Structural Analysis of Stress Concentration

INTRODUCTION:

The elements, which are used for machining purposes offered with geometrical irregularities, which disturb the stress distribution, and therefore, the state of stress in stress concentrated regions cannot be described in machine elements. Thus, the finite element method (FEM) is an important tool used to analyze the stress. The finite element method (FEM) is a numerical method of analysis for stresses and deformations in structures of any given geometry. The structure is discretized into the so-called ‘finite elements’ connected through nodes. And later after discretization, the nodal displacements are obtained by inversion of the stiffness matrix in [F]=[K].[x]. After finding the nodal displacements we can find stress and strains at any point.

Does stress act differently on a structure depending on how many cuts or holes are present in it? Does a structure’s deformation depend on the number of cuts or holes present in it? To find out the answers, we will be designing two similar plates in this project, with similar dimensions and material, and then simulate them in SOLIDWORKS SIMULATION. The only difference being that one of the plates will have more number of holes than the other. From the results obtained, we will be able to compare how the varying number of holes in an element can affect its stress-bearing ability.

OBJECTIVE:

1) To do a baseline simulation to perform a Grid dependency test and select the mesh for further simulation.

2) To perform static structural analysis on two plates of the same dimensions but with different number of holes and analyze the stress, deformation, etc. acting on the plates.

3) To Create Animations for Various Stress, Deformation, and Strain contours.

PROCEDURE:

The Entire Process of FEA analysis is divided into 3 parts

1) Pre-Processing

Geometry Creation

Generation of Mesh

Assignment of Material properties

Boundary Conditions

2) Processing

Governing Equations are applied to the discretized elements and displacements will be calculated.

[F]=[K]*[X]

F=Loads

K= indicates geometric and material properties

X=Displacement

Run the simulation

3) Post-Processing

After the calculation of the displacements across the nodes the Stress and Strains can be calculated at any point.

Create the required Contours and Plots

Interpret the Results

Modify the geometry to get the optimized results.

PRE-PROCESSING:

GEOMETRY AND MATERIAL PROPERTIES:

Both Cases are assigned with Alloy steel

Properties: Alloy-Steel

CASE 1: PLATE WITH SINGLE CENTRAL HOLE

CASE 2: PLATE WITH 3 HOLES

BOUNDARY CONDITIONS:

Here short side is fixed from one end and from other end Force of 1000N is applied at other end such that the plate is stretched.

CASE 1: PLATE WITH SINGLE CENTRAL HOLE

CASE 2: PLATE WITH 3 HOLES

GRID DEPENDENCY TEST:

After performing a baseline simulation, we will be performing Grid dependency test to select the mesh for further simulation.

CASE 1: PLATE WITH SINGLE CENTRAL HOLE

Here the global mesh is selected as an input variable with size varying from 2mm to 15mm of grid size with an increment of 1mm

Stress is selected as a constraint.

Results of the grid dependency test:

As we can see that as the mesh gets refined the amount of stress values changes and we will be using the 5mm grid size for further analysis of CASE 1 as it is best in terms of results and the computational time required will also be less.

CASE 2: PLATE WITH 3 HOLES

Here the global mesh is selected as an input variable with size varying from 2mm to 15mm of grid size with an increment of 1mm

Stress is selected as a constraint.

Results of the grid dependency test:

As we can see that as the mesh gets refined the amount of stress values changes and we will be using the 5mm grid size for further analysis of CASE 2 as it is best in terms of results and the computational time required will also be less.

MESH:

CASE 1: PLATE WITH SINGLE CENTRAL HOLE

CASE 2: PLATE WITH 3 HOLES

PROCESSING:

HIT RUN

Governing Equations are applied to the discretized elements and displacements will be calculated.

[F]=[K]*[X]

F=Loads

K= indicates geometric and material properties

X=Displacement

POST-PROCESSING:

RESULTS AND CONTOURS:

CASE 1: PLATE WITH SINGLE CENTRAL HOLE

STRESS CONTOUR:

Maximum Stress= 1.199MPa

Minimum Stress= 0.021MPa

ANIMATION:

DEFORMATION CONTOUR:

Maximum Deformation= 5.241E-4mm

Minimum Deformation= 1E-30mm

ANIMATION:

STRAIN CONTOUR:

Maximum Strain = 4.558E-6

Minimum Strain= 2.260E-7

ANIMATION:

CASE 2: PLATE WITH 3 HOLES

STRESS CONTOUR:

Maximum Stress= 1.137MPa

Minimum Stress= 0.005MPa

ANIMATION:

DEFORMATION CONTOUR:

Maximum Deformation= 5.604E-4mm

Minimum Deformation= 1E-30mm

ANIMATION:

STRAIN CONTOUR:

Maximum Strain = 4.253E-6

Minimum Strain= 1.398E-8

ANIMATION:

CONCLUSION:

From the above results, the following conclusions can be inferred

Comparison of Maximum Deformation, Stress, and Strains.

1. When the Maximum deformation is compared for both the cases, case 1 has a slightly lesser value of 5.241E-4mm than case 2 value of 5.604E-4mm, the difference is in the range of 3.63e-5mm. Hence, we can conclude the deformation behavior is almost comparable for both the cases.
2. While comparing the stresses, the Maximum Stress for case 1 was higher of value 1.199MPa than case 2 having a value of 1.137. The difference in the Maximum values is in the range of 0.062 MPa.
3. Similar to Stresses, while comparing the Strains, the maximum Strain for case 1 was of higher value 4.558E-6 than case 2 having a value of 4.253E-6. The difference in the Maximum values is in the range of 3.28E-7.
4. From the above analysis, it can be seen that the Stresses developed in case 2 is lower than that developed in case 1, the additional two holes in the second case, due to their geometrical positioning, are acting as stress relief features reducing the effect of stress concentration at the central hole. This is the reason for the lesser value of maximum Von mises stresses in case of the plate with three holes which means the chance of failure is higher in case 1. Hence from an analysis point of view, case 2 is more preferable than case 1.
5. But the same may not hold true from a manufacturing point of view. The geometry of case 2 has more features(holes) than case 1. It involves more amount of machining (drilling of holes) and manhours to fabricate it, which means higher costs will be incurred. This cost may not be justiciable considering that there is not much difference in the stress and deformation values between both cases. So, it can be concluded that case 1 is better from the manufacturing