© MRu 2013
Structural Modeling – AE 4526
Aerospace Structures & Computational Mechanics
Faculty of Aerospace Engineering
D...
© MRu 2013
course administration
course instructor Dr.-Ing. Martin Ruess
Assistant Professor
support Sonell Shroff, M.Sc.
...
© MRu 2013
the finite element method
shell structure (congress hall, Berlin)
What load cases are significant?
What mechani...
© MRu 2013
the finite element method
shell structure (congress hall, Berlin)
Courtesy of P.J. Pahl, TU Berlin
FE model, el...
© MRu 2013
the finite element method
deflection (scaled) under self weight
Courtesy of P.J. Pahl, TU Berlin
Stress concent...
© MRu 2013
FEM history
Aerospace Engineering
 M.J. (Jon) Turner, Boeing 1950-1962
(general. of the Direct Stiffness Appro...
© MRu 2013
FEM history
pioneering work on FEM
by Turner, Clough, Martin,
Topp – 1956
1950 1960 1970 1980 1990 2000 2010
go...
© MRu 2013
FEM history
pioneering work on FEM
by Turner, Clough, Martin,
Topp – 1956
1950 1960 1970 1980 1990 2000 2010
go...
© MRu 2013
 Solid mechanics: static & dynamic analyses
structural design of aerospace, civil, mechanical & electrical
eng...
© MRu 2013
FEM – examples
displacement field von Mises stress distribution
thin shell under selfweight
© MRu 2013
FEM – examples
FE mesh
1st eigenmode
pinned crank shaft
© MRu 2013 eigenfrequencies
FEM – examples
frequency analysis
Bezier element mesh
source: PhD thesis Schillinger 2012
© MRu 2013 stress concentrations
FEM – examples
source: PhD thesis Schillinger 2012
Bezier element mesh
© MRu 2013
FEM – examples
aluminium foam embedded
in a rubber matrix
aluminium foam – open model
large deformation stress ...
© MRu 2013
FEM – examplesmodal analysis
... for rotating machine loading
Frequency [Hz]
© MRu 2013
FEM – examples
hierarchical FEM framework
courtesy of Ernst Rank, CiE, TUM
© MRu 2013
FEM – examples
biomechanics – validated femur bone mechanics
Yosibash et al, Ben- Gurion
University of the Nege...
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Lecture 0 AE4526 Structural Modelling

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The lecture slides of the lecture 0 of the AE4526 Structural Modelling course of Aerospace Engineering of the TU Delft.

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Lecture 0 AE4526 Structural Modelling

  1. 1. © MRu 2013 Structural Modeling – AE 4526 Aerospace Structures & Computational Mechanics Faculty of Aerospace Engineering Delft University of Technology
  2. 2. © MRu 2013 course administration course instructor Dr.-Ing. Martin Ruess Assistant Professor support Sonell Shroff, M.Sc. Noud Werter, M.Sc. course material available via Blackboard homework assignment mandatory performance record assignments+practicals
  3. 3. © MRu 2013 the finite element method shell structure (congress hall, Berlin) What load cases are significant? What mechanical behavior is significant? What boundary conditions? What material properties? What mathematical model? What discretization? ... generation of an analysis suited model requires  Idealization  Discretization  here: mesh generation STEP 1: pre-processing
  4. 4. © MRu 2013 the finite element method shell structure (congress hall, Berlin) Courtesy of P.J. Pahl, TU Berlin FE model, element mesh (shell & solid elements) What load cases are significant? What mechanical behavior is significant? What boundary conditions? What material properties? What mathematical model? What discretization? ...  equilibrium equations  solution of the equations STEP 2: numerical analysis
  5. 5. © MRu 2013 the finite element method deflection (scaled) under self weight Courtesy of P.J. Pahl, TU Berlin Stress concentrations? Maximum deflection? Stability? ...  stresses/strains at any point  interpolation of displacements  interpretation of results STEP 3: post-processing
  6. 6. © MRu 2013 FEM history Aerospace Engineering  M.J. (Jon) Turner, Boeing 1950-1962 (general. of the Direct Stiffness Approach)  B.M. Irons (isoparam. models, shape functions, patch test, frontal solvers)  E.L. Wilson (first open source FEM code)  first mainframe computers in aerospace industry affordable during the 1950’s Popularizers (responsible for transfer from Aerospace Engineering to other engineering disciplines between 1950s & 1960s)  J.H. Argyris (assumed displacement continuum elements)  R.W. Clough, Jun. Professor at U.C. Berkeley (coined the method FEM in 1960)  H.C. Martin , Jun. Professor at U. Washington  O.C. Zienkiewizc (first textbook on FEM, introduced FEM to Civil Engineering)
  7. 7. © MRu 2013 FEM history pioneering work on FEM by Turner, Clough, Martin, Topp – 1956 1950 1960 1970 1980 1990 2000 2010 golden age direct stiffness method variational formulation displacement formulation – 1962 higher order elements math formulation by Strang & Fix consolidation hybrid, mixed formulations error estimates textbooks of Hughes & Bathe Back to the basics hybrid models assumed strain models … source partly: The Origins of The Finite Element Method by Carlos Fellippa, U. Colorado at Boulder Back to the basics fracture mechanics p-FEM Szabo, Babuska, … X-FEM Belytschko IGA Hughes, Höllig, …
  8. 8. © MRu 2013 FEM history pioneering work on FEM by Turner, Clough, Martin, Topp – 1956 1950 1960 1970 1980 1990 2000 2010 golden age direct stiffness method variational formulation displacement formulation – 1962 higher order elements math formulation by Strang & Fix consolidation hybrid, mixed formulations error estimates textbooks of Hughes & Bathe Back to the basics hybrid models assumed strain models … source partly: The Origins of The Finite Element Method by Carlos Fellippa, U. Colorado at Boulder today > 500 text books > 30 scientific journals > 200000 scientific papers over the last 40 years > 1000 commercial software packages > 1 Bilion US$ annual revenue for FEM software systems most important numerical method in engineering, science & technology Back to the basics fracture mechanics p-FEM Szabo, Babuska, … X-FEM Belytschko IGA Hughes, Höllig, …
  9. 9. © MRu 2013  Solid mechanics: static & dynamic analyses structural design of aerospace, civil, mechanical & electrical engineering, automotive design, biomedical engineering, ...  Fluid dynamics: computational fluid dynamics (CFD), fluid structure interaction (FSI) shallow water problems, laminar & turbulent flow, groundwater flow, heat transfer, wave propagation, ...  Physics: reactor scenarios, nuclear engineering, astrophysics, weather forecast, ...  Chemistry: electro-chemical analysis (corrosion), ... FEM is applied for a large variety of field problems described by Partial Differential Equations (PDE) FEM – fields of application
  10. 10. © MRu 2013 FEM – examples displacement field von Mises stress distribution thin shell under selfweight
  11. 11. © MRu 2013 FEM – examples FE mesh 1st eigenmode pinned crank shaft
  12. 12. © MRu 2013 eigenfrequencies FEM – examples frequency analysis Bezier element mesh source: PhD thesis Schillinger 2012
  13. 13. © MRu 2013 stress concentrations FEM – examples source: PhD thesis Schillinger 2012 Bezier element mesh
  14. 14. © MRu 2013 FEM – examples aluminium foam embedded in a rubber matrix aluminium foam – open model large deformation stress analysis of foam structures source: PhD thesis Schillinger 2012
  15. 15. © MRu 2013 FEM – examplesmodal analysis ... for rotating machine loading Frequency [Hz]
  16. 16. © MRu 2013 FEM – examples hierarchical FEM framework courtesy of Ernst Rank, CiE, TUM
  17. 17. © MRu 2013 FEM – examples biomechanics – validated femur bone mechanics Yosibash et al, Ben- Gurion University of the Negev, Israel principal stress linesQCT data
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