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Stress concentration around a hole in a square plate

Model Details and Parameters

Find the stress distribution in a square plate due to the effects of a circular hole at the center under an in-plane uniform line load. Only a quarter model may be analyzed due to symmetry.

Square plate with a hole

 

Structural geometry

 

  • Analysis Type
    2-D static analysis
  • Dimension
    Length: 8.0 in
    Width: 8.0 in
    Thickness: 1.0 in
    Radius of the hole: 0.5 in
  • Plate Type
    Mindlin Plane Stress
  • Material
    Structural Steel
    Young’s Modulus: 1 psi
    Poisson’s Ratio: 0.1
  • Element Property
    Plate Thickness: 1 in
  • Boundary Supports
    Nodes 1 – 9: Constrain Dy, Rx, Ry and Rz (symmetric about X-axis)
    Nodes 64 – 72: Constrain Dx, Rx, Ry and Rz (symmetric about Y-axis)
  • Loads
    Node 9 : 0.5265 lbf, Node 73 : 1.657 lbf, Node 74 : 2.543 lbf, Node 75 : 2.343 lbf, Node 76 : 0.9305 lbf

Analysis model a hole in a square plate

Analysis model

Results

Direct Stress X of the structure (Element 49)

Direct Stress X Stress of the structure (Element 49)

Comparison of Results

Result Location SkyCiv Theoretical Difference 1 Third-Party 2 Difference 2
Direct Stress X Stress of the structure (ksi) Element 49 Top 0.002391  0.002332  2.55% 0.002369 0.93%

Reference

Timoshenko, S. and Goodier, J. N., “Theory of Elasticity”, McGraw-Hill, New York, 1951, pp 78-80

Extra Considerations

  • This verification model was created and checked on 26 April 2020. Since this date, the plate solver and S3D software may have been further improved to achieved greater accuracy.
  • Plates are not exact elements like beam and frame elements and therefore the mesh plays a huge role in the results. Always try to use a structured mesh when it is possible to do so.
  • Results between software will never be exactly the same since different elements are used and the nature of plates are approximate
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