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 likely hood 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.

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.

Sketching and Modeling

CASE 1

Defining the given dimensions for the geometry

Sketching- 300*120 rectangle with hole at centre

CASE2

After Pulling(Extrude) - 30mm

CASE 1

CASE 2

Material

Defined the default material Strctural Steel . Material is same for both cases

Meshing

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.

same size of meshing is used in both cases

Loading Condtions ( Static Structural)

1. Left side is fixed

2. Force applied to right side 

same size of loading is used in both cases

Results

Von Mises Stress in MPa ( Case 1) - With one Hole at centre

Von Mises Stress in MPa ( Case 2) - With three Hole at centre

Total Deformation in mm ( Case 1) - With one Hole at centre

Total Deformation in mm ( Case 1) - With three  Hole at centre

Result Discussion

Deformation Comaparision

By comparing both cases the total deformation is slightly higher in case-2, due to the number of holes in case-2. The more
no. of holes, deformation will be more.

Stress Comparison

By comparing both cases the stress is slightly higher in case-2, due to the number of holes in case-2. The more no. of holes,
stress will be more.

Selection of design as per manufacturing point of view.- ( Case-1 is better)
From the manufacturing point of view, case-1 with a single hole will be better for design because it has a single hole, which
means it takes less time as well as investment to come to the final product.

Selection of design as per analysis point of view. - (case-2 is better)
From an analysis point of view, case-2 is better because it has 3 holes to distribute the stress so we the stress can be
distributed to all the component equally and component has less chance to fail.

 Conclusion :

From the analysis of both the cases, we have successfully investigated the von-misses stress and deformation with some
boundary conditions. We can clearly see that case-1 is better from the manufacturing point of view and case-2 is good from
the stress distribution point of view. All the boundary condition has been applied and simulation has run successfully
without any error. Both two cases have been compared as per the given instruction.

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.