Subject: NONLINEAR FINITE ELEMENT ANALYSIS A short course taught by
T.J.R.Hughes &
T.Belytschko Berlin-Germany 9-13 Sept. 2002, San Diego 9-13
Dec.2002
NONLINEAR FINITE ELEMENT ANALYSIS
A short course taught by T.J.R.Hughes & T.Belytschko
Berlin-Germany 9-13 Sept. 2002, San Diego 9-13 Dec.2002
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,
email:[EMAIL PROTECTED]
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.
COURSE OUTLINE
NONLINEAR FORMULATIONS AND SOLUTION STRATEGIES
Nonlinear FEM in Engineering, Historical Perspective, Role of Nonlinear
FEM in Product Design, Linear Benchmark Problems ;
Patch Tests, Nonlinear Benchmark Problems, Test Problems.
Nonlinear FEM Analysis, Geometric and Material Nonlinearities, Stress
and Strain Measures: Piola-Kirchhoff
stresses, Green Strain, Rate-of-deformation, Examples of Material
Models, Pitfalls in Nonlinear Analysis: Non-unique
Solutions, Localization, Buckling.
SEMIDISCRETIZATION AND SOLUTION METHODS
FE Methods of Nonlinear Mechanics, 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, Algorithmic
Stiffness.
Formulation and Solution Algorithms for Nonlinear Problems , Newton and
Modified Newton Methods, Consistent
Linearization , Line Search, Quasi-Newton Updates ("BFGS", etc.),
Arc-Length Strategies.
Time Integration Procedures, Stability, Consistency, and Convergence,
Survey of Algorithms, Formulation of
Algorithms for Nonlinear Problems, Implicit-Explicit Element
Partitions, Space-Time Finite Elements.
Explicit Dynamic Integration, Implicit and Explicit Methods, Element
Eigenvalue Inequalities; Time Step Selection,
Accuracy and Stability; Mass Lumping, Time Step Partitions; Subcycling,
Implementation on Parallel Computers.
Direct and Iterative Equation Solvers, Direct Solvers : Band, Profile
and Sparse, Anatomy of an Iterative Equation
Solver:Driver Algorithms, Preconditioners, Residual Calculations.
ELEMENT TECHNOLOGY
Element Technology - I : Incompressible and Slightly Compressible Media,
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, 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, C0 and C1 Flexural
Theories; Discrete Kirchhoff Theory, Continuum
Based(Degenerated)Elements, Shear Locking and Elimination of Locking by
Assumed Strain and Projection Methods,
Membrane Locking and Inextensional Modes, Drilling Degrees-of-Freedom,
Hourglass Modes and Control, Shear
Oscillations; Physical Hourglass Control, Assumed Strain Elements;
Referential Components, Survey and Comparison of
Elements.
Element Technology - IV : Multiscale Phenomena, Variational Multiscale
Formulation, Fine-Scale Greens
Function, Hierachical Bases ; + Bubbles ;, Origins of Stabilized Methods
Dirichlet-to-Neumann Formulation,
Subgrid-scale Models.
CONSTITUTIVES MODELS
Rate-Independent Deviatoric Plasticity, Small and Finite Deformation
Formulations, Radial Return Methods,
Algorithms for the Finite Deformation Case, Unstable Materials, Fracture
and Failure, 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,
Geometric Instabilities (Buckling), Molecular Dynamics Coupled to
Continua.
Return Mapping Algorithms for General Classes of Inelastic Materials,
Cutting Plane Algorithm, Closest Point
Projection Algorithm, Elastic Damage and Viscoplastic Models, Operator
Splitting.
OTHER TOPICS
Contact-Impact, Variational Inequalities, Penalty and Lagrange
Multiplier Methods, Perturbed and Augmented
Lagrangian Methods, Regularization of Impact and Friction; Pinball
Algorithm, Crashworthiness Analysis.
Adaptivity and Meshless Methods, p-, h-, and r-Adaptivity, Error
Indicators : Residual, Global and Local Projection,
Strategies for Adaptative Analysis, Smooth Particle Hydrodynamics,
Element-free Galerkin, Extended Finite Elements,
New Discontinuous Elements(XFEM), Level Sets for Evolving
Discontinuities, Levels of Difficulty of Nonlinear
problems.
Fluids - I and II, 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
Mary and Gordon Crary Family Professor of Engineering, Stanford
University
Taught at the University of California, Berkeley, and the California
Institute of Technology before joining Stanford
University. 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.
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 the INTERNATIONAL JOURNAL FOR NUMERICAL
METHODS IN
ENGINEERING.
DETAILS AND REGISTRATION FORM: http://www.zace.com
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