Nonlinear Finite Element Methods, Peter Wriggers,Springer, 2008*

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Nonlinear Finite Element Methods, Peter Wriggers,Springer2008

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Chapter 1 Introduction

Chapter 2 Nonlinear Phenomena

* Geometrical Nonlinearity

Large Displacements of a Rigid Beam

Large Displacements of an Elastic System

Bifurcation Problem

Snap-Through Problem

Physical Nonlinearity

Nonlinearity Due to Boundary Conditions

Chapter 3 Basic Equations of Continuum Mechanics

* Kinematics

Motion and Deformation Gradient

Strain Measures

Transformation of Vectors and Tensors

Time Derivatives

Balance Equations

Balance of Mass

Balance of Linear and Angular Momentum

First Law of Thermodynamics

Introduction of Different Stress Tensors

Balance Equations with Respect to Initial Configuration

Time Derivatives of Stress Tensors

Constitutive Equations

Elastic Material

Elasto-Plastic Material Laws

Visco-Elastic and Visco-Plastic Material Behaviou

Incremental Form of the Material Equations

Weak Form of Equilibrium, Variational Principles

Weak Form of Linear Momentum in the Initial Configuration

Weak Form of Linear Momentum in the Current Configuration

Variational Functionals

Linearizations

Linearization of Kinematical Quantities

Linearization of Constitutive Equations

Linearization of the Variational Formulatio

Chapter 4 Spatial Discretization Techniques

* General Isoparametric Concept

One-Dimensional Interpolations

Two-Dimensional Interpolations

Three-Dimensional Interpolation

Discretization of the Weak Form

FE-Formulation of the Weak Form in Initial Configuration

Linearization of the Weak Form in the Initial Configuration

FE-Formulation of the Weak Form in the Current Configuration

Linearization of the Weak Form in the  Current Configuration

Deformation Dependent Loads

Chapter 5 Solution Methods for Time Independent Problems

*Solution of Nonlinear Systems of Equations

Newton-Raphson Method

Modified Newton Scheme

Quasi-Newton Method

Damped Newton Method, Line-Search

Path-Following or Arc-Length Method

Solvers for Linear Systems of Equations

Direct Solvers

Iterative Solution Methods

Parallel Equation Solver

Examples Related to Algorithms and Equation Solvers

Rubber Block

Solid with an Inclusion

Elasto-Plastic Plate with Hole

Problems Solved on Parallel Computers

General Observations

Problems, Which Occur when Running Actual Simulations

Chapter 6 Solution Methods for Time Dependent Problems

Chapter 7 Stability Problems

Chapter 8 Adaptive Methods

Chapter 9 Special Structural Elements

Chapter 10 Special Finite Elements for Continua

Chapter 11 Contact Problems

Chapter 12 Automation of the Finite Element Method by J. Korelc