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An Introduction to Finite Element Analysis Software

Introduction

In this laboratory session you will gain practical experience of an important mathematical tool

known as Finite Element Analysis or FEA for short. You will be able to draw a component using CAD

tools, define what it is made of and then see how the component reacts to any applied loads.

FEA is one of the most import software tools that a professional engineer can have at their disposal.

In very simple terms you can draw a component using standard CAD tools, you may even be able to

import your design from your favourite CAD package, however today we will use the simple CAD

drawing tool contained in the FEA package. Once you have drawn your components, you can specify

what each of the regions or sub domains are made of, thus for each region of the component you

define its density, Youngs modulus, thermal conductivity etc. Most software packages allow you to

choose from a range of standard engineering materials. You can then define any loads, thermal or

mechanical that are acting on your component. Since the FEA code is going to solve governing

differential equations for your component and the loads acting on it you will also have to define any

fixed points that do not move or are at a fixed temperature. This is just like defining the boundary

conditions when you solve differential equations in analytical mathematics.

For simple components with regular geometries it is often possible to solve the governing

differential equations using standard analytical mathematical techniques, You will almost certainly

have done or will do this during your mathematics course. However for complex or arbitrarily

shaped components it is not easy or indeed possible to solve the governing differential equations.

This is where FEA comes in.

After you have defined your component and the loads acting on the FEA software will divide the

component into a Finite Number of Finite Elements. In the figure below you can see how the

component has been divided into a large number of small triangular elements, or Finite Elements,

hence the name of the technique. The key point is that while the solution of the governing

differential equation for the component may be hard or impossible, it is usually quite straight

forward to write down solutions, or at least very good approximations of the solution for each

element. All that we need to do is to make sure that the solutions for each element agree with each

other. This comes down to solving a great many simultaneous equations, something computers are

very good at.

To summarise we have drawn the component, we have defined its mechanical properties, we have

divided the component up into a lot of Finite Elements, all we do now is to solve the governing

differential equation (thermal, mechanical, electrical etc. etc.) over each element, and make sure

they all agree. For this last step you just click the solve button and the computer will display the

result, as a temperature, stress or distortion map.

We will now guide you through the use of FEA software by working through a simple cantileverbeam example.

Experiment AP2.5 - Finite Element Analysis

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Here is the simple problem that we will be studying.

A simple square section cantilever 53.5cm long, 5.0cm wide and 4.0mm thick is simply supported at

the left hand end, and a point load applied to the free end as shown above. We want to know how

far the free end of the beam will deflect under the load and the subsequent stress distribution

within the beam.

Follow the steps below.

Double click on the COMSOL 3.3 Icon, Dons use version 4.0 as this has a new user interface and it

will confuse the demonstrators and academic staff!

One the Model Navigator window opens expand the COMSOL Multiphysics option file. You should

now see a Structural Mechanics option, expand this option and so select Plane Stress and Static

Analysis and press OK. You will note that there are a great many options covering virtually every

aspect of engineering, this is what makes FEA so useful.

You should now be presented with the COMSOL user interface.

The first thing we need to do is draw our beam. So select Draw, Specify Object, Rectangle and a box

should appear allowing you to set the dimensions of the beam and its position. Leave the position as

(0,0) and edit the Width and Height. Press Apply and OK the beam should appear and the selection

box should disappear.

Having defined the shape of the beam, we must now specify the physics of the problem. Using the

Physics, Sub Domain Setting menu, highlight Subdomain 1 in the Subdomain selection menu and edit

the material properties.

We now have a physical model of our beam, but must in now include the boundary conditions that

define how we are using the beam. So we must now define any loads or constraints that the beam is

subject to.

Using the Physics, Boundary Settings menu highlight each boundary and set the appropriate

conditions. The top and bottom boundaries are free or unconstrained, the left hand boundary

should be constrained(check Rx and Ry) while the right hand end should have a point load applied inthe negative y direction.

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We have now completely defined our beam and the loads and constraints acting on it. All we need

to do now is solve for the resulting displacement and stress distribution.

To do this we must first divide the beam up into a set of Finite Elements. We do this using the Mesh,

Initialise menu option. You will notice that the Mesh option offers many options, since careful

control of the mesh is important if FEA is to yield reliable results.

You should now see that the beam has been divided up into a number of small triangles. All we need

now do is use the Solve, Solve Problem menu option to solve the problem and display the results.

The results are displayed using the various options in the Postprocessing menu option.

Using the Postprocessing menu option display the distorted shape, does it look correct? How do youknow if it is correct? We in this case since we have a simple beam geometry you can use the beam

deflection formula to calculate the expected deflection. Does it agree with the FEA result? You

should also check what happens to the FEA result if you refine or change the mesk. Any results that

are sensitive to the mesh should be regarded with cautions. What happens to the solution time as

you increase the mesh density?

Now you know how to use the FEA package try and model the complex beam shown below.

There are many FEA packages available, COMSOL, Ansys, Abacus, etc etc, they will all have different

user interfaces and offer special feature for different engineering topics, but they will follow the

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same process flow, draw the structure, define the material, define the loads and

constraints(Boundary conditions) mesh, solve and post process.

I hope you find FEA useful, it is great for helping to understand how something is working, but you

will need to validate the results.

M Ward

September 2010