ME elective: Finite Element Analysis

Proof required

Link the public repo with 2.092 homework 1–3 (skip any exercise that cites Bathe's book Finite Element Procedures, which is not free) written up (a typeset PDF, LaTeX source or notebook), and show the self-check: which answers matched and how you fixed the ones that did not.

What gets checked

• Element stiffness matrices are derived, not copied, and assembled with stated boundary conditions.
• Each solution checks equilibrium of the reactions.
• Answers match the published solutions, and misses are reworked.

Common mistakes

• Answers copied from a solution with no working.
• Missing units, or a free-body diagram or sign convention left out.

Powstik Guide

A public write-up of 2.092 homework 1–3 (skip any exercise that cites Bathe's book Finite Element Procedures, which is not free), with the self-check shown.

Steps

1. Study the linked course material.
2. Solve the problems on your own first.
3. Check them against the self-check and rework the misses.
4. Typeset the write-up (LaTeX or a notebook) in a public repo.
5. Ask someone who knows the subject to check it.

README
ME 13: Finite Element Analysis, unit 1: Virtual work and the displacement method
Problems:
Self-check result (matched / reworked):
What I got wrong first and why:

What gets sent back

• No working shown.
• The self-check result is missing.

Resources

What a verifier looks for

• Element stiffness matrices are derived, not copied, and assembled with stated boundary conditions.
• Each solution checks equilibrium of the reactions.
• Answers match the published solutions, and misses are reworked.
• Is the engineering right, not just the final number?

You'll sign in first, then come straight back here.

Proof required

Link the public repo with 2.092 homework 5 (do any ADINA part in CalculiX or FreeCAD FEM; skip exercises that cite Bathe's book), then exam 1; homework 4 and 6 are optional practice in CalculiX (no published solutions) written up (a typeset PDF, LaTeX source or notebook), and show the self-check: which answers matched and how you fixed the ones that did not.

What gets checked

• Integration order is chosen and justified for each element.
• Convergence is shown with at least three meshes.
• Answers match the published solutions, and exam 1 is marked against its solution.

Common mistakes

• Answers copied from a solution with no working.
• Missing units, or a free-body diagram or sign convention left out.

Powstik Guide

A public write-up of 2.092 homework 5 (do any ADINA part in CalculiX or FreeCAD FEM; skip exercises that cite Bathe's book), then exam 1; homework 4 and 6 are optional practice in CalculiX (no published solutions), with the self-check shown.

Steps

1. Study the linked course material.
2. Solve the problems on your own first.
3. Check them against the self-check and rework the misses.
4. Typeset the write-up (LaTeX or a notebook) in a public repo.
5. Ask someone who knows the subject to check it.

README
ME 13: Finite Element Analysis, unit 2: Isoparametric elements, numerical integration and convergence
Problems:
Self-check result (matched / reworked):
What I got wrong first and why:

What gets sent back

• No working shown.
• The self-check result is missing.

Resources

What a verifier looks for

• Integration order is chosen and justified for each element.
• Convergence is shown with at least three meshes.
• Answers match the published solutions, and exam 1 is marked against its solution.
• Is the engineering right, not just the final number?

You'll sign in first, then come straight back here.

Proof required

Link the public repo with 2.092 homework 7–8, then exam 2 written up (a typeset PDF, LaTeX source or notebook), and show the self-check: which answers matched and how you fixed the ones that did not.

What gets checked

• Time integration states its method and step, with stability checked.
• Mode shapes are checked for M- and K-orthogonality.
• Exam 2 is marked against its solution, with the score stated.

Common mistakes

• Answers copied from a solution with no working.
• Missing units, or a free-body diagram or sign convention left out.

Powstik Guide

A public write-up of 2.092 homework 7–8, then exam 2, with the self-check shown.

Steps

1. Study the linked course material.
2. Solve the problems on your own first.
3. Check them against the self-check and rework the misses.
4. Typeset the write-up (LaTeX or a notebook) in a public repo.
5. Ask someone who knows the subject to check it.

README
ME 13: Finite Element Analysis, unit 3: Dynamics by finite elements
Problems:
Self-check result (matched / reworked):
What I got wrong first and why:

What gets sent back

• No working shown.
• The self-check result is missing.

Resources

What a verifier looks for

• Time integration states its method and step, with stability checked.
• Mode shapes are checked for M- and K-orthogonality.
• Exam 2 is marked against its solution, with the score stated.
• Is the engineering right, not just the final number?

You'll sign in first, then come straight back here.

Proof required

Link the public repo with the code or model files, the one command that reruns it, the convergence (mesh or step-size) study and the hand-calculation check, and a README that says how to rerun it and what limits the result.

What gets checked

• The mesh study shows the peak stress converging (less than 2% change on the last refinement).
• The hand calculation and the converged value are in a table, with the gap explained.
• The model files rerun from the repo, with loads, supports and material stated.

Common mistakes

• A result that nobody else can rerun from the repo.
• A table with no explanation of the gaps.

Powstik Guide

A finite element model of a loaded L-bracket with a filleted inside corner, or a plate with a hole, in CalculiX or FreeCAD FEM, in a public repo.

Steps

1. Write down what you expect before you start.
2. Predict the peak stress by hand: beam theory times a published stress-concentration factor for the fillet, or a published factor for the hole. Spread loads over a face; never read stresses at a point load or a fixed support, where they never converge. Use second-order elements. Run at least four meshes, refining near the peak, and plot peak stress against element count. Report the converged value, compare it with the hand answer for the same stress component, and explain the gap.
3. Fill the predicted-vs-measured (or hand-vs-simulated) table.
4. Explain every gap with a cause someone can check.
5. Write the README and ask someone who knows the subject to check it.

README
ME 13: Finite Element Analysis — Analyse a bracket with a mesh study and a hand check
What I expected:
How to rerun it:
Predicted vs measured:
Why they differ:
Safety: hand tools and eye protection only

What gets sent back

• No convergence study, or no hand calculation that checks it.
• Machine tools, welding, pressure vessels, combustion, or springs and flywheels storing dangerous energy without a trained supervisor.

Resources

What a verifier looks for

• The mesh study shows the peak stress converging (less than 2% change on the last refinement).
• The hand calculation and the converged value are in a table, with the gap explained.
• The model files rerun from the repo, with loads, supports and material stated.
• Check the engineering and the numbers, not just that it exists: do the units, the hand calculation and the table agree?
• Build photos show hand tools only and eye protection worn: no machine tools, welding, pressure vessels, combustion, or springs and flywheels storing dangerous energy (unless a trained supervisor and a proper workshop are shown).

You'll sign in first, then come straight back here.