Browsing by Author "Dr. F. G. Yuan, Committee Chair"

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    Calculation of the Generalized Stress Intensity Factors for a V-notched Anisotropic Body
    (2002-04-30) Shipman, Benjamin Howard; Dr. J. W. Eischen, Committee Member; Dr. E. C. Klang, Committee Member; Dr. F. G. Yuan, Committee Chair
    A robust method for calculating a generalized stress intensity factor for a V-notched anisotropic body under symmetric and/or anti-symmetric deformation is derived for plane stress or plane strain. The compact formulation for the generalized stress intensity factors is derived based on Stroh formalism. A path-independent line integral together with an auxiliary field solution, called the interaction M-integral, is utilized to solve for these generalized stress intensity factors. Through numeric evaluation of the interaction M-integral using a finite element solution, the generalized stress intensity factors can be found. These generalized stress intensity factors can be used to predict the failure conditions without the need for a detailed notch-tip field solution. Since the interaction M-integral is path-independent, the calculation can be carried out in the region away from the notch tip where a conventional finite element solution is sufficient to perform this analysis. Numeric results for the generalized stress intensity factors are given for a thin rectangular plate with double edge notches. The specimen geometry used follows that in the ASTM standard D 5379/D 5379M-93 for shear property testing of fiber-reinforced composite materials. The method is first verified for three example problems. Then, the generalized stress intensity factors are given for a wide range of notch depths and angles for isotropic and anisotropic material property cases. Two in-plane fiber orientations of a unidirectional fiber-reinforced graphite/epoxy composite are considered. Two loading cases are given to produce symmetric and anti-symmetric deformation. The generalized stress intensity factor results given here for anti-symmetric deformation are unprecedented.
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    A Probabilistic Approach to Damage Localization in Structural Health Monitoring.
    (2005-04-29) Harb, Hussein Said; Dr. F. G. Yuan, Committee Chair; Dr. K. Peters, Committee Member; Dr. J. Eischen, Committee Member
    A probabilistic framework for on-line structural health monitoring of plate-like structures, which addresses the issue of uncertainties inherent in the problem of damage detection, is presented. This work answers the following question in a probabilistic approach: Based on the available data, and acknowledging the uncertainty inherent in the problem, what is the probability that the damage occurs at a certain location in a structure? Gaussian probability density functions (PDF) have been used to model the different types of uncertainties. These uncertainties that are presented in this work, include stochastic and model uncertainties. Considering these types of uncertainties, the main objective is to locate the damage in a plate structure in a probabilistic form. Also, the sensitivity of damage localization to the levels of uncertainties is presented in this work. The probabilistic structural health monitoring employed in this study can be presented in the following steps: Firstly, an elastic wave energy decay model in relation to the propagation distance for the damage localization problem in isotropic plates is chosen. A Gaussian PDF is used to represent the uncertainty that is due to the underlying assumptions, which simplify the physical model. Secondly, the uncertain measured sensor data (stochastic uncertainty) is modeled as a Gaussian PDF. Thirdly, a least-squares damage localization technique is applied to iteratively search for the location of the damage based on elastic wave energy measurements. To model the PDFs of the stochastic and model uncertainties, and to solve for the resultant PDF of the location of the damage (output) using the PDFs of the measured and modeled data (input), the Monte Carlo method is used. Lastly, probabilistic diagrams for the damage location can be constructed using the moments (mean, variance, etc) of the resulting PDF of the damage location parameters. Based on the efforts described in this work, a number of conclusions can be drawn: First, a SHM method that accounts for uncertainty in the SHM problem in a structured fashion has been successfully established. Second, the Monte Carlo simulation is suited to model uncertainties when dealing with statistical analysis. Third, the probabilistic approach is capable of showing the effect of the level of uncertainties on the damage localization, which proves that the damage localization is more sensitive to the stochastic uncertainty than the model uncertainty, implying that the elastic wave energy decay model is accurate and robust. Also, a conclusion can be drawn that the key aspect of the probabilistic approach is the minimization of false-positive and false-negative indicators from the damage localization process. False- positive refers to the situation where damage is indicated when in fact none is present. False- negative refers to the situation where damage is not indicated, even though it is present. Fourth, the method is an active damage detection technique, which is suitable for the applications of SHM. Lastly, the method uses the all time series data information collected by each sensor, not only the time-of-flight or time of arrival. Experimental and simulation results show that the estimated damage location by least-squares method makes good agreement with the targeted location.