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Nonlinear Finite Elements for Continua and Structures

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ISBN-10: 0471987743

ISBN-13: 9780471987741

Edition: 2000

Authors: Ted Belytschko, Wing Kam Liu, Brian Moran

List price: $110.00
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Description:

Adopting an integrating approach to enable readers to gain an understanding of the fundamental methods, this text provides a comprehensive description of the major methodologies of nonlinear finite element analysis for solid mechanics.
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Book details

List price: $110.00
Copyright year: 2000
Publisher: John Wiley & Sons, Incorporated
Publication date: 10/3/2000
Binding: Paperback
Pages: 672
Size: 6.75" wide x 9.75" long x 1.50" tall
Weight: 2.442
Language: English

Preface
List of Boxes
Introduction
Nonlinear finite elements in design
Related books and a brief history of nonlinear finite elements
Notation
Mesh descriptions
Classification of partial differential equations
Exercises
Lagrangian and Eulerian finite elements in one dimension
Introduction
Governing equations for total Lagrangian formulation
Weak form for total Lagrangian formulation
Finite element discretization in total Lagrangian formulation
Element and global matrices
Governing equations for updated Lagrangian formulation
Weak form for updated Lagrangian formulation
Element equations for updated Lagrangian formulation
Governing equations for Eulerian formulation
Weak forms for Eulerian mesh equations
Finite element equations
Solution methods
Summary
Exercises
Continuum mechanics
Introduction
Deformation and motion
Strain measures
Stress measures
Conservation equations
Lagrangian conservation equations
Polar decomposition and frame-invariance
Exercises
Lagrangian meshes
Introduction
Governing equations
Weak form: principle of virtual power
Updated Lagrangian finite element discretization
Implementation
Corotational formulations
Total Lagrangian formulation
Total Lagrangian weak form
Finite element semidiscretization
Exercise
Constitutive models
Introduction
The stress-strain curve
One-dimensional elasticity
Nonlinear elasticity
One-dimensional plasticity
Multiaxial plasticity
Hyperelastic-plastic models
Viscoelasticity
Stress update algorithms
Continuum mechanics and constitutive models
Exercises
Solution methods and stability
Introduction
Explicit methods
Equilibrium solutions and implicit time integration
Linearization
Stability and continuation methods
Numerical stability
Material stability
Exercises
Arbitrary Lagrangian Eulerian formulations
Introduction
ALE continuum mechanics
Conservation laws in ALE description
ALE governing equations
Weak forms
Introduction to the Petrov-Galerkin method
Petrov-Galerkin formulation of momentum equation
Path-dependent materials
Linearization of the discrete equations
Mesh update equations
Numerical example: an elastic-plastic wave propagation problem
Total ALE formulations
Element technology
Introduction
Element performance
Element properties and patch tests
Q4 and volumetric locking
Multi-field weak forms and elements
Multi-field quadrilaterals
One-point quadrature elements
Examples
Stability
Exercises
Beams and shells
Introduction
Beam theories
Continuum-based beam
Analysis of CB beam
Continuum-based shell implementation
CB shell theory
Shear and membrane locking
Assumed strain elements
One-point quadrature elements
Exercises
Contact-impact
Introduction
Contact interface equations
Friction models
Weak forms
Finite element discretization
On explicit methods
Voigt notation
Norms
Element shape functions
Glossary
References
Index