NONLINEAR COMPUTATIONAL SOLID & FLUID MECHANICS ...

NONLINEAR COMPUTATIONAL SOLID & FLUID MECHANICS:
Theoretical formulation, FEM technology and computations
taught by
Prof. Robert L. Taylor, University of California at Berkeley, USA
Prof. Adnan Ibrahimbegovic, Ecole Normale Superieure, Cachan, France
Prof. Hermann G. Matthies, Technical University of Braunschweig, Germany
organised by
the DFG Graduate College Interaction of Fluids and Structures
and the Institute of Scientific Computing
TU Braunschweig
Dates: Monday, 24 April 2006 – Friday, 28 April 2006
Place: Technische Universität Braunschweig
Contact person: Ms S. Fischer
Institut für Wissenschaftliches Rechnen
TU-Braunschweig, Germany
Phone: +49 (0) 531/391-3000
Fax: +49 (0) 531/391-3003
Web-site: http://www.wire.tu-bs.de/nocosoflume
E-Mail: nocosoflume@tu-bs.de
Course Objectives
The main objective of this course is to provide engineers who use computer codes, graduate
students, and researchers with an extensive review of FE based numerical models and solution
algorithms for nonlinear mechanics. It presents the current state-of-the-art in finite element
modeling of nonlinear problems in solid and structural mechanics, and their coupling with
thermal fields and fluids. It will illustrate the difficulties (and their solutions), which appear in
a number of applications from mechanical, aerospace, or civil engineering and material
science. All the sources of nonlinear behavior are presented in a systematic manner, related to
kinematics, equilibrium, constitutive equations, or boundary and coupling conditions. Special
attention is paid to dealing with a class of problems with nonlinear constitutive behavior of
materials, large deformations, and rotations of structures, contact and instability problems
with either material (localization) or geometric (buckling) nonlinearities, which are needed to
fully grasp any weakness of a particular structural design near the ultimate limit state. In
addition, multi-physics models will be addressed, with a special emphasis of thermal coupling
and fluid-structure interaction.
The course will also provide insight into the practical aspects of the Finite Element Method,
related to making the choice of a particular element type, the constitutive model, or
integration scheme among those available in advanced computer codes. Our second objective
is thus to provide the participants with a solid basis for using the FEM based models and
software in trying to achieve the optimal design, and/or to carry out a refined analysis of
nonlinear behavior of structures or multibody systems. The course finally provides a basis to
account for any pertinent multi-physics and multi-scale effects, which are likely to achieve a
significant break-through in a number of industrial applications.

Participants:
The course is suitable for all engineers and researchers who want to improve their skills with
using a refined modeling approach in nonlinear mechanics. In particular, those who are
developing their own tools (with an illustration of the research code FEAP), and those who
seek to make a more efficient use of existing codes (with a demonstration of the codecoupling
interface CTL) will find the course very helpful. Moreover, all those who would like
to reinforce their understanding of the theoretical basis of problems in nonlinear mechanics
and an illustration of current research in Computational Mechanics will be well served
through the course notes and a book. This course (in a somewhat reduced format) has already
been held several times since 2000 in France, and has proved very successful. Among the
previous participants, those with background in engineering or applied mathematics, as well
as those with previous knowledge of basic FEM procedures for linear problems, found the
course most profitable.
Professors:
Robert L. Taylor obtained his PhD in Engineering in 1963 at the University of California at
Berkeley, USA. Subsequently, he was appointed professor in mechanics at the Department of
Civil Engineering, where he currently holds the appointment of the Professor at the UC
Berkeley Graduate School. He has become a member of US National Academy of Engineers
in 1992, and since has received a number of distinctions (including the von Neumann Medal
of IACM) and honorary doctorates, such as the ones from University of Wales at Swansea,
UK and University of Hannover, Germany. The scientific contribution of Prof. Taylor count
more than 200 papers in scientific journals, co-authorship with Prof. Zienkiewicz of the most
well-known books on finite element method, as well as the finite element computer program
FEAP which is used by a large number of universities in the USA and Europe. Perhaps the
best confirmation of extraordinary teaching skills of Prof. Taylor is an impressive list of wellknown
researchers who were his students and scholars.
Adnan Ibrahimbegovic has obtained his engineering education in Sarajevo (winner of 1986
Fulbright Grant), PhD at the University of California at Berkeley, USA and Habilitation at the
University of Pierre and Marie Curie (Paris VI), France. He has held professorships and
research positions at four different universities (including UC Berkeley, EPFL in Switzerland
and UTC in France). Since 1999, he is the Head of Civil Engineering Division of LMT-
Cachan, the largest French laboratory in mechanics. He has received a number of international
distinctions, including NSERC fellowship for Canada and Humboldt Prize for senior
researchers for Germany. He has published over 100 papers in scientific journals and a couple
of advanced textbooks in nonlinear computational solid mechanics.
Hermann G. Matthies has obtained his initial degree from the TU Berlin, Germany; and his
doctoral degree in mathematics at MIT, Cambridge, USA in 1978, working on FEM and
plasticity. Subsequently he has worked in various positions in industrial research and
engineering in diverse fields such as wind, offshore, and ice engineering. Since 1995 he heads
the Institute of Scientific Computing at the TU Braunschweig, Germany; and since 1996 he is
additionally the director of the University Computing Centre. He has received several
international distinctions, among them the Fellowship Award of the IACM. He has published
over 100 papers, as well as edited conference proceedings and topical special issues on
scientific journals.

Course Program
Monday, 24 April 2006
1. Introduction: variational formulations in nonlinear solid mechanics (AI)
• Strong, weak and variational forms of 1D BVP in linear and nonlinear
elasticity
• Basic solution methods: Gauss elimination and Newton iterations
• FEM technology in 1D problems: truss/bar element
2. Numerical implementation in FEM codes (example of FEAP) (RLT)
• FEM technology in 1D structural problems: Euler-Bernoulli and
Timoshenko beam models
• Macro command programming language
• Programming in FEAP environment
3. Numerical solution of discrete models in BVP (HGM)
• Direct solvers, iterative solvers
• Nonlinear problem solvers
• Algorithm analysis
• Time-integration schemes
4. FEM technology for 2D/3D BVP in elasticity (AI)
• 2D/3D models: thermal and mechanics problems
• Isoparametric elements and numerical integration
• Non-conventional interpolations and solid elements with drilling
degrees of freedom
Tuesday, 25 April 2006
5. Enhancing FEM performance – element technology (RLT)
• Structural models: plates and shells
• Hybrid and mixed models
• Enhanced strain models

6. Inelastic constitutive behavior at small strains (AI)
• Thermomechanics with internal variables
• Refined constitutive models of plasticity, damage and coupled damageplasticity
• Solution of weak form with internal variables
7. Implementation and performance of nonlinear constitutive models in FEM framework
(RLT)
• Integration of evolution equations
• Operator split method and consistent tangent modulus
• Locking problems in plasticity
• Choice of element type
8. Solution techniques for non-linear transient problems (HGM)
• Nonlinear heat transfer, nonlinear dynamics
• Explicit vs. implicit integration schemes
• Generalized a-scheme and schemes for stiff equations
• Galerkin method in time
Wednesday, 26 April 2006
9. Nonlinear solid mechanics problems at large displacements (AI)
• Kinematics and strain measure at large displacement
• Lagrangian and Eulerian formulations; Consistent linearisation
• Nonlinear elasticity and poly-convexity conditions
• Constitutive law at large deformations: plasticity
10. Contact problems (RLT)
• Formulation of contact problems (penalty, augmented Lagrangian)
• Implementation of mortar method and stress computation
• Impact dynamics and contact

11. Nonlinear fluid mechanics problems at large displacements (HGM)
• Navier-Stokes equations
• Arbitrary Lagrangian-Eulerian formulation
• Alternative techniques to FEM
12. Nonlinear structural mechanics / I (AI)
• Computational aspects of large 3D rotations
• Geometrically exact beam model of Reissner and Simo
• Locking problems for structures
Thursday, 27 April 2006
13. Non stationary evolution problems and coupled problems (HGM)
• Fluid-solid interaction
• Solution of coupled problems
• Solution of constrained differential equations (DEA)
14. Nonlinear structural mechanics / II (AI)
• Geometrically exact shell models with or without drilling rotations
• Locking problems in shells
• Dynamics and time-integration schemes for shells
15. Flexible multibody system dynamics (RLT)
• Formulation of multibody systems: holonomic and non-holonomic
constraints
• Modeling of flexible multibody systems and cost reduction: rigid
component approximation
16. Instability of structures and systems (HGM/AI)
• Geometric instability: (buckling) vs. material instability (localization)
• Solution of problems in presence of critical points
• Classification of equilibrium critical points

• Dynamic instability problems
Friday, 28 April 2006
17. Advanced aspects of multi-physics and multi-scale problems (RLT/AI)
• Modeling of nonlinear multi-physics problems: example of
themomechanical coupling
• Multi-scale models of inelastic behavior
18. Solution methods for coupled and interaction problems within multi-physics and multiscale
framework (HGM)
• Illustration of fluid-solid interaction problems
• Software architecture and code coupling
• Including the stochastic aspects

COURSE ORGANIZATION
Registration
Early registration is suggested because enrollment is limited.
For registration please see:
http://edu2.zfw.etc.tu-bs.de/nocosoflume/registration.html
For further questions please mail to:
E-Mail: nocosoflume@tu-bs.de
Course Materials
The course material will consist of copies of transparencies from the lectures, survey papers
by the lecturers, recent manuscripts not yet in press, lecture notes, and the advanced textbook
edited by A. Ibrahimbegovic on “Multi-physics and multi-scale computer models for
nonlinear analysis and optimal design of engineering structures under extreme conditions”.
The copies of computer codes Finite Element Analysis Program (FEAP), written by Prof.
Robert L. Taylor at UC Berkeley, and the Component Template Library (CTL) for codecoupling
and parallel-computing platform, developed at TU Braunschweig, and the complete
volume of notes is available only to attendees.
Fee
The registration fee for this course is 2075 €, and includes admission to the lectures, coffee
breaks, an evening reception, and the course notes and texts. Full-time university affiliates
and members of public research centres are entitled to a reduced fee of 1675 €. A limited
number of PhD students (proof of status required) will be entitled to a reduced fee of 675 €.
Location
The course will be held at the TU Braunschweig
Accommodations
There are a number of Hotels in the area. Arrangements should be made directly. Also, the
Tourist Office can help: www.bs-touristoffice.com.
Daily Schedule
Registration starts at 8:30 on Monday.
The lectures start at 9:00 and end at 17:00, Monday-Thursday (4 lectures each 1h15),
and 9:00 to 12:00, Friday (2 lectures each 1h15)
Lunch and coffee breaks are provided for all participants to be taken with the lecturers.
Cancellation Policy
For cancellations made prior to 24 March 2006, the full registration fee will be refunded.
After that date, 100 € cancellation charge will be deducted. No refunds will be made after 17
April 2006. However, registration is transferable to another member of the same organisation.