Analysis on a Plate with hole using Finite Element Analysis

AIM

To perform a Static Analysis on two models of plate with holes.

OBJECTIVES

• To create the models of the plates with the given dimensions in SolidWorks.
• To simulate the Finite Element Analysis for the two plates using given conditions.
• To compare the results of Stress,Displacement and Strain for all the three cases

INTRODUCTION

Finite element analysis (FEA) is the process of simulating the behaviour of a part or assembly under given conditions so that it can be assessed using the finite element method (FEM).

The simulations used in FEA are created using a mesh of millions of smaller elements that combine to create the shape of the structure that is being assessed. Each of these small elements is subjected to calculations, with these mesh refinements combining to produce the final result of the whole structure.These approximate calculations are usually polynomial, with interpolations occurring across the small elements, meaning that values can be determined at some but not all points. The points where the values can be determined are called nodal points and can usually be found at the boundary of the element.

A machine component is bound to have irregularities like a hole in its geometry for various design reasons. These irregularities can contribute immensely to the strength of the part. Configuring the structures with discontinuities is one of the most important topics in the construction of ships, aero-planes, cars etc. Examples of problems in which discontinuities play prominent role in the physical behavior of a system are numerous.So, the Finite Element Analysis of such geometry gives insight into Stress patterns due the presence of this irregularities i.e. holes.

THEORY

Almost all metallic structures consist of assembly of simple elements, which are connected to each other by connecting plates using bolts or rivets. These plates have hole to place the bolts or rivets; these make the structure weak and susceptible to the failure. Therefore, it is necessary to investigate the state of stress in the plate around the hole. It is very important to understand the behavior of the steel structure with holes or notches. The stress analysis of plate is done by using finite element method. Auxiliary holes are provided for stress relief. Around 35% of reduction in stress concentration in plate is observed by introducing auxiliary hole of optimum shape at optimum distance. Because of these auxiliary holes the flow of the tensile stresses will get smooth and it results in a increased life of that plate.

GIVEN DATA

The dimensions for the plates are as follows:

CASE 1

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

CASE 2

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

Two holes of 30 mm diameter which are placed 90mm away from the central hole on both sides.

Boundary conditions

Short side(120mm x 30mm) of the plate-Fixed

Force at the opposite side = 1000N(Tensile)

CASE SETUP

1. First, the 3D models of both the plates are made using the dimensions provided.
2. Then a new study was created after enabling SOLIDWORKS Simulation from SOLIDWORKS Add-ins.
3. Then for each of these, the simulation is carried out in the following way.
4. The material is defined as the default ‘Alloy Steel’.
5. Then using the Fixtures option, one face(120mm x 30mm) of the plate is fixed.
6. Then ,the Force at the opposite face is defined as 1500 N(Tensile) under the External Loads option.
7. Then the mesh is created with a Mesh size of 6mm.
8. Then, finally the simulation is run and the results are obtained.

Plates with the Mesh,Fixtures and Load applied

Case-1

Case-2

RESULTS & OBSERVATION

Comparison of-

• Stress contours

Here, the Maximum induced Stress follows the order-

Case-1(0.591 MPa) > Case-2(0.573 MPa)

And the Yield Strength for the material is 620.422 MPa

• Displacement/Deformation contours

Here, the Maximum Displacement follows the order-

Case-2(0.0002826038 mm) > Case-1(0.0002612438 mm)

• Strain contours

Here, the Maximum Strain follows the order-

Case-1(0.0000021613) > Case-2(0.0000021268)

EXPLANATION

• The results show that the Stress and Strain induced in the plates with 3 holes(Case-2) is less.
• And the Displacement in the plate with 3 holes(Case-2) is greater than the plate with one hole(Case-1) by a value of(0.00002136 mm) This shows that increase in number of holes reduces stress concentration.

CONCLUSION

Therefore, on the basis of Static Analysis,it can be concluded that providing holes reduces stress induced in the member.