior capabilities: (i) a more accurate representation of fields in the vicinity of the crack tip singularity and (ii) alleviation of the need for costly re-meshing as the crack size changes. Apart from the classical four-term asymptotic enrichment functions in XFEM, we also propose to incorporate higher-order functions, aiming to further improve the accuracy of strain fields upon which the reflection intensity spectra are based. The wavelength of the reflection intensity spectra is extracted as a damage sensitive quantity, and a baseline model with five parameters is established to quantify its correlation with the crack size. In order to test the feasibility of the predictive model, we design FBG sensor-based experiments to detect fatigue crack growth in structures. Furthermore, a Bayesian method is proposed to update the parameters of the baseline model using only a few available experimental data points (wavelength versus crack size) measured by one of the FBG sensors and an optical microscope, respectively. Given the remaining data points of wavelengths, even measured by FBG sensors at different positions, the updated model is shown to give crack size predictions that match well with the experimental observations.