Introduction
Nonlinear Finite Element Methods for Solids
Summer semester 2017
Instructors: Prof. Roger A. Sauer, sauer@aices.rwth-aachen.de
Dr. Stephan Wulfinghoff, stephan.wulfinghoff@rwth-aachen.de
Lectures: Thursday & Friday 12.15pm – 13:45pm in kl. Physik
(Rogowski building)
Lecture and exercise notes available on L2P
Office hours: after lectures and by appointment
Examination: Projects and Oral Examination
the course is worth 5CP
Sauer / Wulfinghoff
Nonlinear Finite Element Methods for Solids
Summer 2017
Participants
Name
Sauer / Wulfinghoff
Email
Studies
Nonlinear Finite Element Methods for Solids
basic basic adv. basic matlab
mech conti conti FEM
Summer 2017
Course outline (tentative)
0.
Preliminaries
1.
Introduction
2.
Mechanics of a nonlinear 1D bar
3.
1D finite element formulations
4.
Elastoplasticity in 1D
5.
Review of continuum mechanics
6.
2D finite element formulations
7.
Boundary conditions
8.
Mesh generation
9.
Postprocessing
10. Error estimation
Sauer / Wulfinghoff
Nonlinear Finite Element Methods for Solids
Summer 2017
Finite element literature
Belytschko, T., Liu, W.K and Moran, B.: Nonlinear Finite Elements for Continua
and Structures, Wiley & Sons, 2006
Oden, J.T.: Finite Elements of Nonlinear Continua, Dover Ed., 2006
Wriggers, P.: Nonlinear Finite Element Methods, Springer, 2008
Literature on continuum mechanics:
Chadwick, P.: Continuum Mechanics – Concise Theory and Problems, Dover,
1999
Holzapfel, G.A.: Nonlinear Solid Mechanics – A Continuum Approach for
Engineering, 2nd Ed., Wiley & Sons, 2000
Sauer / Wulfinghoff
Nonlinear Finite Element Methods for Solids
Summer 2017
Challenges in finite element analysis
•
Large deformations
•
Material modeling: Viscoelasticity, Damage (Plasticity, Fracture)
•
Accurate, efficient & robust computational formulations
•
Different phyical length scales (Multiscale modeling)
•
Coupling of different methods, e.g. FEM - DEM
•
Multi-physical modeling
•
Contact, friction & adhesion
•
Structural stability
•
Large scale computations
Car crash simulation
Sauer / Wulfinghoff
Nonlinear Finite Element Methods for Solids
Summer 2017
Historical review (up to the 1970s)
• 17th & 18th century: Development of variational methods
• Leibniz (1696): Brachistochrone minimization problem; solved by using
piecewise linear functions
• Schellbach (1851): Plateau problem, solved by piecewise linear triangles
• Riemann/Hilbert: Variational approach to Poisson’s equation
• Rayleigh/Ritz (1909/10): Minimization with global functions
• Galerkin (1915): Weak formulation with trial and test functions
• Courant (1943): “Courant element”, the linear triangle
• 1940s and 50s: First engineering analysis on analog computers
• Turner (1952/53): Aircraft analysis at Boeing; origin of modern FEM
• Clough (1960): Introduced the term “Finite Element method”
• Wilson (1963): First modern FEM code
• Zienkiewicz (1967): Major FEM book
• 1960s and 70s: Mathematical proofs and books
Sauer / Wulfinghoff
Nonlinear Finite Element Methods for Solids
Sources:
Babuska (2011),
Belytschko et al. (2006)
Summer 2017
Historical review (nonlinear focus)
• 1960s: implicit FE code NOSAP (Berkeley)
• Constantino (1964): first explicit FE code
• Argyris (1965), Marcal & King (1967): First major nonlinear FEM papers
• late 1960s, early 70’s: commercial nonlinear FEM codes
ANSYS (J. Swanson), ABAQUS (D. Hibbitt), ADINA (K.-J. Bathe)
• Belytschko (1969/72): SAMSON and WRECKER codes featuring an
element-by-element computation
• 1970s and 80s: pioneering work by Berkeley researchers: Hughes, Taylor,
Simo, Bathe, Felippa, Bergan, Willam, Ramm, Ortiz
• further pioneers: Oden, Belytschko, Crisfield, Stein, Zienkiewicz
• Hallquist (1976): DYNA code; later distributed commercially as LSDYNA
• textbooks on nonlinear FEM: Oden (1972), Kleiber (1989), Crisfield (1991),
Zhong (1993), Belytschko et al. (2000), Wriggers (2001)
Sources:
Babuska (2011),
Belytschko et al. (2006)
Sauer / Wulfinghoff
Nonlinear Finite Element Methods for Solids
Summer 2017