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Structural Modeling – AE 4526

Aerospace Structures & Computational Mechanics Faculty of Aerospace Engineering

Delft University of Technology

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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

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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

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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

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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

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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)

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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, …

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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

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FEM – examples

FE mesh

1st eigenmode

pinned crank shaft

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FEM – examples

frequency analysis

Bezier element mesh

source: PhD thesis Schillinger 2012

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FEM – examples source: PhD thesis Schillinger 2012

Bezier element mesh

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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

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FEM – examples modal analysis ... for rotating machine loading

Frequency [Hz]

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FEM – examples

hierarchical FEM framework courtesy of Ernst Rank, CiE, TUM

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FEM – examples

biomechanics – validated femur bone mechanics

Yosibash et al, Ben- Gurion University of the Negev, Israel

principal stress lines QCT data