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Steak, shake or break – and other applications of FEM

Steak, shake or break – and other applications of FEM. TMA4220. Outline. Present the governing equations (3 of them) Building your FEM code Mesh generation Experimentation Integration with other courses. Time dependent Poisson. “Steak”: Heat transfer

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Steak, shake or break – and other applications of FEM

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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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