I started with a problem I created for a final exam because I found it both very interesting and very comprehensive in requiring most of the skills I expect the students to learn over a large portion of the course.  I realized later that it could be introduced on the first day of class to show how the skills from this class could be used to solve problems that were entirely out of reach using the hand calculation methods of the prerequisite courses.  The "solution" found on day 1 will not be a very good one, but it establishes a much more active learning environment than just presenting theory for weeks before attempting a problem of this sort on an exam.

Each subsequent class period offers an opportunity to revisit the analysis with new skills that are learned (mesh type, mesh refinement, solution convergence, simplification using symmetry, 2D simplification, boundary conditions, single part vs. assembly analysis, fatigue analysis).  Groups can then debate on if or how to apply the skill learned in that particular class period to improve the analysis on the original problem.  One member of one group is randomly selected to present in a short, informal design review to the class.   The entire class then performs a reflection activity to compare their group's analysis to the group in the design review as well as how their group functioned during the activity.

List of lectures and the methods/techniques introduced before working on this activity:

1. Problem introduction/demo
2. Mesh refinement (decreasing size of h-element until solution converges)
3. Mesh refinement in only critical areas, differing types of 3D meshing styles
4. Placing sensors to record outputs at specific spots, h-adaptive and p-adaptive solutions
5. 2D simplification (plane strain, plain stress), planar symmetry simplification
6. Nonlinear analysis (geometric nonlinearity, material model nonlinearity)
7. Assemblies and idealized connectors (bolts with material and tightening properties)

At the end of the module, each group posts a video they create as a final review of the design of the part to the class site on our learning management system.  They are also required to post substantive comments about 2 of the other groups' submissions.

I have utilized 3D printed versions of the part analyzed in class.  I will post the file here.

I have also used water jet-/laser-cut aluminum and steel versions of the part geometry (thinner than real life for manufacturability reason).  I will post the geometry for that here, as well.  SendCuSend.com was used as a vendor.  The thickest steel they could produce with this geometry was .059", and the thickest aluminum was .080".  For reference, the actual part is 6 mm thick (.236").  Parts were roughly $2/each when purchased at a quantity of 10.

I was looking for an interesting problem to put on a final exam 2 years ago when I came across a video on YouTube that showed an interesting engineering design being used on the James Webb Space Telescope ( https://youtu.be/5MxH1sfJLBQ?si=gc4jaD3vAXSb22Qm ). At 5:25 in the video, it shows an FEA simulation of the part that is very much like what I expect my students to be able to do in the class.  I also thought the problem would interest my students as a real life example, and I think the video's ~500,000 view in 2 years shows that to be the case (though it is less than the popular Smarter Every Day channel's JWST episode, which was released at a similar date and has >3.5 million views: https://youtu.be/4P8fKd0IVOs?si=0MMoP4bsO0HrrqBI ).

The following semester, I decided to start the first class of the year by having groups of students work through the problem.  The first objective was to have a first lecture experience that was not a boring reading of a syllabus followed by a firehose of finite element theory, especially since I teach in a mechanical engineering technology program, and most of my students don't have meaningful (if any) linear algebra coursework.

The second objective was to create an active, collaborative learning environment in my class that incorporates KEEN's 3 Cs in order to improve attendance, engagement, and student performance.  My class meets twice a week for 110-minute sessions, so having each class period contain several modules of content helps from boring the students.  I use this project as one of those modules, along with traditional lecture, presenting the results from the previous class's homework and covering the muddiest points, etc.

I introduce the problem by showing some of the YouTube video. I then say we are faced with a problem--the James Webb Space Telescope has now been launched and is fully operational, but the demand for scientific experiments using its instruments far outpaces the supply of time the JWST has in its operational lifetime.  Seeing that the JWST ran 15 years and $10 billion over budget, I propose to build a Jeff Kinkaid Space Telescope (that's my name) by reverse-engineering the JWST and building it for much less than $10 billion.  If successful, it will provide greatly increased scientific knowledge to the world, and great profits for the Jeff Kinkaid Space Telescope Design Corporation (of which they are employees).  I say the first step is to reverse engineer the flexure featured in the YouTube video.  As this is an analysis class and not a design class, I am providing them with the part file to analyze--I downloaded files from the YouTube video's creator, printed out images of the part at true scale, then measured all the dimensions as best I could to reverse-engineer the part and create my own geometry completely from scratch.  The problem I state to them is that I don't know if my geometry will perform exactly the same as the one in the video (and on the JWST).  I need to determine how far the output surface will move when the input surface is moved--I hope to move the input 1 mm and see the output move 10 µm.  If that movement causes stress to exceed yield strength in the part (and I know it will), I want them to find out how far we could move the input while keeping stress below yield, and how far the output moves in that case.  Later in the course, we'll look at how far we can move the input while expecting the part to last not just one cycle, but infinite cycles (as the JWST sits too far away from Earth for astronauts to repair it).

I then randomly generate groups of students and assign those students to find one another to work on an activity and let them know they'll be working in these groups for the rest of the semester. I have them start with an icebreaker, then work on an activity where I ask them how they would try to solve for displacement and stress in the flexure by hand, using techniques from prerequisite classes.  I know that it's well beyond what they can do, but some do come up with ideas from mechanisms (treating the flexing spots as pins) to solve for displacement and statics (treating sections between flexing spots as cantilevered beams) for stress. I randomly call on specific students to share with the broader class the ideas their group has formulated.  I want them to get used to sharing results with the class, so I remind them I will be doing this consistently throughout the semester.  But I want the stakes to be low and the rewards to be high to reduce their anxiety, so I also let them know that any time they are chosen randomly to present throughout the semester (and they are in attendance and present their results) they will receive extra credit points.

I hope at this point they are in the zone of proximal development--they see why the problem needs to be solved, but can't perform the analysis without being shown how.  I then close out the first class period by walking them through the simplest path to a finite element analysis solution--boot up the software, load the part file, assign a material, assign fixtures to the feet, assign a simple displacement to the input surface, create a default mesh, and run the simulation.  I have them all record the results of their simulation and submit them to me, knowing I'll hand them back the next class period when we'll refine our understanding of simulation techniques and hopefully revise our best solution for the problem to a more realistic one.

For subsequent class meetings where we revisit this analysis, I give a handout for them to take notes and assign each group to re-analyze the part using (or not using, if they don't feel it's applicable) the new techniques we've covered in the lecture, text, and traditional homework since the last look at the project.  After roughly 30 minutes, I select one random individual to present their group's finidings.  I then assign a reflection activity (in the form of a quiz on our learning management software) to everyone in the class and allow 5-10 minutes for everyone to complete it.

I use this process for many topics for static analysis, but when we get to analyzing for fatigue, I make that final step the 'final project.'  Here, each group works together to record a presentation showing their analysis choices and results to show the results of three studies: 1) given an input of 1 mm, how far does the output surface move, and what stress is predicted? 2) how much of an input can be used to keep the part from yielding (stress below yield strength) and how much output movement does that create? 3) How much input movement can be used to keep the part from ever breaking under repeated movement (stress below adjusted fatigue strength) and how much output movement does that produce?

For the final project, each group must post their final video to the class learning management system.  Each individual is also assigned to review the presentation from 2 randomly assigned groups and post substantive comments on what that group did differently, what they did well, and where they think that group could improve.