ANALYSIS OF STRESS CONCENTRATION IN FLAT PLATE

1.Problem ststement:

The objective of the problem is to analyze the stress concentration in a flat plate with a hole in centre and determine the maximum deformation and stress developed in flat plate due to given load.

1.1.Model description:

The model is modelled using ANSYS design modeller. The model is modelled as per dimensions given in figure below

Plate dimensions:

Length=10in

Height=4in

Thickness=1.5in

Circular Hole at the center:Diameter=2in

1.2.Analysis steps:

The model is modelled thorugh Ansys design modeller. This model is meshed using ANSYS meshing software using tetrahedral elements with a avergae mesh qality of 0.8. The model is given boundary conditions given below and corressponding governing equations are solved to obtain the results. A static structural model is used to obtain the required results.

Boundary Conditions:

Plate fixed at left face

Load of 10000lbs along X-direction on the right face

1.3.Analysis results:

The deformation plot and von misses stress plot obtained are shown in figure below. The maximum deoformation and von misse stress obtained are shown in figure below

Results summary

Derformation results (in m)

Max deformation:1.9229e-5

Min deformation:0

Von misses stress results (in Pa)

Max stress:4.9731e7

Min stress:9.9775e5

1.4.Conclusion:

From the figures, it is evident that the max stress is found at centre because of the discontinuity caused in geometry by the presence of the hole at  the centre. As a result, the stress concentration lines get concentrated at the centre which cause high stress at centre of the hole. With respect to the deformation, as expected, max deformation is found at right hand side of plate as plate is pulled in direction of applied load. Since the left hand side of the plate is fixed, the deoformation in this side is 0m.

1.5.Referencess:

Nil

2.Problem ststement:

The objective of the problem is to analyze the stress concentration in a flat plate with a hole in centre  and 2 holes on either side of centre hole and determine the maximum deformation and stress developed in flat plate due to given load. 

2.1.Model description:

The model is modelled using ANSYS design modeller. The model is modelled as per dimensions given in figure below 

Plate dimensions:

Length=10in

Height=4in

Thickness=1in

Circular Hole at the center:Diameter=2in

Diameter of smaller holes: Diamter=1in.

Distance of smaller holes from centre holes=3in.

2.2.Analysis steps:

The model is modelled thorugh Ansys design modeller. This model is meshed using ANSYS meshing software using tetrahedral elements with a avergae mesh qality of 0.8. The model is given boundary conditions given below and corressponding governing equations are solved to obtain the results. A static structural model is used to obtain the required results. 

Boundary Conditions:

Plate fixed at left face

Load of 10000lbs along X-direction on the right face

2.3.Analysis results:

The deformation plot and von misses stress plot obtained are shown in figure below. The maximum deoformation and von misse stress obtained are shown in figure below      

Results summary

Derformation results (in m)

Max deformation:2.0803e-5

Min deformation:0 

Von misses stress results (in Pa)

Max stress:4.7674e7

Min stress:1.2347e5

2.4.Conclusion:

Similar to the previous case, the von mises stress is maximum at the centre becuase of more concentration of stress lines and this stress reduces gradually as we move away from hole at the centre. Similar to the previous case are deformation results. The maximum deformation is is found to be on right hand side of plate as this side of plate is pulled by load in direction of load while the deformation is found to be minimum on left hand side of plate as this side of plate is fixed.

2.5.References:

Nil

3.(i) The deformation is found to be maximum for second case of flat plate with one hole at the centre and two holes at either sides of hole. However this difference is more or less negligible when compared with that of 1st case. With respect to maximum von mises stress, the stress is found to be more for case 1 corresponding to flate plate with only single hole at the centre as compared to 2nd case

(ii) From an analysis point of view, I would select the geometry corresponding to 2nd case. This is because the maximum stress developed in geometry corresponding to case 2 is less when compared to goemtery corresponding to case 1. Thus, the design with respect to 2nd case has a better life and factor of safety when compared to case 1. In addition this,the stress concentration in geomtery corresponding to case 2 is less than stress concentration corresponding to geometry of 1st case. This is because with respect to geometry of 2nd case, there exists 3 holes, with large hole in centre and two smaller holes in centre.This helps the stress flow lines to reduce gradually in their magnitude as they reach the end of the plate making this desing more safe as compared to design of geometry of case 1. 

(iii) From an manufacturing point of view, I would select geomtery 2 beacuse the magnitude of stress conecentration is reduced gradually with 2 smaller holes from large centre hole as compared with geomtetry of case 1 where the stress concentraion magnitude is very large surrounding the holes. Also due to high stress concentation, the material with design of case 1 may fail below its yeild strength or ultimate strength. Morever, if material corresponding to design 1 is manufactured, owing to high stress concentration, a crack may propogate from centre of hole making the material more weaker. This is not the case with design of case 2 where even if a crack generates, its effect is weaked by the presence of 2 smaller holes at either ends of centre hole.