Abstract
Minimizing the stress concentration around holes in uniaxially loaded finite plates is an important consideration in engineering design. One method for reducing the stress concentration around a central circular hole in a uniaxially loaded plate is to introduce smaller auxiliary holes on either side of the original hole to help smooth the flow of the tensile principal-stress trajectories past the original hole. This method has been demonstrated by Heywood and systematically studied by Erickson and Riley. Erickson and Riley show that for a central-hole diameter-to-plate width ratio of 0.222, the maximum stress reduction is up to 16 percent. In recent work, Durelliet al. show that the stress concentrations around holes in uniaxially loaded plates can be minimized by changing the hole shape itself till an optimum hole profile with constant stress values respectively on the tensile and compressive segments of the hole boundary is reached. By this technique the maximum stress reduction obtained for the above case is up to 20 percent.
In the present work, starting with the optimum sizes and locations of central and auxiliary circular holes for a finite plate given by Erickson and Riley, a systematic study of the hole-shape optimization is undertaken. A two-dimensional photoelastic method is used. For a central-hole diameter-to-plate width ratio of 0.222, the reduction in stress-concentration factor obtained after hole-shape optimization is about 30 percent. It is also shown that it is possible to introduce the ‘equivalent ellipse’ concept for optimized holes.
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Abbreviations
- b :
-
major axis of equivalent ellipse
- d :
-
diameter of central hole/minor axis of equivalent ellipse
- d a :
-
diameter of auxiliary holes
- l :
-
distance between centers of central hole and auxiliary holes
- w :
-
plate width
- θ, α:
-
polar angles
- \(\sigma _{nom} \) :
-
nominal stress
- \(\sigma _\theta ,\sigma _\alpha \) :
-
tangential stress
References
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Rajaiah, K., Naik, N.K. Hole-shape optimization in a finite plate in the presence of auxiliary holes. Experimental Mechanics 24, 157–161 (1984). https://doi.org/10.1007/BF02324999
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DOI: https://doi.org/10.1007/BF02324999