## Analysis Of Stress Concentration On Plate With Hole

# Analysis Of Stress Concentration On  Plate With Hole

ABSTRACT

This project is carried out to identify the maximum deformation and stress developed in the plate with a hole geometry and to perform comparative study between two models, case-1 Plate with Single hole Case-2 plate with multiple Holes both made up of Structural steel material. The models are subjected to loading condition of 500N. Ansys- Static Structural workbench is employed to do the simulation. Two mechanical responses Deformation & Stress are considered in Solution. The results show the localization of high stress in vicinity of discontinuity i.e. Hole Geometry. And model with multiple Hole developed comparatively lesser Stress and higher deformation than model with single hole geometry.

INTRODUCTION

Stress Concentration

Stress concentration is the localization of high stresses in the vicinity of discontinuity present in the component.Because of the presence of irregularites and abrupt changes in the sectional areas stress rises in the areas adjacent or close to it, and this phenomenon is refered as concentration of stress.

These discontinuities and abrupt changes are unavoidable, due to certain features of the component like shoulders, screw thread, holes for oil and lubrication passage, holes for handling, grooves, keyways and splines etc. Therefore it become imperative to study the phenomenon of Stress concentration and include in the component design & analysis.

EXAMPLE: Stress rises in vicinity of discontinuity (here hole)

From theory of elasticity, stress distribution in this case is given by,

sigma_r = sigma_o /2(2 + d^2/(4*r^2) +3/16*d^4/r^4)

where d is the diameter of hole & r is the distance from the center of hole

Causes of Stress Concentration

- Variation in properties of materials within the component (Non-Homogeneous Properties)

- Discontinuity & abrupt changes in section

-machining scratches etc.

Stress Concentration Factor (theoretical) is defined as a dimensionless number, which is the ratio of maximum stress developed to the reference stress or nominal stress obtained by elementary equations for minimum cross-section. Its magnitude signify the extent of stress concentration in the component and depends on the geometry of the component. Its value is determined by two methods the mathematical model based on theory of elasticity and experimental methods like photo-elasticity.

Stress concentrations are, in general, of more concern in brittle materials than in ductile materials. Ductile materials are able to yield locally, which redistributes the stress more evenly across the cross section. On the other hand, brittle materials, which cannot yield, are susceptible to abrupt failure caused by stress concentrations.

OBJECTIVE

The objective of this project is to carry of Static Structural analysis on a Plate with Hole geometry using Ansys Workbench

Case 1: Plate with a hole (increased thickness).

Case 2: Plate with multiple holes.

And determine the maximum deformation and stress developed in the models.

THEORETICAL ANALYSIS

Using Data from Stress concentration factor Charts, For Rectangular Plate with Transverse Hole in Tension or Compression

For the given problem Maximum Stress in the component is turned out to be equal to 0.5922MPA (tension) because of Stress Concentration.

COMPUTATIONAL ANALYSIS

Step 1. Material Selection - Structural Steel for both the cases (as specified)

Default Structural Properties of Structural Steel

Step 2. Creating Geometry - With the help of Space-Claim CAD modelling Software  Geometry is created as specified in the problem

Case-1. Plate With Single Hole Geometry

Plate dimensions:

Length=300mm
Height=120mm
Thickness=30mm
Circular Hole at the center:
Diameter=60mm

* Global Co-ordinate Sytem is located at the center of the geometry as shown in the above figure

Case 2. Plate With Multiple Holes

Plate dimensions:

Length=300mm
Height=120mm
Thickness=30mm
Circular Hole at the center: Diameter=60mm

smaller holes 90mm away from the center: Diameter=30mm

* Global Co-ordinate Sytem is located at the center of the geometry as shown in the above figure

Step 3. Mesh Generation

Case 1. Plate With Single Hole Geometry

Features

• Element Type - tetrahedrons
• Algorithm - Patch Conforming method
• Element Size - 5mm
• Element Order - Program Controlled
• Statistics : Nodes - 11885       Elements - 6414
• Avg. Element Quality ~ 0.73

Case 2. Plate with Multiple Holes

Features

• Element Type - tetrahedrons
• Algorithm - Patch Conforming method
• Element Size - 5mm
• Element Order - Program Controlled
• Statistics : Nodes - 13462       Elements - 7291
• Avg. Element Quality ~ 0.72

Step 4. Setup or Applying Boundary Conditions - As given in the question component is acted by a 500N Axial force on one side (i.e. right side) and has fixed support on the other side (i.e. left side).

Case 1

Case 2

Step 5. Solution Generation

In Solution generation, 2 mechanical resposes are considered

1. Deformation - Directional (i.e. along the loading direction) & Total deformation

2. Stress - Normal Stress and Equivalent Stress

Case 1

Directional Deformation                                              Total Deformation

Normal Stress                                                 Equivalent Stress

Case 2

Directional Deformation                                     Total Deformation

Normal Stress                                                Equivalent Stress

COMPARISON OF RESULTS

 Model Directional Deformation(mm)           Max. Total Deformation(mm)           Max. Normal Stress(MPA)  Max. Equivalent Stress (MPA)          Max. Plate with Single Hole 2.7477e-004 2.7479e-004 0.62635 0.6159 Plate with Multiple Holes 2.9697e-004 2.9701e-004 0.59889 0.58248

From the Results, it is clear that Deformation is comparativly more in case of Plate having multiple holes than Plate with single hole. While Stress developed is more in case of Plate with single hole geometry than the Plate with multiple holes.

Discussion

From Analysis Standpoint, design with multiple holes in plate must be considered. Since, basic motive of the analysis is to study the effect of all essential features when the component is placed in the actual environment conditions. Therefore design must have all essential features included in it so that its effect on design can be studied.

From Manufacturing Standpoint, design must be simpler and easy to build therefore Design with lesser complexity i.e Plate with Single Hole should be selected. Since manufacturing is basically the conversion of raw material into useful components, so depending upon the availability of tools & machines, time, and skilled labors an optimal design must be selected. In above case manufacturing multiple holes in a plate is comparatively complex than manufacturing single hole.

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