OBJECTIVE

• To perform a static analysis on two models of plate with holes.
• To create the model in Solidworks and perform the analysis.
• To Run the analysis and compare the results for stress, strain and displacement.

INTRODUCTION

FEA

Finite Element Analysis or FEA is the simulation of a physical phenomenon using a numerical mathematic technique referred to as the Finite Element Method, or FEM. This process is at the core of mechanical engineering, as well as a variety of other disciplines. It also is one of the key principles used in the development of simulation software. Engineers can use these FEM to reduce the number of physical prototypes and run virtual experiments to optimize their designs.

Complex mathematics is required in order to understand the physical phenomena that occur all around us. These include things like fluid dynamics, wave propagation, and thermal analysis.

Analyzing most of these phenomena can be done using partial differential equations, but in complex situations where multiple highly variable equations are needed, Finite Element Analysis is the leading mathematical technique

Plate with hole

The story of the analysis of stress concentrations begins in 1898 with Ernst Gustav Kirsch's linear elastic solution for stresses around a hole in an infinite plate. Kirsch's solution contains the well-known factor-of-three stress concentration at the hole under uniaxial loading. But there is more to the story. The stress concentration can in fact vary from two to four for more complex loading conditions, i.e., stress states different from uniaxial tension.

We begin by first reviewing Kirsch's solution for the basic case of uniaxial tension, and then use superposition techniques to develop solutions for the more complex cases of equibiaxial tension and shear. This is followed by the solution for general 2-D loading. And the page concludes with stress concentrations in finite width plates.

PROCEDURE

• First we are going to create the 3D model of part and center hole with 60mm diameter and we will select the simulation in Solidworks add-in.
• In simulation select new case study and click on static analysis and then choose the material by right clicking on part and select the alloy steel.
• Then click on fixed geometry and select the small side area and then click on load give the load as 1000N.
• Click on the mesh and create mesh with 5mm fine mesh and then click on mesh with run and wait for the result.
• After that we will get the result of stress, strain and displacement and then we can compare the results.
• And then repeat the same procedure for the second case.

CASE-1: Model-1

A flat plate length is 300mm, height is 120mm and thickness is 30mm with center circle of 60mm diameter

All the dimensions are in mm

Model Information

Model name: Part2 Current Configuration: Default
Solid Bodies
Document Name and Reference	Treated As	Volumetric Properties	Document Path/Date Modified
Boss-Extrude1	Solid Body	Mass:7.66286 kg Volume:0.000995177 m^3 Density:7700 kg/m^3 Weight:75.0961 N	C:\Users\USER\Desktop\COURSES\FEA in Solidworks\analysis of plate with hole\Part2.SLDPRT Jun 27 13:22:32 2020

Material Properties

Model Reference	Properties	Components
	Name: Alloy Steel Model type: Linear Elastic Isotropic Default failure criterion: Max von Mises Stress Yield strength: 6.20422e+008 N/m^2 Tensile strength: 7.23826e+008 N/m^2 Elastic modulus: 2.1e+011 N/m^2 Poisson's ratio: 0.28 Mass density: 7700 kg/m^3 Shear modulus: 7.9e+010 N/m^2 Thermal expansion coefficient: 1.3e-005 /Kelvin	SolidBody 1(Boss-Extrude1)(Part2)

Loads and Fixtures Fixture name Fixture Image Fixture Details Fixed-1 Entities: 1 face(s) Type: Fixed Geometry Load name Load Image Load Details Force-1 Entities: 1 face(s) Type: Apply normal force Value: -1000 N

Mesh information

Mesh type	Solid Mesh
Mesher Used:	Standard mesh
Automatic Transition:	Off
Include Mesh Auto Loops:	Off
Jacobian points	4 Points
Element Size	5 mm
Tolerance	0.25 mm
Mesh Quality Plot	High

Study Results Name Type Min Max Stress1 VON: von Mises Stress 0.020 N/mm^2 (MPa) Node: 51209 1.204 N/mm^2 (MPa) Node: 77652 Part2-Static 1-Stress-Stress1 Name Type Min Max Displacement1 URES: Resultant Displacement 0.00000 mm Node: 264 0.00052 mm Node: 192 Part2-Static 1-Displacement-Displacement1 Name Type Min Max Strain1 ESTRN: Equivalent Strain 2.217e-007 Element: 34864 4.513e-006 Element: 14258 Part2-Static 1-Strain-Strain1

Comparison of stress, strain and displacement

CASE-2: MODEL-2

A flat plate length is 300mm, height is 120mm and thickness is 30mm with center circle of 60mm diameter and two other circles is 30mm diameter apart from the center circle is 90mm

All the dimensions are in mm

Model Information Model name: Part1 Current Configuration: Default Solid Bodies Document Name and Reference Treated As Volumetric Properties Document Path/Date Modified Boss-Extrude1 Solid Body Mass:7.33629 kg Volume:0.000952765 m^3 Density:7700 kg/m^3 Weight:71.8957 N C:\Users\USER\Desktop\COURSES\FEA in Solidworks\analysis of plate with hole\Part1.SLDPRT Jun 27 12:57:58 2020

Mesh information

Mesh type	Solid Mesh
Mesher Used:	Standard mesh
Automatic Transition:	Off
Include Mesh Auto Loops:	Off
Jacobian points	4 Points
Element Size	5 mm
Tolerance	0.25 mm
Mesh Quality Plot	High

Material Properties Model Reference Properties Components Name: Alloy Steel Model type: Linear Elastic Isotropic Default failure criterion: Max von Mises Stress Yield strength: 6.20422e+008 N/m^2 Tensile strength: 7.23826e+008 N/m^2 Elastic modulus: 2.1e+011 N/m^2 Poisson's ratio: 0.28 Mass density: 7700 kg/m^3 Shear modulus: 7.9e+010 N/m^2 Thermal expansion coefficient: 1.3e-005 /Kelvin SolidBody 1(Boss-Extrude1)(Part1)

Loads and Fixtures Fixture name Fixture Image Fixture Details Fixed-1 Entities: 1 face(s) Type: Fixed Geometry Load name Load Image Load Details Force-1 Entities: 1 face(s) Type: Apply normal force Value: -1000 N

Comparison of stress, strain and displacement

CONCLUSION

• In the first case-1 where plate having a hole at the center. The stress concentration across the section is more and maximum stress induced compare to the case-2 and it chances of fail while continuously increasing the load.
• In the second case-2 reduction in the stress concentration because of two extra hole at a distance from the center of the bigger hole.
• The deformation in the case-2 is 0.00057mm which is slightly more than the case-1 i.e. 0.00052mm and also stress is reduced in the second case i.e. 1.159 N/mm^2 and stress in the first case is 1.204 N/mm^2.
• So it’s better to choose the second case (plate with three circles). It gives less stress concentration.

REFFERENCES

• https://www.google.com/search?q=plate+with+hole&tbm=isch&ved=2ahUKEwiv0v3O36HqAhV9BLcAHShaBMAQ2-cCegQIABAA&oq=plate+with+hole&gs_lcp=CgNpbWcQAzIECAAQQzICCAAyAggAMgIIADICCAAyBggAEAcQHjIGCAAQBxAeMgYIABAHEB4yBggAEAcQHjIGCAAQBxAeOgQIIxAnOgYIABAIEB46CAgAEAgQBxAeUIn3AVjaggJgpIYCaABwAHgAgAGkAYgBggiSAQMwLjeYAQCgAQGqAQtnd3Mtd2l6LWltZw&sclient=img&ei=Fxr3Xu_qF_2I3LUPqLSRgAw&bih=625&biw=1366&rlz=1C1CHBF_enIN845IN846&safe=active
• https://interestingengineering.com/what-is-finite-element-analysis-and-how-does-it-work