## Engineering

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Objective:

• To discuss the concept of “stress Discontinuity” in a typical 2 D FEA problem.

Example Problem:

• Consider a case as shown in the next slide, a filleted bar made of structural steel is subjected to a tension of 50 kN. The dimensions and other boundary conditions employed are depicted in the fig.

Fig. 1. Model with same boundary condition is used in the problem

Structural Discontinuity:

• What is Structural Discontinuity ?
• Structural discontinuity in an object can be generated by an abrupt change in its geometry i.e. brake or gap, sharp corners, that alters its behavior under load.

Example:

1. Holes: Holes are often used to lighten an aerospace

structure or to rivet component together.

2. Cracks: Cracks are usually generated by the result of

material imperfections or area of high stress.

• A plate with a hole is subjected to a tensile load from both the ends, stress concentration can be seen around the hole, this is because of structural discontinuity which is generated by the hole.

Fig. 2

• In fig. 2 tensile load is applied from both the ends due to which the stress lines will generate in the direction of applied load. The stress lines are shown in fig. 3.
• The stress lines shown in the fig.3 supposed to go straight because of uniform loading.

Fig. 3

• At the mid of the plate the stress lines are supposed to go straight but due to the hole present in between the plate, the stress lines doesn’t find any material, therefore it takes the available path and go ahead.
Hence, due to the deflection of stress lines around the hole, stress discontinuity can be observed and because of that stress concentration can be seen around the hole.
• If we see the case of filleted bar, it is also under the tensile load, and the generation of stress lines in it are shown below:

Fig. 4

• Stress lines over the filleted area gets deformed and then go ahead, due to deformation of stress lines, stress discontinuity occurs over the filleted area.
• Due to this reason the stress concentration can easily be observed over the filleted area.
• After applying the boundary conditions we solved the problem for x-axis directional deformation, x-axis normal stress and for normal stress.
• The problem was solved by applying the following boundary conditions and mesh parameters.

Fig. 5

Fig. 6

Mesh Parameters:

Fig. 7

Equivalent Stress:

Fig. 8

• The stress concentration over the filleted area and its discontinuity can easily be seen in fig. 8
• For reducing the stress discontinuity we refined the mesh from element size 10 to element size 0.6.
• After refining the mesh we observed that the stress concentration and the stress discontinuity has reduced over the filleted area.
• Therefore, the stress discontinuity can be reduced by finer mesh.

Fig. 9

Conclusion:

The concept of “stress discontinuity” and its occurence has been understood successfully.