Three-Dimensional Free Vibration Analyses of Preloaded Cracked Plates of Functionally Graded Materials via the MLS-Ritz Method

In this study, the moving least squares (MLS)-Ritz method, which involves combining the Ritz method with admissible functions established using the MLS approach, was used to predict the vibration frequencies of cracked functionally graded material (FGM) plates under static loading on the basis of the three-dimensional elasticity theory. Sets of crack functions are proposed to enrich a set of polynomial functions for constructing admissible functions that represent displacement and slope discontinuities across a crack and appropriate stress singularity behaviors near a crack front. These crack functions enhance the Ritz method in terms of its ability to identify a crack in a plate. Convergence studies of frequencies and comparisons with published results were conducted to demonstrate the correctness and accuracy of the proposed solutions. The proposed approach was also employed for accurately determining the frequencies of cantilevered and simply supported side-cracked rectangular FGM plates and cantilevered internally cracked skewed rhombic FGM plates under uniaxial normal traction. Moreover, the effects of the volume fractions of the FGM constituents, crack configurations, and traction magnitudes on the vibration frequencies of cracked FGM plates were investigated.

Comparison of J Integral Assessments for Cracked Plates and Pipes

The purpose of this article is to compare two predictive methods of J integral assessments for center-cracked plates, single-edge cracked plates and double-edge cracked plates produced from X52 and X70 steels, and a longitudinally cracked pipe produced from X70 steel. The two methods examined are: the GSM method and the Js procedure of the French RCC-MR construction code, designated here as the FC method. The accuracy of J integral predictions by these methods is visualized by comparing the results obtained with the “reference” values calculated by the EPRI method. The main results showed that both methods yielded similar J integral values, although in most cases, the GSM predictions were slightly more conservative than the FC predictions. In comparison with the “reference” values of the J integral, both methods provided conservative results for most crack configurations, although the estimates for cracks of a relative length smaller than 1/8 were not found to be so conservative. The prediction of burst pressures for external longitudinal semielliptical part-through cracks in X70 steel pipe showed that the magnitudes of predicted burst pressures came very close to each other, and were conservative compared to FEM (finite element method) calculations and experimentally determined burst pressures.

Evaluation of Stress Intensity Factor of Cracked Plates

Structures are subjected to undesirable changes in their structural properties mainly due to errors in design and construction, heavy loads, fatigue or other degradation. Plate structures are highly sensitive to the formation of cracks and its growth which adversely affects its performance. Notches, induced or self occurring defects, holes acts as stress concentration zone which initiates the crack formation. Knowledge about the severity of cracks is important to predict the component’s life. According to linear elastic fracture mechanics, a key parameter in determining the crack severity is stress intensity factor. Years ago , high factor of safety was chosen to account for unforeseen factors. Development of fracture mechanics enables a designer to use a lower factor of safety, thereby reducing structural components cost. The components weight is also reduced and their reliability is thus enhanced. In this work, experimental and analytical determination of combination of stress intensity factors for rectangular plates with inclined through crack subjected to uniaxial load at failure is found out.

Parameter identification of crack-like notches in aluminum plates based on strain gauge data

The identification of crack parameters and stress intensity factors in aluminum plates under tensile loading is in the focus of the presented research. In this regard, data of strain gauges, distributed along the edges of the samples, are interpreted. In the experiments, slit-shaped notches take the role of cracks located in the interior of the specimens. Their positions, inclinations and lengths as well as the magnitudes of external loadings are identified solving the inverse problems of cracked plates and associated strain fields. Exploiting the powerful approach of distributed dislocations, based on Green’s functions provided by the framework of linear elasticity, in conjunction with a genetic algorithm, allows for a very efficient identification of the sought parameters, thus being suitable for in situ monitoring of engineering structures. Tested samples exhibit one or two straight crack-like notches as well as a kinked one.