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FEM Applications: Steak, Shake, or Break

Explore the applications of Finite Element Method (FEM) in heat transfer, stress analysis, and eigenmode analysis. Build your FEM code, generate meshes, and conduct experimentation with different geometries, material properties, and boundary conditions. Integrate with other courses such as numerical linear algebra and mathematical modeling. Be creative, play on your strengths, and unleash the power of FEM!

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FEM Applications: Steak, Shake, or Break

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  1. Steak, shake or break – and other applications of FEM TMA4220

  2. Outline • Present the governing equations (3 of them) • Building your FEM code • Mesh generation • Experimentation • Integration with other courses

  3. Time dependent Poisson • “Steak”: Heat transfer • The way heat propagates through objects

  4. Linear elasticity • “Break”: Stress analysis • How things bend and deform

  5. Vibration analysis • “Shake”: Eigenmode analysis • Natural frequency of which things oscillate

  6. Building your FEM code • Series of problems 1a) – 3b) • Gauss quadrature • FEM theory • Sample 2d problem • Sample 3d problem • Your choice and experimentation (Problem 4)

  7. How to work • On problem 1-3: answer short and answer right • On problem 4: Elaborate as much as possible

  8. Mesh generation • Lots of issues (probably the most understated part of FEM training) • 3 options • Pre-made by myself • GMSH (free, easy-to-use mesh tool, readable output) • I’ll get back to #3 later

  9. Experimentation • Find your own problem • Choose an equation • Choose a geometry • Choose an objective • Analyze the results • Experiment with geometry, material properties and/or boundary conditions

  10. Example 1: beef • How to cook the optimal beef • Choose an equation • Choose a geometry • Choose an objective • Optimality criterium? • Too short cooking – raw and unedible • Too long cooking – dry and tasteless • Too varying temperature – all of the above • Experimentation

  11. Example 2: Structural analysis • Linear elasticity • Choose an equation • Choose a geometry • Choose an objective • http://www.youtube.com/watch?v=v5fS4RF3ht0 • Max stress lower than material critical point • Will it withstand gravity? • Will it withstand external forces? (creepers?)

  12. Example 3: free vibration • What are the natural frequencies of your geometry (and material)? • Choose an equation • Choose an objective • Find the natural frequencies • Resonance with enviromental frequencies (wind, noise etc) • Sound/music (harmonic overtones) • Purely visual • Choose a geometry

  13. Integration with other courses • Numerical linear algebra (TMA4205) • Mathematical Modeling (TMA4195) • Experts in Team (TMA4850)

  14. Practicalities • 2 persons to each group • Deadline: 18th Nov. • Written report and presentation • No min/max pages • Access to computer lab • I’m away next week, Anne away the next 2 weeks

  15. Summary • Choose your own problem • Be creative • Play on your strengths • Geometry modeling • Visualization • Physical Experiments • CPU speed

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