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Complexity
Volume 2018 (2018), Article ID 9034865, 21 pages
https://doi.org/10.1155/2018/9034865
Research Article

Statistical Identification of Parameters for Damaged FGM Structures with Material Uncertainties in Thermal Environment

1School of Mechano-Electronic Engineering, Xidian University, Xi’an 710071, China
2School of Aerospace, Xi’an Jiaotong University, Xi’an 710049, China

Correspondence should be addressed to Yalan Xu; nc.ude.naidix.liam@uxly

Received 12 December 2017; Accepted 20 February 2018; Published 29 March 2018

Academic Editor: Minvydas Ragulskis

Copyright © 2018 Yalan Xu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Considering that the statistic numerical characteristics are often required in the probability-based damage identification and safety assessment of functionally graded material (FGM) structures, an stochastic model updating-based inverse computational method to identify the second-order statistics (means and variances) of material properties as well as distribution of constituents for damaged FGM structures with material uncertainties is presented by using measurable modal parameters of structures. The region truncation-based optimization method is employed to simplify the computational process in stochastic model updating. In order to implement the forward propagation of uncertainties required in the stochastic model updating and avoid large error resulting in the nonconvergence of the iteration process, an algorithm is proposed to compute the covariance between the modal parameters and the identified parameters for damaged FGM structures. The proposed method is illustrated by a numerically simulated damaged FGM beam with continuous spatial variation of material properties and verified by comparing with the Monte-Carlo simulation (MCS) method. The influences of the levels and sources of measured data uncertainties as well as the boundary conditions on the identification results are investigated. The numerical simulation results show the efficiency and effectiveness of the presented method for the identification of material parameter variability by using the measurable modal parameters of damaged FGM structures.