Interaction effect of number of circular holes in a circular plate
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The problem of circular tube sheet with uniform tension at its circular boundary and nine holes in the square pitch pattern at its centre is solved using complex stress functions. The Schwarz Alternating technique is used to find the interaction effect of the holes on each other and then the superposition method is used to obtain desired geometry of the nine holes. This superposition gives the stress free boundary at the central hole exactly satisfied. When these results are compared with those obtained by Ukadgaonker and Kale by finite element method (FEM) it is found that the theoretical solutions give higher stress concentration than FEM by about 20% for a large outer radius. When the outer radius is reduced the stress concentration factor increases considerably and the difference in the analytical and the FEM solution also increases to a large extent. The analytical solution found in the present paper is verified with the FEM and photoelasticity solution obtained by Ukadgaonker and Kale earlier. This problem is further generalized for a rhombic pitch pattern, which can be reduced to particular cases such as square pitch pattern, trangular pitch pattern, diagonal pitch pattern by changing the angle of the rhombus. The stress concentration facor around the central hole varies very little for various ligament efficiencies which is given in percentage.
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