Steak, shake or Steak, shake or break – and other break – and other

applications of applications of FEMFEMTMA4220TMA4220

OutlineOutline

Present the governing equations (3 Present the governing equations (3 of them)of them)

Building your FEM codeBuilding your FEM code Mesh generationMesh generation ExperimentationExperimentation Integration with other coursesIntegration with other courses

Time dependent PoissonTime dependent Poisson

““Steak”: Heat transferSteak”: Heat transfer The way heat propagates through The way heat propagates through

objectsobjects

0u

ut

Linear elasticityLinear elasticity

““Break”: Stress analysisBreak”: Stress analysis How things bend and deformHow things bend and deform

( )u f

Vibration analysisVibration analysis

““Shake”: Eigenmode analysisShake”: Eigenmode analysis Natural frequency of which things Natural frequency of which things

oscillateoscillate

( ) 0u u

Building your FEM codeBuilding 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 workHow to work

On problem 1-3: answer On problem 1-3: answer short short and and answer answer rightright

On problem 4: Elaborate as much as On problem 4: Elaborate as much as possiblepossible

Mesh generationMesh generation

Lots of issues (probably the most Lots of issues (probably the most understated part of FEM training)understated part of FEM training)

3 options3 options

GMSH (free, easy-to-use mesh tool, readable output)GMSH (free, easy-to-use mesh tool, readable output)

Pre-made by myselfPre-made by myself

I’ll get back to #3 laterI’ll get back to #3 later

ExperimentationExperimentation

Find your own problemFind your own problem Choose an equationChoose an equation Choose a geometryChoose a geometry Choose an objectiveChoose an objective Analyze the resultsAnalyze the results

Experiment with geometry, material Experiment with geometry, material properties and/or boundary properties and/or boundary conditionsconditions

Example 1: beefExample 1: beef

How to cook the optimal beefHow to cook the optimal beef

0u

ut

Choose an equationChoose an equation Choose a geometryChoose a geometry Choose an objectiveChoose an objective Optimality criterium?Optimality criterium? Too short cooking – raw and unedibleToo short cooking – raw and unedible Too long cooking – dry and tastelessToo long cooking – dry and tasteless Too varying temperature – all of the aboveToo varying temperature – all of the above

ExperimentationExperimentation

( ) 225u

Example 2: Structural Example 2: Structural analysisanalysis

Linear elasticityLinear elasticity Choose an equationChoose an equation Choose a geometryChoose a geometry Choose an objectiveChoose an objective

( )u f

http://http://www.youtube.com/watch?vwww.youtube.com/watch?v=v5fS4RF3ht0=v5fS4RF3ht0 Max stress lower than material critical pointMax stress lower than material critical point

Will it withstand gravity?Will it withstand gravity? Will it withstand external forces? (creepers?)Will it withstand external forces? (creepers?)

Example 3: free vibrationExample 3: free vibration

What are the natural frequencies of your What are the natural frequencies of your geometry (and material)?geometry (and material)?

Choose an equationChoose an equation

Choose a geometryChoose a geometry Choose an objectiveChoose an objective

( ) 0u u

Find the natural frequenciesFind the natural frequencies Resonance with enviromental frequencies (wind, noise etc)Resonance with enviromental frequencies (wind, noise etc) Sound/music (harmonic overtones)Sound/music (harmonic overtones) Purely visualPurely visual

Integration with other Integration with other coursescourses

Numerical linear algebra (TMA4205)Numerical linear algebra (TMA4205) Mathematical Modeling (TMA4195)Mathematical Modeling (TMA4195) Experts in Team (TMA4850)Experts in Team (TMA4850)

PracticalitiesPracticalities

2 persons to each group2 persons to each group Deadline: 18Deadline: 18thth Nov. Nov. Written report and presentationWritten report and presentation No min/max pagesNo min/max pages Access to computer labAccess to computer lab I’m away next week, Anne away the I’m away next week, Anne away the

next 2 weeksnext 2 weeks

SummarySummary

Choose your own problemChoose your own problem Be creativeBe creative Play on your strengthsPlay on your strengths

Geometry modelingGeometry modeling VisualizationVisualization Physical ExperimentsPhysical Experiments CPU speedCPU speed