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. 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