Week 1 Stress Concentration on a Plate with hole

Aim : To perform static structural analysis to determine the stress concentration on a plate with holes.

Objectives :

1) Design a plate with a hole model. (Case 1)

2) Design a plate with three holes of different diameter. (Case 2)

3) Determining the maximum deformation and stress developed in both models.

4) Comparing the result of two cases and deciding which cases to select on analysis and manufacturing point of view.

Introduction :

The stress at the edge of a hole, or at a notch root, has a higher value than the remote stress. This phenomenon is called stress concentration.

a) In the presence of ductile yielding, stress concentrations are relatively unimportant since the yielding which will occur at the concentration, e.g. the tip of a notch, will merely redistribute the stresses and not necessarily lead to failure. If, however, there is only marginal ductility, or in the presence of low temperatures, then stress concentrations become more significant as the likelihood of brittle failure increases. It is wise, therefore, to keep stress concentration factor as low as possible.

b) For brittle material like cast iron, internal stress concentrations arise within the material due to the presence of, e.g., flaws, impurities or graphite flakes. These produce stress increases at least as large as those given by surface stress concentrations which, therefore, may have little or no effect on failure. A cast iron bar with a small transverse hole, for example, may not fracture at the hole when a tensile load is applied.

Given :

For Case 1 :

Plate dimensions:

Length=300mm
Height=120mm
Thickness=30mm
Circular Hole at the center:
Diameter=60mm

For Case 2 :

Plate dimensions:

Smaller holes 90mm away from the center:

Diameter=30mm

Circular Hole at the center:
Diameter=60mm

Length=300mm
Height=120mm
Thickness=30mm

Boundary Conditions for both the Cases:
Plate fixed at left face.
Load of 500N on the right face

Procedure :

1) For both cases, we use static structural tool in the analysis system tool box to define the geometry and other input parameters for the same.

2) In the engineering data we input the material and its properties. (e.g. Structural steel)

3) To design the model with given dimensions, spaceclaim is used in the geometry tab. For case 1 and case 2 is given below pictures.

Defining the given dimensions for the geometry

Extruding the geometry to three dimensional geometry.

The resulting geometry for Case 1 is given below :

The resulting geometry for Case 2 is given below :

4) By opening the modelling the tab, we mesh the geometry with element size of 7mm and method of solving used is tetrahedron element type. Generating the mesh thereafter by right clicking on the Mesh icon.

Meshing of Geometry for Case 1 :

Meshing of Geometry for Case 2 :

5) Now, to define the boundary conditions, we specify the faces for the fixed support and load.

Defining fixed support for Case 1 on the left side

Defining fixed support for Case 2 on the left side

Defining force Load for Case 1 on the right side in the positive X direction

Defining force Load for Case 2 on the right side in the positive X direction

6) Selecting the type of solution and solving it for Total deformation and Equivalent stress for results.

Total deformation for Case 1 :

Total deformation for Case 2 :

Equivalent stress for Case 1 :

Equivalent stress for Case 2 :

Results :

Sr.No	Solution	Plate with a hole(Case 1)	Plate with three hole(Case 2)
1.	Total deformation(Maximum)	2.7488e-004 mm	2.9282e-004 mm
2.	Total deformation(Minimum)	0	0
3.	Equivalent stress(Maximum)	0.59395 MPa	0.5733 MPa
4.	Equivalent stress(Minimum)	1.4868e-002 MPa	1.4372e-003 MPa

Conclusion :

1) From the results above, we can conlcude that the plate with a hole has less deformation than the plate with three hole.

2)Stress level in plate with a hole has is higher than the plate with three holes.

3)From analysis point of view, we can say that choosing plate with one hole because if we compare the stresses for both cases its minimal level. We can also choose plate with three holes,which is computationally inexpensive at the cost of result which we produced.

4)From manufacturing point of view, we can choose plate with one hole because it has less number of holes which in turn causes less work for applicaton, thus resulting in saving total production cost.