The bracket shown in the diagram below is assumed to be made from 6061 aluminium:
When a static FEA was carried out this gave a maximum von Mises stress of approximately 350 MPa. in the fillet between the horizontal and vertical leg.
CAE - Optimisation - FEA COSMOSWorks - Notes |
1. Introduction
Initially FEA was used to assess a new or existing design. If the analysis
revealed unacceptably high stresses, then the design had to be changed and the
analysis repeated, sometimes this would need to be done several times and the final
design chosen might still not have been particularly efficient. Modern FEA packages
are able to assist the design process in a much more useful, interactive manner.
Frequently this will involve an optimisation which will seek to produce an efficient
design, typically minimum mass which keeps the maximum stress below a specified level.
2. Procedure
Typically one proposed design will be analysed to investigate the feasibility of
the optimisation, then an optimisation study is set up which will specify the design variable(s)
and the constraints. The software then runs several analysis with suitable variation
of the design variables until it judges that it can estimate the optimum design to
meet the contraints.
3. Example
The bracket shown in the diagram below is assumed to be made from 6061 aluminium:
When a static FEA was carried out this gave a maximum von Mises stress of approximately
350 MPa. in the fillet between the horizontal and vertical leg.
If it is specified that the maximum allowable von Mises stress is 250 MPa, it appears that one way to reduce current maximum value to this would be to increase the radius of the fillet. However an efficient design is required so the minimum mass design is needed, which will be achieved in this case by using only the minimum radius needed.
4. Procedure
After the static FEA has been set up and run (the 'rear' face of the vertical leg
was restrained from translation in all three directions), the Optimisation study was
set up.
Having set up the optimisation, ('Study 2') there should be three icons under
this in the COSMOSWorks tab window on the left of the screen. The 'Objective',
'Design Variables' and 'Constraints' need to be specified. Right click on the
'Objective', click on 'Add', ensure the 'Minimise' button is on and the default
'Mass' is showing in the drop down menu in the Objective Goal box. Click green tick, OK.
Right click on 'Design Variables', click on Add. If the dimensions are not displayed on the model, move the cursor over the picture of the model and double left click which will display the dimensions. Left click once on the R=10 fillet radius, this is then highlighted in red, then pale green. Values of 5 and 15 appear in the Bounds boxes. Change the + one from 15 to 50 and click the green arrow for OK.
Right Click on 'Constraints' then left click on Add. Ensure the Entry in the 'Response' box is 'Static' and 'Study 1', 'Static' should appear below. Ensure 'Nodal Stress and von Mises appear in the two drop down menus at the bottom of this box. In the bottom box 'Bounds', with N/m^2 set in the drop down menu, leave the - entry as 0 and change the + value to 250000000. Click the green arrow for OK.
Run the Study 2. At the end a message Optimisation Succeeded should appear. If a message indicating that optimisation failed appears then the entries must be checked.
The diagram of the part indicates that the fillet radius is much bigger than the
original 10mm. Double left clicking on the model, which displays the dimensions,
shows the fillet radius is 31.78mm.
Expanding and plotting the Design History graph, shows a total of 5 iterations
were carried out.
Expanding and plotting the 'Design Local Trend Graph' shows how the component
design objective (mass) varies with the variation in the design variable (fillet radius).
The mass of the initial (unsatisfactory) model was 0.15178kg and that of the optimised
model was 0.15705kg.
Looking at the results of the updated model shows that the maximum von Mises stress
was actually 255MPa, slightly above the maximum specified, but not significantly.
The initial optimisation involved only varying the fillet radius. After the results from this had been examined, it was deleted and a second optimisation set up with two design variables, allowing variation in fillet radius and in depth of the vertical leg (initially 20mm) of between 10 and 30mm.
The results from this study indicated that the optimum fillet radius was 38.53mm
and the optimum depth of the vertical leg was 10.02mm. This took 11 iterations and gave
a final mass of 0.13824kg, significantly less than that achieved by only changing
the fillet radius.
However it should be noted that the minimum depth of the vertical leg can reduced
to non feasible thickness of 1mm, which will meet the constraint and give an even
lower mass. However sensible judgement about practicality of manufacture and possible
alternative approaches must be kept in mind at all stages.
Increasing the number of design variables causes a rapid increase in the number of iterations required to determine the optimum design, his will greatly lengthen the time for computation. It is generally best to specify only a small number of design variables, perhaps 1 to 5. Experience and understanding are needed to ensure appropriate design variables are selected.
David J Grieve, 26th February 2007.