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A Semi-Analytical Approach for Stress Concentration of Cantilever Beams with Holes Under Bending

Published online by Cambridge University Press:  05 May 2011

J.-T. Chen  and
P.-Y. Chen
J.-T. Chen*
Affiliation:
Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung, Taiwan 20224, R.O.C.
P.-Y. Chen*
Affiliation:
Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung, Taiwan 20224, R.O.C.
*
*Life-Time Distinguished Professor
**Master student
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Abstract

In the paper, the degenerate kernels and Fourier series expansions are adopted in the null-field integral equation to solve bending problems of a circular beam with circular holes. The main gain of using degenerate kernels in integral equations is free of calculating the principal values for singular integrals. An adaptive observer system is addressed to fully employ the property of degenerate kernels for circular boundaries in the polar coordinate. After moving the null-field point to the boundary and matching the boundary conditions, a linear algebraic system is obtained without boundary discretization. The unknown coefficients in the algebraic system can be easily determined. The present method is treated as a “semi-analytical” solution since error only attributes to the truncation of Fourier series. Stress concentration is also our concern. Finally, several examples, including two holes and four holes, are given to demonstrate the validity of the proposed method. The results are compared with those of Naghdi and Bird and Steele. Also, the position where the maximum concentration factor occurs is examined. The present formulation can be extended to handle beam problems with arbitrary number and various positions of circular holes by using the developed general-purpose program.

Keywords

Null-field integral equationDegenerate kernelFourier seriesCircular holesCantilever beamStress concentration.
Type
Articles
Information
Journal of Mechanics , Volume 23 , Issue 3 , September 2007 , pp. 211 - 222
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2007

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