Stress analysis on a plate with single and multiple holes

Case1:-

The above picture is the model and boundary conditions for case 1.

Looking into the deformation contour, the maximum deformation has happened at the end where the force was applied and minimum deformation (i.e.) zero deformation at the end where the plate was fixed. Due to the Poisson\'s effect, there is lateral deformation when the plate was pulled in tension. We could also observe that the hole which was circular, has now turned into ellipse due to applied tension on the plate. But since the plate is within the elastic limit, when the tension force on the plate is removed, the plate will come back to its original shape.

The stress contours show that stress concentration in the above plot with max and min. Changes in the stress contours happen only at the region closer to the hole. This is due to the sudden change in the geometry along the path of stress flow.

Case 2:-

Looking into the deformation contour, the maximum deformation has happened at the end where the force was applied and minimum deformation (i.e.) zero deformation at the end where the plate was fixed. Due to the Poisson\'s effect, there is lateral deformation when the plate was pulled in tension. We could also observe that the hole which was circular, has now turned into ellipse due to applied tension on the plate. But since the plate is within the elastic limit, when the tension force on the plate is removed, the plate will come back to its original shape.

The stress contours show that stress concentration in the above plot with max and min. Changes in the stress contours happen only at the region closer to the hole. This is due to the sudden change in the geometry along the path of stress flow.

Conclusion:-

It is observed that sudden change in stress flow lines causes the stress to rise abruptly. Through a gradual change in the gradient of flow lines mitigation of stress is observed. The rise in the stress concentration factor reaches to its maximum value 3 at the periphery of the circular hole. The work compiled above shows that this maximum SCF value can be reduced either by material removal at the vicinity or by shape optimization or by strengthening the hole by the inclusion of additional stronger material.

In the above image, crowding and bending of flow lines near obstructions helps to visualize the concentration of stresses and strains near the notches. The large section (on the right with smooth transition of stress) and the small section (on the left with stress concentration) are the same in both cases, but the transitions are different.

The deformation at case 1 is slightly higher than case 2 this is due to the above fact of stress and strain concentration at the hole which is along the direction of the stress flow.

From an analysis point of view, case 2 design can be chosen because of the lesser stress concentration. But whereas from the manufacturing point of view, case 1 will be chosen because of the less work needed to prepare the geometry at the manufacturing unit which will economically benefit the company.