Steak, shake or break –
and other applications of
FEM
TMA4220
Outline
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Present the governing equations (3 of them)
Building your FEM code
Mesh generation
Experimentation
Integration with other courses
Time dependent Poisson
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“Steak”: Heat transfer
The way heat propagates through objects
u
 u 0
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Linear elasticity
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“Break”: Stress analysis
How things bend and deform
 ( u )  f
Vibration analysis
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“Shake”: Eigenmode analysis
Natural frequency of which things oscillate
 u   (u ) 0
Building your FEM code
Series of problems 1a) – 3b)
 Gauss quadrature
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FEM theory
Sample 2d problem
Sample 3d problem
Your choice and experimentation (Problem 4)
How to work
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On problem 1-3: answer short and answer right
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On problem 4: Elaborate as much as possible
Mesh generation
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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)
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I’ll get back to #3 later
Experimentation
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Find your own problem
Choose an equation
 Choose a geometry
 Choose an objective
 Analyze the results
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Experiment with geometry, material properties
and/or boundary conditions
Example 1: beef
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How to cook the optimal beef
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Choose an equation
Choose a geometry
Choose an objective
 Optimality criterium?
Experimentation
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Too short cooking – raw and unedible
Too long cooking – dry and tasteless
Too varying temperature – all of the above
uu()225
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t
Example 2: Structural analysis
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Linear elasticity
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Choose an equation
Choose a geometry
 http://www.youtube.com/watch?v=v5fS4RF3ht0
Choose
an objective
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Max stress lower than material critical point
Will it withstand gravity?
Will it withstand external forces? (creepers?)
 ( u )  f
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Example 3: free vibration
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What are the natural frequencies of your geometry (and
material)?
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Choose an equation
Choose an objective
 Find the natural frequencies
Choose
a geometry
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Resonance with enviromental frequencies (wind, noise etc)
Sound/music (harmonic overtones)
Purely visual
 u   (u ) 0
Integration with other courses
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Numerical linear algebra (TMA4205)
Mathematical Modeling (TMA4195)
Experts in Team (TMA4850)
Practicalities
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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
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Choose your own problem
Be creative
Play on your strengths
Geometry modeling
 Visualization
 Physical Experiments
 CPU speed
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