Pictures of course in Paris 2003
Pictures of course in Berlin 2007
last update 6.2007
|
Paris, France, Dec. 2008, |
last update 6.2007
COURSE
OBJECTIVES
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
_____________________________________________________
COURSE
OUTLINE
NONLINEAR
FORMULATIONS
AND SOLUTION STRATEGIES
Nonlinear FEM
in Engineering
(TB)
Historical Perspective
Linear Benchmark Problems; Patch Tests
Nonlinear Benchmark Problems, Test
Problems
Nonlinear FEM
Analysis
(TB)
Geometric and Material
Nonlinearities
Stress and Strain Measures:
Piola-Kirchhoff stresses,
Green Strain, Rate-of-deformation
Examples of Material Models: Hypoelastic,
Hyperelastic,
Elastic-plastic, Damage Models
Conservation
Equations
_____________________________________________________
SEMIDISCRETIZATION AND SOLUTION METHODS
FE Methods of
Nonlinear Mechanics
(TB)
Semidiscretization of
Continuum Equations
Static and Dynamic Discrete Equations
Lagrangian, Eulerian, and Arbitrary
Lagrangian Eulerian (ALE)
meshes
Frame Invariant Stress Rates
Total and Updated Lagrangian Formulations
Material and Geometric Stiffness
Solution
Algorithms for Nonlinear Problems
(TH)
Consistent Linearization
Line Search
Quasi-Newton Updates ("BFGS",
etc.)
Arc-Length Strategies
Time
Integration Procedures
(TH)
Stability, Consistency, and
Convergence
Survey of Algorithms
Formulation of
Algorithms for Nonlinear Problems
Implicit-Explicit
Element Partitions
Space-Time
Finite Elements
Explicit
Dynamic Integration
(TB)
Implicit and Explicit
Methods
Element Eigenvalue Inequalities; Time Step
Selection
Accuracy and Stability; Mass Lumping
Time Step Partitions; Subcycling
Symplectic and Energy Conserving
Integrators
Direct and
Iterative Equation Solvers
(TH)
Direct Solvers : Band,
Profile and Sparse
Anatomy of an Iterative Equation Solver:
Driver Algorithms, Preconditioners,
Residual Calculations
CAD and
Finite
Elements
(TH)
Computational Geometry
Geometrical Errors
NURBS
Comparison of p- and k-refinement Methods
Isogeometric Structural Analysis
__________________________________________________
ELEMENT
TECHNOLOGY
Element
Technology - I : Incompressible and
Slightly Compressible Media
(TH)
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
Element
Technology - II : Underintegrated
Elements
(TB)
Element selection
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
Element
Technology - III : Plates and Shells
(TB)
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 Instabilities; Physical Hourglass
Control
Survey and Comparison of Elements
_______________________________
CONSTITUTIVE
MODELS
(TH)
Rate-Independent
Deviatoric Plasticity
Small and Finite
Deformation Formulations
Radial Return Methods
Algorithms for the
Finite Deformation Case
Unstable
Materials, Fracture and Failure
(TB)
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 Elemennts (XFEM,
others)
Level Sets for Evovling Discontinuities
Quantum/Molecular/Continuum Multiscale Methods
Return
Mapping Algorithms for General Classes of
Inelastic Materials
(TH)
Cutting Plane Algorithm
Closest Point Projection Algorithm
Elastic Damage and Viscoplastic Models
Operator Splitting
_____________________________________________________
OTHER TOPICS
Contact-Impact
(TB)
Variational Inequalities
Penalty and Lagrange Multiplier Methods
Augmented Lagrangian
Methods
Regularization of Impact and Friction;
Pinball Algorithm
Crashworthiness Analysis
Adaptivity
and Meshfree Methods
(TB)
p-, h-, and r-Adaptivity
Error Indicators : Residual, Global and
Local Projection
Strategies for Adaptative Analysis
Smooth Particle Hydrodynamics
Element-free Galerkin Method
RKPM,
Petrov-Galerkin meshfree methods
Moving least
square and radial basis functions
Visibility
method for discontinuities, smoothing
Integration
methods: background mesh; stress-points
Extended and Generalized Finite Element
Methods (XFEM)
Partitions of Unity
Fluid-Structure Interaction: Level Set
Methods, Immersed FEM Methods
Fluids - I
and II
(TH)
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
Turbulence, LES
Variational
Multiscale Methods
Isogeometric Fluid Analysis
Acoustic Wave
Propagation
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
LECTURERS
_____________________________________________________
THOMAS J.R.
HUGHES
Computational
and Applied Mathematics Chair III
The
Previously
taught at the
TED BELYTSCHKO
Walter P.
Murphy Professor of Computational
Mechanics, Northwestern University
He is the
author of over 300 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 the International
Journal for Numerical Methods in Engineering. He has
received the Timoshenko and Pi Tau Sigma Medals from ASME, the USACM
von
Neumann Medal and Computational Structural Mechanics Award, the
Gauss-Newton
Medal from IACM, the von Karman Medal, the Aerospace Structures and
Materials
Award and the Walter L. Huber Research Prize from ASCE, the Thomas
Jaeger Prize
from IASMIRT, the Computational Mechanics Award of the Japan Society of
Mechanical Engineers, the IACM Computational Mechanics Award, the Baron
Medal
and Honorary Doctorates from the University of Liège, University
of Lyon 1, and
Ecole Centrale, Paris. He is past
Chairman of the Engineering Mechanics Division of ASCE, the Applied
Mechanics
Division of ASME, past and the U.S. National Committee on Theoretical
and
Appplied Mechanics, past President of USACM and the