Advanced Structural Analysis using Solidworks simulation - Stress concentration on plates with holes

Title:

OBJECTIVE:

The project involves performing a static structural analysis using Solidworks simulation, on two models to find out and compare the deformation and maximum stress in two plates and their behaviour around stress concentration regions like holes.

INTRODUCTION:

The entire process of performing a solidworks simulation can be divided into four parts.

1. Part design

Includes making the part file of the model to be analyzed and material assignment to the components.

2. Setting up of boundary conditions

Includes setting up the fixed supports, reactions and external loads.

3. Meshing

The type, size and various other mesh parameters are setup.

4. Solver Analysis

The solver is run giving out the results for Von mises stresses, strains and displacements at all the nodes and identifying the minimum and maximum values of those to determine the critical regions.

1. MODELS UNDER ANALYSIS (Part Design)

The external block dimensions of both the plates are 300mmx120mmx30mm.

Case 1: Plate with a hole of 60 mm dimeter in the centre as shown in the figure below.

Case 2: Plate with 2 additional holes of diameter 30mm on either side of the main hole at
90mm from the centre

Material properties:

The material of both the plates is chosen to be Alloy steel, the properties of which are given in the below table.

Name:	Alloy Steel
Model type:	Linear Elastic Isotropic
Default failure criterion:	Max von Mises Stress
Yield strength:	6.20422e+08 N/m^2
Tensile strength:	7.23826e+08 N/m^2
Elastic modulus:	2.1e+11 N/m^2
Poisson's ratio:	0.28
Mass density:	7700 kg/m^3
Shear modulus:	7.9e+10 N/m^2
Thermal expansion coefficient:	1.3e-05 /Kelvin

2. BOUNDARY CONDITIONS:

Once the model has been developed, the next step is to establish fixtures and loads on the plates which are responsible for their deformation.

The boundary conditions imposed on the plates are a fixture on one side and a load of 1000N on the other side - 120 X 30 mm surface.

Case 1

Case 2

3. MESHING:

Meshing of the plates is done successfully with the default mesh size and the meshed part is shown below.

CASE 1

MESH INFORMATION:

Mesh type	Solid Mesh
Mesher Used:	Standard mesh
Automatic Transition:	Off
Include Mesh Auto Loops:	Off
Jacobian points	4 Points
Element Size	0.0099862 m
Tolerance	0.00049931 m
Mesh Quality Plot	High

Total Nodes	11535
Total Elements	7121
Maximum Aspect Ratio	2.949
% of elements with Aspect Ratio < 3	100
% of elements with Aspect Ratio > 10	0
% of distorted elements(Jacobian)	0

CASE 2

MESH INFORMATION

Mesh type	Solid Mesh
Mesher Used:	Standard mesh
Automatic Transition:	Off
Include Mesh Auto Loops:	Off
Jacobian points	4 Points
Element Size	0.00984229 m
Tolerance	0.000492114 m
Mesh Quality Plot	High

Total Nodes	11310
Total Elements	6856
Maximum Aspect Ratio	3.6048
% of elements with Aspect Ratio < 3	99.9
% of elements with Aspect Ratio > 10	0
% of distorted elements(Jacobian)	0

RESULTS:

The results of the analysis performed are given in three plots with values at various nodes throughout the body. The maximum values of these indicate the critical node and thus the critical areas in the given model which is more prone to failure.

STRESS PLOT

CASE 1

Name	Type	Min	Max
Stress1	VON: von Mises Stress	4.152e+04 N/m^2 Node: 692	1.187e+06 N/m^2 Node: 29

CASE 2

Name	Type	Min	Max
Stress1	VON: von Mises Stress	1.311e+04 N/m^2 Node: 747	1.134e+06 N/m^2 Node: 9852

STRAIN PLOT

CASE 1

Name	Type	Min	Max
Strain1	ESTRN: Equivalent Strain	2.738e-07 Element: 714	4.223e-06 Element: 3288

CASE 2

Name	Type	Min	Max
Strain1	ESTRN: Equivalent Strain	5.045e-08 Element: 1990	4.043e-06 Element: 4437

DISPLACEMENT PLOT

CASE 1

Name	Type	Min	Max
Displacement1	URES: Resultant Displacement	0.000e+00 mm Node: 99	5.237e-04 mm Node: 433

CASE 2

Name	Type	Min	Max
Displacement1	URES: Resultant Displacement	0.000e+00 mm Node: 176	5.658e-04 mm Node: 10371

CONCLUSIONS:

S.No Quantity Plate with one hole Plate with three holes

1 Max Von mises stresses(N/m^2) 1.187e+06 1.134e+06

2 Max Strain 4.223e-06 4.043e-06

3 Max Displacement (mm) 5.237e-04 5.658e-04

• The plate with a single central hole experiences higher maximum stress than the plate with three holes. This seems counter-intuitive at first since the plate in the second case has a higher number of stress concentration regions and hence expected to experience higher maximum stress. But in reality what is happening is that 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.
• The maximum displacement, on the other hand, is higher in case of a plate with three holes since the extra holes reduce the load-bearing capacity of the plate due to the reduction in the load-bearing material volume. Hence more deformation occurs in the plate with three holes than in the plate with a single hole for the same applied load.
• Strain depends on the amount of displacement of the nodes and also the initial dimensions (ratio of deformation to the initial value of the dimension). Hence, the maximum strain doesn't follow the same trend as displacement due to the difference in the initial geometry of the plates.