Analysis on a Plate with a Hole

Aim: To design and perform a static analysis on a plate having holes for different cases.

Case 1 - Rectangular plate with a centre hole

Case 2 - Rectangular plate with 3 holes

Input for Simulation:

Input	Value
Material	Alloy Steel
Mesh Size	2 mm
Load	1000N
L x B x H	300x120x30 mm^3
Centre hole	60 mm diameter
Fixed	Small face

GIven: Sketch according to the given drawings and extrude as per the given dimensions.

The models obtained are as follows:

Body of Content

Introduction:

Stress concentration is the increase in stress along the cross-section that may be caused by a point load or by any another discontinuity such as a hole which brings about an abrupt change in the cross-sectional area. It is the ratio of the maximum to the average stress is called a stress concentration factor.

Results

Case 1 - Rectangular plate with centre hole

Mass = 7.66286 kg

Volume = 0.000995177 m^3

Density = 7,700 kg/m^3

Weight = 75.0961 N

Material Properties

Properties	Components
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	Rectangular plate with centre hole
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

Stress Plot

Displacement Plot

Strain Plot

Case 2 - Rectangular plate with 3 holes

Mass = 7.66286 kg

Volume = 0.000952765 m^3

Density = 7,700 kg/m^3

Weight = 71.8957 N

Material Properties

Properties	Components
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	Rectangular plate with three holes
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

Stress Plot

Displacement Plot

Strain Plot

Table for static analysis result

Properties	Rectangular pate with centre hole	Rectangular plate with three holes
Stress	Min - 0.014 MPa Max - 1.212 MPa	Min - 0.001 MPa Max - 1.161 MPa
Displacement	Min - 0 mm Max - 0.000524 mm	Min - 0 mm Max - 0.000567 mm
Strain	Min - 0.0000001236 Max - 0.000004747	Min - 0 Max - 0.000005
Mesh Size	2mm	2mm
Total Nodes	1007280	949026
Total Elements	719822	675004
Load	1000N	1000N
Material	Alloy Steel	Alloy Steel

Conclusion:

1. The Von mises stress generated in the plate having a single hole is greater than in the plate having three holes.
2. The strain and displacement are greater in the plate having three holes as compared to the pate having a single hole but the difference is so small that they may be considered equal.
3. The weight of the plate having three holes is less than the weight of the plate having a single hole.
4. Extra holes help in stress relief factor.
5. The plate having three holes is much more effective to use than the plate having a single hole.