Dr Andrei Lozzi
Machine Design & CAD
MECH3460
School of Aerospace Mechanical
& Mechatronic Engineering
Finite Element Exercise
Handed out:
11 am Monday 27th July 2015
To be collected: 5 pm, Monday 17th August 2015
This assignment should take an average student 18 hours to complete to achieve a pass, which
requires just the application of principle.
All students are required to submit a signed statement of compliance, with this University’s policy on
plagiarism, with all work submitted for assessment.
Preliminary Tutorials. You may begin by reviewing a selection of FEA tutorials made available
online whenever the SolidWorks Simulation software is installed. They are accessible by selecting
Help\SolidWorks, Simulation, Simulation tutorials. Examine the range of topics covered by the
tutorials to get an overview of what is available, in case you need to apply some of their functions
later. You are then to use Simulation to develop one or more of the designs described here. In this
assignment you can unleash your native ingenuity, but it is best to seek understanding and begin
with a plan. Some changes will make things worse, some better. It is as important for you to
understand what makes things worse as it is for what makes things better. With a little care you will
be able, maybe in a seesaw fashion, to progressively improve your designs.
It may be necessary to ‘add in’ Simulation, if it had not been used in your PC before. After SW is
running, start a new part, from the top menu then select - Tools, add in, then Simulation. More
advanced tutorials and user manuals of SW and SWS in pdf format, may be copied from
www.aeromech.usyd.edu/units-of-study.php, then select MECH3460, course documents..
The Assignment
Problems. The files of the SW models referred to in these problems, shown on figure 1 to 5, are
also included in the above folder. You may assume that these models are adequately functional but
they need to have their stress distribution improved and for some their deflection reduced. You are
to select two or more of these and develop their detail designs along the lines prescribed.
What to submit. You are to submit a written report (ie on paper not by email) that shows and
describes how you progressed, from beginning to end, comparing design changes with
improvements or otherwise. Use objective aspects such as deflection, stress, mass, complexity or
other indicators that may be relevant. You really must try one geometric change at the time, if you
do not you will not know for sure what change has caused what effect. Keep your SW and SWS
files and studies in the event that we ask you to provide them to us, for examination.
1
For each of the problems that you tackle your report must begin with a summary of your preferred
design. You must make clear what you have learned from your analysis and what is your best
design, do not leave that to the reader or worse still you marker, they may get it wrong.
Materials. All parts may be assumed to be made from steel or aluminium alloy. SW files for all
the parts provided for analysis are contained in the folder made available to you.
Some General advice
Cross-sections The shape and cross-sections of a part should reflect the sort of loads transmitted
through it. For example, where the bending moment is high, one can reduce the normal stresses on
the surfaces, by increasing the second moment of area (I) of the section. In a welded part, it is
practical to increase I by adding webs. If torque is being transmitted then a high polar moment of
area is appropriate, that is a tubular cross section. Where compressive forces are the problem,
leading possibly to buckling, tubular cross section is also most effective. Tensile forces may be
dealt with just by simply increasing the cross sectional area, provided he stress is fairly uniform.
Improvements in a design may be said to have taken place if the under-stressed and over-stressed
areas are reduced. For some, an ideal design is one where a part is completely uniformly stressed,
that is, where the safety margin against failure is the same everywhere. We may strive for this
condition, but we may never quite achieve it in practice, except possibly in the simplest of cases.
The critical point to notice is that FEA does not reveal what is creating the stresses, and what are
appropriate ways to control them, you have to arrive at those conclusions yourself.
A good design is also relatively stiff, that is it undergoes a relatively small amount of deflection
under load. Deflection often gets neglected, partly because it has less dramatic consequences if it
becomes excessive, causing just malfunction rather than catastrophic failure and partly because
without FEA, deflection calculations carried out by hand are messier and have been used less often
than their stress counterpart. You may therefore be surprised by the magnitude of the deflections
and distortions that occurs in mechanical components, and the ingenuity that is required just to
keep it within acceptable limits.
Stress concentration There is a simple rule to follow to obtain improved uniformity of stress in a
component, add material where the stress is high and take it away where the stress is low! It is
really quite simple to say, but we quickly come up against the limits of our imagination at changing
and inventing new shapes.
Learn from others but do not copy them. Education and real world practice in design includes
examining other people’s work, understanding their ideas and how they executed them, so that you
may apply them and at best, improve on them. While working in industry, you must be careful not
to actually copy competitors’ designs, as opposed to just learn from them, or you may end up in
court. For this class you can and should discuss and develop ideas with others, but submit your own
unique designs. Also, please note that there is no perfect design; you can spend your life chasing
just some ideal, only to have someone point out its faults. Hence my advice is not to spend too long
on any one problem, move on to others, then return to the troublesome ones with fresh ideas.
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1. The stepped cylindrical bar shown on Fig 1 is transmit only torsion from one end face to the
other. The concave corners cause stress concentration at the steps in the shaft. Investigate means to
reduce that effect, by for example adding fillets, cutting grooves and or chamfers. Compare your
observations of surface stress concentration ratios with those tabulated at the back of many Design
and Properties of Solids references. Assuming that the stress concentration factor given in reputable
references to be exact, you can arrive at an estimate of the accuracy obtainable by this FEA
package. You should also try different methods in setting up the FEA analysis, to observe how
closely these methods converge to an answer, hence the precision available by using different
parameters within the package.
2. The Rocker arm or balance lever on Fig 2 has an initial shape of a rectangular prism. A
perpendicular force is applied at the central rectangular pad while equal reactions are taken at the two
circular pads on the opposite sides. Sculpture this rectangular prism into an elegant shape, which
reflects the type of loads being transmitted through it, achieving reasonably even stress distribution.
You must not alter the size and location of the circular pads, while the rectangular may have its 30
mm width reduced, but not its 13 mm length.
3. Examine the connections between vertical columns and horizontal base plates that are installed
on the NSW railways, as seen from trains and at stations (as well as many other industrial and
civilian sites). Consider the square hollow section welded to the circular base plate shown on Fig
3. You are to reduce the deflection, stress and stress concentration by modifying how this section is
connected to the base plate. You may alter the size and shape of the base plate, add webs, fillets
and possibly other features, together with a number of carefully located hold-down holes. No fillet,
web or other added component is to be higher than 150 mm above the base plate. To apply a load to
this weldment, you may fix the bolt holes, attach a thick plate to the top of the column, and apply
two horizontal 10 kN forces to that plate, parallel to the base plate and perpendicular to each other.
4. The 200 mm high, 400 mm long and 200 mm wide L bracket shown on Fig 4 has to be
stiffened and reinforced to carry a vertical force at each of the outer holes of each of 1000 N
downward, and a force of 1000 N laterally at the single inner hole. You may presume that the
vertical leg of this bracket may be attached at any location you chose to the wall behind it, by using
any number of bolts. You are required to modify the shape of this bracket, such that with the loads
indicated its deflection is reduced by a factor of 30. In order to make the modified bracket
relatively practical to manufacture, you are initially advised to make the modifications using steel
plate of the same thickness as the unmodified bracket. You may add webs, welds, bosses, lighting
holes, in your quest to achieve lightness and rigidity. The bracket is made from low carbon steel,
Report on the highest von Mises stress that your designs archives and compare it to the stress in the
unmodified bracket.
5. This is an invitation to determining the most efficient cross-section and profile of a column in
compression. Figure 5 shows two columns, one a cylinder the other barrel. You are to test these
columns with axial compressive loads; to determine which one is more resistant to buckling. In
order to compare apples to apples some critical aspects of the tube and barrel have to be kept
constant, eg average diameter, total mass, second moment of section, or other. You may like to
investigate the more general circumstances in which a one would be preferable to the other, when
subjected to some combination of loads.
3
1.
Dumb bell
2. Rocker arm - balance lever
3. Square post & base
4. Columns in compression
3. L bracket, 200 long 100 wide
4