FEA of plates with holes

AIM: Perform finite element analysis on two plates and compare the results.

OBJECTIVE:

• Model the plates.
• Perform FEA simulation.
• Derive the results.
• Draw the conclusion based on result.

THEORY:

Static FEA is based on the assumption that time does not play important role and its influence on the results can be ignored. In case of solid mechanics simulations, it means that load and response to it are static. In case of fluid mechanics and heat transfer analyses it means that we only get the stationary solution - when there are no more temperature/velocity/pressure differences and no flow (fluid or heat) occurs. So basically, all static analyses search for equilibrium state, be it mechanical, thermodynamics etc.

Stress is the force per unit area on a body that tends to cause it to change shape.

Stress is a measure of the internal forces in a body between its particles. These internal forces are a reaction to the external forces applied on the body that cause it to separate, compress or slide. External forces are either surface forces or body forces. Stress is the average force per unit area that a particle of a body exerts on an adjacent particle, across an imaginary surface that separates them.

The formula for uniaxial normal stress is: σ = F/A

where σ is the stress, F is the force and A is the surface area.

In SI units, force is measured in newtons and area in square metres. This means stress is newtons per square meter, or N/m2. However, stress has its own SI unit, called the pascal. 1 pascal (symbol Pa) is equal to 1 N/m2.

Displacement is the distance moved by a particle or body in a specific direction. It can also be defined as the amount to which a particular point in a body is displayed.

Strain, represented by the Greek letter ε, is a term used to measure the deformation or extension of a body that is subjected to a force or set of forces. The strain of a body is generally defined as the change in length divided by the initial length.

ε = ΔL/L

Factor of Safety is the ratio of a structure's absolute strength (structural capability) to actual applied load; this is a measure of the reliability of a particular design. In engineering, a factor of safety (FoS), also known as safety factor (SF), expresses how much stronger a system is than it needs to be for an intended load. Safety factors are often calculated using detailed analysis because comprehensive testing is impractical on many projects, such as bridges and buildings, but the structure's ability to carry a load must be determined to a reasonable accuracy.

Many systems are intentionally built much stronger than needed for normal usage to allow for emergency situations, unexpected loads, misuse, or degradation (reliability).

PROCEDURE:

Modelling

Model two plates as per the given dimensions

The dimensions for the first case are as follows:

CASE 1

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

The dimensions for the second case are as follows:

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.

Simulation

Following inputs are given for setting up the simulation-

For Plate 1

For Plate 2

RESULT:

For Plate 1,

No. of nodes = 11601

No. of elements = 7163

No. of DOF = 34278

Stress

Displacement

Strain

Factor of Safety

For plate 2,

No. of nodes = 11313

No. of elements = 6855

No. of DOF = 33396

Stress

Displacement

Strain

Factor of Safety

Observation Table

Parameters	Plate with 1 hole	Plate with 3 holes
Maximum Stress [N/mm^2(MPa)]	1.219	1.138
Maximum Displacement [URES (mm)]	5.238e-04	5.658e-04
Maximum Strain [ESTRN]	4.238e-06	4.058e-06
Minimum Factor of Safety	5.090e+02	5.450e+02
Maximum Factor of Safety	1.486e+04	9.617e+04

From above table we observe that the values of stress and strain are more in plate with one hole as compared to plate with three holes. Also, the values of displacement and min/max factor of safety are more in plate with three holes as compared to plate with one hole. The more the factor of safety the better is the option. So, plate with three holes is better choice over the plate with one hole.

This happens due to the fact that stress lines get contracted & concentrated due to single hole while multiple holes tend to uniformly distribute the stress lines over the geometry resulting in less stresses & increased strength.

CONCLUSION:

By comparing all the parameters, it is concluded that the plate with three holes is better option over plate with one-hole i.e. case 2 plate is better than case 1 plate.