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TECHNICAL PAPERS

Three-Dimensional Sharp Corner Displacement Functions for Bodies of Revolution

[+] Author and Article Information
C. S. Huang1

Department of Civil Engineering, National Chiao Tung University, 1001 Ta-Hsueh Road, Hsinchu, Taiwan, ROCcshuang@mail.nctu.edu.tw

A. W. Leissa

Department of Mechanical Engineering, Colorado State University, Fort Collins, CO 80523

1

To whom correspondence should be addressed.

J. Appl. Mech 74(1), 41-46 (Apr 26, 2005) (6 pages) doi:10.1115/1.2178358 History: Received July 26, 2004; Revised April 26, 2005

Sharp corner displacement functions have been well used in the past to accelerate the numerical solutions of two-dimensional free vibration problems, such as plates, to obtain accurate frequencies and mode shapes. The present analysis derives such functions for three-dimensional (3D) bodies of revolution where a sharp boundary discontinuity is present (e.g., a stepped shaft, or a circumferential V notch), undergoing arbitrary modes of deformation. The 3D equations of equilibrium in terms of displacement components, expressed in cylindrical coordinates, are transformed to a new coordinate system having its origin at the vertex of the corner. An asymptotic analysis in the vicinity of the sharp corner reduces the equations to a set of coupled, ordinary differential equations with variable coefficients. By a suitable transformation of variables the equations are simplified to a set of equations with constant coefficients. These are solved, the boundary conditions along the intersecting corner faces are applied, and the resulting eigenvalue problems are solved for the characteristic equations and corner functions.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

Body of revolution with a sharp corner boundary discontinuity

Grahic Jump Location
Figure 2

Cylindrical (r,z) and sharp corner (ρ,ϕ) coordinates

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