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TECHNICAL PAPERS

Sharp Corner Functions for Mindlin Plates

[+] Author and Article Information
O. G. McGee, J. W. Kim

Georgia Institute of Technology, Atlanta, GA

A. W. Leissa

Ohio State University, Columbus, OH

J. Appl. Mech 72(1), 1-9 (Feb 01, 2005) (9 pages) doi:10.1115/1.1795221 History: Received June 05, 2002; Revised January 08, 2004; Online February 01, 2005
Copyright © 2005 by ASME
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References

Williams, M. L., 1952, “Surface Stress Singularities Resulting From Various Boundary Conditions in Angular Plates Under Bending,” Proc. of First U.S. National Congress of Applied Mechanics, ASME, New York, pp. 325–329.
Williams,  M. L., 1952, “Stress Singularities Resulting Form Various Boundary Conditions in Angular Corners of Plates in Extension,” ASME J. Appl. Mech., 19, pp. 526–528.
Leissa,  A. W., McGee,  O. G., and Huang,  C. S., 1993, “Vibrations of Sectorial Plates Having Corner Stress Singularities,” ASME J. Appl. Mech., 60(1), pp. 134–140.
Leissa,  A. W., McGee,  O. G., and Huang,  C. S., 1993, “Vibrations of Circular Plates Having V-Notches or Sharp Radial Cracks,” J. Sound Vib., 161(2), pp. 227–239.
McGee,  O. G., Leissa,  A. W., Huang,  C. S., and Kim,  J. W., 1995, “Vibrations of Circular Plates With Clamped V-Notches or Rigidly Constrained Radial Cracks,” J. Sound Vib., 181(2), pp. 185–201.
McGee,  O. G., Leissa,  A. W., and Huang,  C. S., 1992, “Vibrations of Cantilevered Skewed Plates With Corner Stress Singularities,” Int. J. Numer. Methods Eng., 35, pp. 409–424.
McGee,  O. G., Leissa,  A. W., and Huang,  C. S., 1992, “Vibrations of Cantilevered Skewed Trapezoidal and Triangular Plates With Corner Stress Singularities,” Int. J. Mech. Sci., 34(1), pp. 63–84.
Huang,  C. S., McGee,  O. G., Leissa,  A. W., and Kim,  J. W., 1995, “Accurate Vibration Analysis of Simply Supported Rhombic Plates by Considering Stress Singularities,” ASME J. Vibr. Acoust., 117, pp. 245–251.
McGee,  O. G., Kim,  J. W., Kim,  Y. S., and Leissa,  A. W., 1996, “Corner Stress Singularity Effects on the Vibrations of Rhombic Plates With Combinations of Clamped and Simply Supported Edges,” J. Sound Vib., 193(3), pp. 555–580.
Leissa, A. W., 1969, Vibration of Plates, NASA SP-160, U.S. Government Printing Office, Washington, DC (reprinted 1993 by Acoustical Society of America).
Haggeblad,  B., and Bathe,  K. J., 1990, “Specifications of Boundary Conditions for Reissner/Mindlin Plate Bending Finite Elements,” Int. J. Numer. Methods Eng., 30, pp. 981–1011.
Mindlin,  R. D., 1951, “Influence of Rotatory Inertia and Shear on Flexural Motions of Isotropic, Elastic Plates,” ASME J. Appl. Mech., 18, pp. 31–38.
Mindlin,  R. D., and Deresiewicz,  H., 1954, “Thickness-Shear and Flexural Vibrations of a Circular Disk,” J. Appl. Phys., 25, pp. 1329–1332.
Reismann, H., 1988, Elastic Plates: Theory and Application, Wiley, New York.

Figures

Grahic Jump Location
Variation of minimum values of Re(λ) with vertex angle α based on Mindlin plate theory (υ=0.3)
Grahic Jump Location
Variation of minimum values of λ̄ with vertex angle α based on Mindlin plate theory (all ν)
Grahic Jump Location
Variation of minimum values of Re(λk) with vertex angle α based on classical plate theory (υ=0.3)

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