Week 1 Stress Concentration on a Plate with hole

Aim:

The aim of this report is to make a design choice by making a comparison between the two design case scenarios as explained below:

Case 1: Model a plate with a single hole at the middle and analyse maximum stress and deformation.

Case 2: Model a plate with 3 holes 1 at the centre and 2 equally apart from the centre and analyse maximum stress and deformation.

Problem definition:

The length of the plate is given as 300mm, height 120mm and the thickness is 30mm. The hole at the centre is of 60mm diameter. The case 2 small holes are of 30mm diameter. The left side of the plate is fixed and the right side of the plate is given a load of 500N.

Domain:

The domain of the problem is set using Ansys SpaceClaim. A rectangular plate with the above-given dimensions has been modelled.

Mesh:

In both cases, the mesh used was the tetrahedron and mesh size for body as 7.5mm. The number of elements in case 2 is 19786 whereas in case 1 is 20547.

Model Setup:

Governing Equations: The governing equations the model is solving are:

Differential equations of equilibrium, Stress-Strain relationship and strain-displacement relationship.

Boundary conditions: The boundary conditions are the plate is fixed in all x,y,z directions at the left boundary whereas the right boundary is loaded in the positive x-direction with 500N magnitude force.

Results:

Case1: The results of max stress and max deformation are shown in image 1 and image 2. The maximum stress occurs at the centre of the hole in the longitudinal direction as the plate is under compression, as it is being pulled in the transverse direction. The deformation is expected to be high at the right end of the plate because the load is being applied.

Image 1: Maximum stress

Image2: Total Deformation

Case 2: The results of case 2; maximum stress and total deformation are shown in image 3 and image 4. The stress is distributed over the three holes which lead to the reduction of the maximum stress in case 2. But the deformation at the right end is increased in this case as the strength of the material is decreased with the reduction of material with more holes. The comparison of the results is shown in table 1.

Image 3: Maximum stress

Image4: Total deformation

	Case1	Case2
Total Deformation	0.00027488mm	0.00029717mm
Max principal stress	0.6123MPa	0.59399MPa

Conclusions:

The decision lies in the application of the plate i.e; what is the purpose of the plate. If we want to model a part with less strength and more evenly distributed stresses case 2 is ideal but if we want the model to be more rigid and less costly we would go with case1.