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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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© MRu 2013
Structural Modeling – AE 4526
Aerospace Structures & Computational Mechanics Faculty of Aerospace Engineering
Delft University of Technology
© 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
© 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
© 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
© 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
© 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)
© 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, …
© 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, …
© MRu 2013
Solid mechanics: static & dynamic analysesstructural design of aerospace, civil, mechanical & electricalengineering, 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
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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 analysis of foam structures
source: PhD thesis Schillinger 2012
© MRu 2013
FEM – examples modal 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 Negev, Israel
principal stress lines QCT data
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