Browsing by Author "McGee, O. G., III"

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Three-dimensional vibrations of cracked rectangular parallelepipeds of functionally graded material
(2013-05-01)
Huang, C. S.
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McGee, O. G., III
;
Wang, K. P.
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土木工程學系
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Department of Civil Engineering
A novel examination of the three-dimensional (3-D) vibrations of rectangular parallelepipeds of functionally graded material (FGM) having side cracks is summarized. Employing 3-D theory of elasticity and a variational Ritz methodology, new hybrid series of mathematically complete orthogonal polynomials and crack functions as the assumed displacement fields are proposed to enhance the convergence modeling of the stress singular behavior of the crack terminus edge front in a rectangular FGM parallelepiped. The proposed admissible hybrid series properly describe the theta(1/root r)3-D stress singularities at the terminus edge front of the crack, allowing for displacement discontinuities across the crack sufficient to explain the most general 3-D "mixed modes" of local crack-edge deformation and stress fields typically seen in fracture mechanics. The correctness and validity of the vibration analysis are confirmed through comprehensive convergence studies and comparisons with published results for cracked rectangular FGM parallelepipeds modeled as homogeneous rectangular plates with side cracks and FGM rectangular plates with no cracks based on various plate theories. Two types of FGM parallelepipeds, Al/Al2O3 and Al/ZrO2, are included in the study. The locally effective material properties are estimated by a simple power law and the effects of the volume fraction on the frequencies are investigated. For the first time in the published literature, this work reports frequency data and nodal patterns for FGM rectangular parallelepipeds modeled as moderately thick plates with several combinations of hinged, clamped, and completely free kinematic and stress conditions along the four side faces, and having side cracks with varying crack size effects implying flaw-size influence in FGM parallelepiped vibration and fracture, including crack length ratios (d/a and d/b), crack positions (c(x)/a and c(y)/b), and crack inclination angles (alpha). (C) 2012 Elsevier Ltd. All rights reserved.
Vibrations of cracked rectangular FGM thick plates
(2011-06-01)
Huang, C. S.
;
McGee, O. G., III
;
Chang, M. J.
;
土木工程學系
;
Department of Civil Engineering
Accurate first-of-its-kind solutions of the free vibration characteristics of side-cracked rectangular functionally graded material (FGM) thick plates are reported. From a brief review summary of available shear deformable plate theories, the well-established Reddy third-order plate theory apropos to cracked FGM thick plates is utilized. A novel Ritz procedure is developed incorporating special admissible functions appropriately named in this study as crack functions - that properly account for the stress singularity behaviors in the neighborhood of a crack tip, and that properly account for the discontinuities of displacements and slops across a crack. Material properties of the FGM plates are assumed to vary continuously in the thickness direction according to the Mori-Tanaka scheme or a simple power law. The proposed special admissible functions accelerate the convergence of the extensive non-dimensional frequency solutions summarized. The first known non-dimensional frequencies of simply-supported and cantilevered cracked aluminum (Al) and ceramic (zirconia (ZrO(2))) or alumina (Al(2)O(3)) FGM thick plates of moderate thickness ratio (side-length to plate thickness, b/h = 10) are accurately determined. The effects of the volume fraction in the modeling of material distribution in the thickness direction and of cracks with different lengths, locations and orientations on the non-dimensional frequencies are investigated. (C) 2011 Elsevier Ltd All rights reserved.