Numerics in geotechnics and structures Symposium Lausanne 30-31.8. 2010 |
|
|
 |
|
|
 ZACE Services Ltd |
|
Numerics in geotechnics and structures Symposium Lausanne 30-31.8. 2010 |
|
|
|
|
|
|
|
ZACE Services Ltd |
| Course Topics |
Course Topics
Course Topics Table Of Contents:
NONLINEAR FORMULATIONS AND SOLUTION STRATEGIES
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)
- Newton and Modified Newton Methods
- 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: Isogeometric Analysis (TH)
- Computational Geometry
- NURBS, T-splines
- Comparison of p- and k-refinement Methods
- Structural, Vibration and Wave Propagation Analysis
- Fluid-Structure Interaction: ALE method
- Cardiovascular Modeling
ELEMENT TECHNOLOGY
Element Technology - I : Incompressible and Slightly Compressible (TH)
- 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 (TB)
- Elements Element accuracy and rates of convergence
- 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
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
Rate-Independent Deviatoric Plasticity (TH)
- Small and Finite Deformation Formulations
- Radial Return Methods
- Algorithms for the Finite Deformation Case
Material Instabilities, 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 Elements (XFEM, others)
- Level Sets for Evolving Discontinuities
- Coarse graining of failure processes
- Hierarchical and concurrent multiscale methods
- 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)
- 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
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
Partitions of Unity
Fluid-Structure Interaction: Immersed FEM, level sets
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
- Phase Field Modeling
Copyright 2008 Hughes - Belytschko
