Steak shake or break and other applications of fem
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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

Steak, shake or break – and other applications of FEM

TMA4220


Outline

Outline

  • Present the governing equations (3 of them)

  • Building your FEM code

  • Mesh generation

  • Experimentation

  • Integration with other courses


Time dependent poisson

Time dependent Poisson

  • “Steak”: Heat transfer

  • The way heat propagates through objects


Linear elasticity

Linear elasticity

  • “Break”: Stress analysis

  • How things bend and deform


Vibration analysis

Vibration analysis

  • “Shake”: Eigenmode analysis

  • Natural frequency of which things oscillate


Building your fem code

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)


How to work

How to work

  • On problem 1-3: answer short and answer right

  • On problem 4: Elaborate as much as possible


Mesh generation

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


Experimentation

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


Example 1 beef

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


Example 2 structural analysis

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?)


Example 3 free vibration

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


Integration with other courses

Integration with other courses

  • Numerical linear algebra (TMA4205)

  • Mathematical Modeling (TMA4195)

  • Experts in Team (TMA4850)


Practicalities

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


Summary

Summary

  • Choose your own problem

  • Be creative

  • Play on your strengths

    • Geometry modeling

    • Visualization

    • Physical Experiments

    • CPU speed


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