NONLINEAR FINITE ELEMENT ANALYSIS

A short course taught by

Thomas J.R. HUGHES & Ted BELYTSCHKO

REGISTRATION


dec 8-12. 2008, Paris, France


Pictures of course in Berlin 2002
Pictures of course in Paris 2003

last update 04.2008

COURSE OBJECTIVE

The purpose of this course is to provide engineers, scientists, and researchers with a critical survey of the state-of-the-art of finite element methods in solids, structures, and fluids, with an emphasis on methodologies and applications for nonlinear problems. The fundamental theoretical background, the computer implementations of various techniques and modeling strategies will be treated. Advantages and shortcomings of alternative methods and the practical implications of recent research developments will be stressed. Recent mathematical and algorithmic developments will be explained in terms comprehensible to engineers.

WHO ATTENDS

This seminar is designed for engineers in industry, government, and academia who wish to obtain an overview and understanding of nonlinear finite element methods. A background in engineering or applied sciences and some previous exposure to finite element methods are necessary for understanding the material covered in this course. The course has been offered annually in the U.S. and Europe since 1985. The attendees are engineers and scientists from: corporations, such as Dassault, Boeing, General Motors, Ford, Daimler Benz, BMW, Fiat, PSA, Renault, Philips, Fujitsu, IBM, EDF, Siemens; software companies; government laboratories, such as Livermore, Argonne, Sandia; government offices, such a NSF and the Defense Nuclear Agency; U.S. Navy, NASA, ESA and Air Force Laboratories and universities.


COURSE OUTLINE

NONLINEAR FORMULATIONS AND SOLUTION STRATEGIES

     Historical Perspective
     Linear Benchmark Problems; Patch Tests
     Nonlinear Benchmark Problems, Test Problems      Geometric and Material Nonlinearities
     Stress and Strain Measures: Piola-Kirchhoff stresses, Green
     Strain, Rate-of-deformation
     Examples of Material Models
     Conservation Equations

SEMIDISCRETIZATION AND SOLUTION METHODS

     Semidiscretization of Continuum Equations
     Static and Dynamic Discrete Equations
     Lagrangian, Eulerian, and Arbitrary Lagrangian Eulerian (ALE) meshes
     Frame Invariant Stress Rates
     Incremental objectivity
     Total and Updated Lagrangian Formulations
     Material and Geometric Stiffness
     Equilibrium Solution and Stability      Newton and Modified Newton Methods
     Consistent Linearization
     Line Search
     Quasi-Newton Updates ("BFGS", etc.)
     Arc-Length Strategies      Stability, Consistency, and Convergence
     Survey of Algorithms
     Formulation of Algorithms for Nonlinear Problems
     Implicit-Explicit Element Partitions
     Space-Time Finite Elements      Implicit and Explicit Methods
     Element Eigenvalue Inequalities; Time Step Selection
     Accuracy and Stability; Mass Lumping
     Time Step Partitions; Subcycling
     Implementation on Parallel Computers      Direct Solvers : Band, Profile and Sparse
     Anatomy of an Iterative Equation Solver
     Iterative Solvers : Driver Algorithms, Preconditioners,
     Residual Calculations
     Isogeometric structural Analysis

ELEMENT TECHNOLOGY

     Mixed and Displacement Methods
     Volumetric Locking
     Babuska-Brezzi (BB) Condition
     Survey of Effective Elements
     Reduced and Selective Integration Techniques
     Pressure Oscillations
     Strain Projection Methods: B-bar; Linear and Nonlinear Cases      Stiffness Matrix Rank and Rank Deficiency
     Spurious Singular Modes (Hourglassing)
     Mixed Variational Principles : Hu-Washizu
     Stabilization by Perturbation, Assumed Strain, and Variational
     Methods; Physical Hourglass Control
     Convergence Rates of  Elements      C0 and C1 Flexural Theories; Discrete Kirchhoff Theory
     Continuum Based(Degenerated)Elements
     Shear Locking and Elimination of Locking by Assumed Strain
     Membrane Locking and Inextensional Modes
     Hourglass Modes and Control
     Shear Oscillations; Physical Hourglass Control
     Assumed Strain Elements; Referential Components
     Survey and Comparison of Elements      Variational Multiscale Formulation
     Fine-Scale  Green’s Function
     Hierachical Bases ; « Bubbles »
     Origins of Stabilized Methods
     Dirichlet-to-Neumann Formulation
     Subgrid-scale Models

CONSTITUTIVE MODELS

     Small and Finite Deformation Formulations
     Radial Return Methods
     Algorithms for the Finite Deformation Case      Material Instabilities : Strain-Softening, Nonassociated Plasticity
     Loss of Ellipticity (Hyperbolicity); Localization
     Regularization: Viscous, Gradient, Nonlocal
     Explicit and Smeared Crack Models
     Failure Modeling : Static and Dynamic Crack Propagation
     Discontinuous Elements (X-FEM)
     Level Sets for Evolving Discontinuities
     Problems in Nanomechanics
     Molecular Dynamics Coupled to Continua; Nanomechanics      Cutting Plane Algorithm
     Closest Point Projection Algorithm
     Elastic Damage and Viscoplastic Models
     Operator Splitting

OTHER TOPICS

     Variational Inequalities
     Penalty and Lagrange Multiplier Methods
     Augmented Lagrangian Methods and Surface Smoothing
     Regularization of Impact and Friction; Pinball Algorithm
     Crashworthiness Analysis      p-, h-, and r-Adaptivity
     Error Indicators : Residual, Global and Local Projection
     Strategies for Adaptative Analysis
     Smooth Particle Hydrodynamics
     Element-free Galerkin (EFG method)
     Extended Finite Elements
     New Discontinuous Elements (XFEM)      Scalar Advection-Diffusion Equation
     SUPG and Galerkin/Least-Squares Method
     Space-Time Generalizations
     Discontinuous Galerkin Method
     Advective-Diffusive Systems
     Incompressible Euler and Navier-Stokes Equations
     Stokes Equations; Methods which Circumvent the BB-Condition
     Compressible Euler and Navier-Stokes Equations
     Entropy Variables
     Conservation and Physical Variables
     Shock-Capturing Operators
     Domain Decomposition
     Iterative Procedures; GMRES
     Matrix Free Algorithms
     Parallelism ; Turbulence


 
 

LECTURERS

THOMAS J.R. HUGHES
Professor of Aerospace Engineering and Engineering Mechanics, Computational and Applied Mathematics Chair III, The Texas Institute for Computational and Applied Mathematics (TICAM)
The University of Texas at Austin

Taught at the University of California, Berkeley, and the California Institute of Technology, and Stanford University before joining the University of Texas. He is the author of over 300 works on numerical analysis and continuum mechanics, with emphasis on finite element methods.Author or editor of eighteen books, including the popular text: THE FINITE ELEMENT METHOD : LINEAR STATIC AND DYNAMIC FINITE ELEMENT ANALYSIS. He has received the Bernard Friedman Memorial Prize in Applied Mathematics from the University of California, Berkeley, the Walter L. Huber Research Prize from the ASCE, the Melville Medal from the ASME, the Computational Mechanics Award of the Japan Society of Mechanical Engineers the von Neumann Medal of  USACM, the Gauss-Newton Medal of IACM, and the Worcester Reed Warner Medal of ASME, and Honorary Doctorate from The Catholic University in Louvin. He has held theCattedra Galileiana ( Galileo Galilei Chair), Scuola Normale Pisa, and Eshbach Professorship, Northwestern University. He is co-editor of the International Journal COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, past Chairman of the Applied Mechanics Division of ASME, past President of the USACM,  and IACM, and a member of the National Academy of Engineering.

TED BELYTSCHKO

Walter P. Murphy Professor of Computational Mechanics, Northwestern University

He is the author of over 250 works on a wide variety of applied mechanics problems, with emphasis on explicit finite element methods. Editor of seven books, including  COMPUTATIONAL METHODS FOR TRANSIENT ANALYSIS (with T.J.R. Hughes). He is author of  the recent book : NONLINEAR FINITE ELEMENTS FOR CONTINUA AND STRUCTURES.  He is editor of INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING. He has received theTimoshenko and  Pi Tau Sigma Gold Medal from the ASME, the USACM von Neumann Medal and Computational Structural Mechanics Award, the von Karman Medal and  the Walter L. Huber Research Prize from  ASCE, the Thomas Jaeger Prize from IASMIRT, the ASCE Aerospace Structures and Materials Award, the Computational Mechanics Award of the Japan Society of Mechanical Engineers,an Honorary Doctorate from the University of Liège, the Computational Mechanics Award and Gauss-Newton Medal of IACM and the Baron Medal.  He is past Chairman of the Engineering Division of ASCE and the Applied Mechanics Division of ASME,  past President of the USACM and a member of the National Academy of Engineering.

Both lecturers are listed among the 100 most cited engineers



COURSE ORGANIZATION

______________________________________________________

 

Registration

Mail or fax in the completed registration form with check, or copy of money transfer order. Early registration is suggested because enrollment is limited.

Course Materials

The course materials will consist of copies of transparencies from the lectures, survey papers by the lecturers, recent manuscripts not yet in press, lecture notes, and the textbooks: The Finite Element Method: Linear Static and Dynamic Finite Element Analysis by T.J.R. Hughes, Nonlinear Finite Elements for Continua and Structures by T. Belytschko & al., and Computational Inelasticity by J.C.Simo & T.J.R.Hughes. The complete volume of notes is available only to attendees.

Fee

 The registration fee for this course is Euros 2375. A reduced rate of Euros 2175 applies for early registration and payment  (until Oct.24.2008).The fee includes admission to the lectures, coffee breaks, an evening reception and the course notes and texts. Full-time university affiliates who register and pay before   Oct.24.2008  are entitled to a reduced registration fee of Euros 1875, and 2075 after that date. A limited number of Ph.D students (proof of status required) will be entitled to a reduced registration fee of Euros 1575, if they register and pay before  Oct.24.2008.

Please transfer payment to Credit Suisse CH-Lausanne, account: 121242-82-1, IBAN: CH69 0442 5012 1242 8200 1, SWIFT: CRESCHZZ10A with the mention "ZACE H&B 2008 Seminar Fee" and your name.

Location

The course will be held at Evergreen Laurel,8 Place Georges Pompidou 92300 Levallois-Perret, Paris,  France. (T)+33(0)1 47 58 88 99, (F)+33(0)1 47 58 88 88

Accommodations

<>A limited block of rooms has been reserved at special rates(180EUR) at Hotel Evergreen Laurel; to qualify for special rates you must mention that you are attending the Hughes-Belytschko short course organized  by Zace Services limited and make your reservation before nov.12th. Arrangements should be made directly with the hotel,
Fax +33(0)1 47 58 91 03, Tel +33(0)1 47 58 91 05,  email: elhpar@evergreen-hotels.com.

Daily Schedule

Registration starts at 8.30 a.m. on Monday. The lectures start at 9 a.m. and end at 5.30 p.m., Monday-Thursday, 9 a.m. to 12.00 p.m., Friday.

Cancellation Policy

For cancellations made prior to  Oct.24, 2008, the full registration fee will be refunded. After that date, an Euros 100.- cancellation charge will be deducted. No refunds will be made for cancelleations after Nov.28, 2008. Registration is transferable to another member of the same firm.

 

 

For additional informations, contact

 


ZACE SERVICES Ltd, P.O.Box 2-CH-1015 Lausanne 15, Switzerland, Phone +41/21/802 46 05, fax +41/21/802 46 06

http://www.zace.com,                              e-mail: info@zace.com