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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