Anderlen stress analysis

The stress concentration in a plate
with a single central hole.

Introduction.

This is an analysis of the stress concentrations in a plate with a single central hole under axial tensile loading. This work is an investigation of how closely the published stress concentration data match a representative analyses. This is not intended as original work and is for interest value only.

Finite Element Model.

A finite element model of a quarter of the plate is used, with symmetrical constraints applied at the cut surfaces. FEM Designer has been used for the analysis, since this is very easy to set up with equations to change the hole size so that the model is remeshed by changing only one value.

Loading and Constraints.

The plate has a tensile load of 200 MPa applied to the right hand edge. The solution sequence is linear static, and the material properties are linear. The hole edges are free to deflect, the hole is not filled and is free to deflect. The elements used are 2D plane stress. All models used the same number of elements, only the hole radius has been changed.

Radius 3
s1 stress.

Radius 5
s1 stress.

Radius 10
s1 stress.

Radius 15
s1 stress.

Radius 20
s1 stress.

Radius 25
s1 stress.

Radius 30
s1 stress.

Radius 35
s1 stress.

Results.
Table 1

This shows the stresses tabluated for comparison.

The Sn column is the net stress across a section through the hole centre. This shows the expected average stress if there was no concentration. Ktn is the stress concentration on the net section stress.
Ktn * Sn is therefore the concentrated stress at the hole section. This can also be calculated from the gross stress concentration factor, Ktg times the applied gross stress away from the hole.
Column Ktg * Sg shows that the same result is obtained by both methods. The FE max S1 stress column shows the result from the FE model. The S1 stress is in the axial or x direction only and can be compared directly with the previous values.
Note that this is a linear analysis; so the concentrations can lead to stresses that are far above the material ultimate allowable. This means that the section has become plastic and may not necessarily cause failure, but it will certainly give large deflections, depending on how ductile the material is.

Conclusions.

The analysis shows very close agreement at small hole diameters when the plate width is effectively very large.
With small holes, the net concentration factor is greater than with large holes. At very large hole diameters the results are still surprisingly accurate.

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Updated 5/1/2008

Anderlen stress analysis The stress concentration in a plate with a single central hole.

The stress concentration in a plate with a single central hole.

Anderlen stress analysis

The stress concentration in a plate
with a single central hole.

The stress concentration in a plate
with a single central hole.