Search

A numerical method is proposed for estimating piecewise-constant solutions for Fredholm integral equations of the first kind. Two functionals, namely the weighted total variation (WTV) functional and the simplified Modica-Mortola (MM) functional, are introduced. The solution procedure consists of two stages. In the first stage, the WTV functional is minimized to obtain an approximate solution fTV*. In the second stage, the simplified MM functional is minimized to obtain the final result by using the damped Newton (DN) method with fTV* as the initial guess. The numerical implementation is given in detail, and numerical results of two examples are presented to illustrate the efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

It has been shown that impact damage to composite materials can be revealed by embedded Fiber Bragg Gratings (FBG) as a broadening and splitting of the latter's characteristic narrow peak reflected spectrum. The current work further subjected the impact damaged composite to cyclic loading and found that the FBG spectrum gradually submerged into a rise of background intensity as internal damages progressed. By skipping the impact, directing the impact to positions away from the FBG and examining the extracted fibers, we concluded that the above change is not a result of deterioration/damage of the sensor. It is caused solely by the damages initiated in the composite by the impact and aggravated by fatigue loading. Evolution of the grating spectrum may therefore be used to monitor qualitatively the development of the incurred damages. [ABSTRACT FROM AUTHOR]