TY  - BOOK
AU  - Belytschko,Ted
AU  - Liu,W.K.
AU  - Moran,B.
AU  - Elkhodary,Khalil I.
TI  - Nonlinear finite elements for continua and structures
SN  - 9781118632703 (pbk.)
PY  - 2014///
CY  - Chichester, West Sussex
PB  - John Wiley & Sons, Ltd.
KW  - Finite element method
KW  - Continuum mechanics
KW  - Structural analysis (Engineering)
N1  - Includes bibliographical references and index; 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 -- XFEM -- INTRODUCTION -- PARTITION OF UNITY AND ENRICHMENTS -- ONE DIMENSIONAL XFEM -- MULTI-DIMENSION XFEM -- WEAK AND STRONG FORMS -- DISCRETE EQUATIONS -- LEVEL SET METHOD -- XFEM IMPLEMENTATION STRATEGY -- INTEGRATION -- AN EXAMPLE OF XFEM SIMULATION -- EXERCISE -- Introduction to multiresolution theory -- MOTIVATION: MATERIALS ARE STRUCTURED CONTINUA -- BULK DEFORMATION OF MICROSTRUCTURED CONTINUA -- GENERALIZING MECHANICS TO BULK MICROSTRUCTURED CONTINUA -- MULTISCALE MICROSTRUCTURES AND THE MULTIRESOLUTION CONTINUUM THEORY -- GOVERNING EQUATIONS FOR MCT -- CONSTRUCTING MCT CONSTITUTIVE RELATIONSHIPS -- BASIC GUIDELINES FOR RVE MODELS -- FINITE ELEMENT IMPLEMENTATION OF MCT -- NUMERICAL EXAMPLE -- FUTURE RESEARCH DIRECTION OF MCT MODELING -- EXERCISES -- Single-crystal plasticity -- Introduction -- Crystallographic description of cubic and non-cubic crystals -- Atomic origins of plasticity and the burgers vector in single crystals -- Defining slip planes and directions in general single crystals -- Kinematics of single crystal plasticity -- Dislocation density evolution -- Stress required for dislocation motion -- Stress update in rate-dependent single-crystal plasticity -- Algorithm for rate-dependent dislocation-density based crystal plasticity -- Numerical example -- Exercises -- Appendix 1. Voigt notation -- Appendix 2. Norms -- Appendix 3. Element shape functions -- Appendix 4. Euler angles from pole figures -- Appendix 5. Example of dislocation density evolutionary equations
N2  - 'Focuses on the formulation and solution of the discrete equations for various classes of problems encountered in the application of the finite element method to solid and structural mechanics'--
UR  - http://catalogimages.wiley.com/images/db/jimages/9781118632703.jpg
ER  -