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Nonlinear Finite Elements for Continua and Structures

Author: Ted Belytschko; Wing Kam Liu; Brian Moran; Khalil Elkhodary
Publisher: Hoboken : Wiley, 2013.
Edition/Format:   eBook : Document : English : 2nd edView all editions and formats
Database:WorldCat
Summary:
This updated and expanded edition of the bestselling textbook provides a comprehensive introduction to the methods and theory of nonlinear finite element analysis. New material provides a concise introduction to some of the cutting-edge methods that have evolved in recent years in the field of nonlinear finite element modeling, and includes the eXtended finite element method (XFEM), multiresolution continuum theory  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Belytschko, Ted.
Nonlinear Finite Elements for Continua and Structures.
Hoboken : Wiley, ©2013
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Ted Belytschko; Wing Kam Liu; Brian Moran; Khalil Elkhodary
ISBN: 9781118700051 1118700058
OCLC Number: 862049684
Notes: 3.5.9 Conservation of Energy.
Description: 1 online resource (834 pages)
Contents: Nonlinear Finite Elements for Continua and Structures Second Edition; Copyright; Contents; Foreword; Preface; List of Boxes; 1 Introduction; 1.1 Nonlinear Finite Elements in Design; 1.2 Related Books and a Brief History of Nonlinear Finite Elements; 1.3 Notation; 1.3.1 Indicial Notation; 1.3.2 Tensor Notation; 1.3.3 Functions; 1.3.4 Matrix Notation; 1.4 Mesh Descriptions; 1.5 Classification of Partial Differential Equations; 1.6 Exercises; 2 Lagrangian and Eulerian Finite Elements in One Dimension; 2.1 Introduction; 2.2 Governing Equations for Total Lagrangian Formulation; 2.2.1 Nomenclature. 2.2.2 Motion and Strain Measure2.2.3 Stress Measure; 2.2.4 Governing Equations; 2.2.5 Momentum Equation in Terms of Displacements; 2.2.6 Continuity of Functions; 2.2.7 Fundamental Theorem of Calculus; 2.3 Weak Form for Total Lagrangian Formulation; 2.3.1 Strong Form to Weak Form; 2.3.2 Weak Form to Strong Form; 2.3.3 Physical Names of Virtual Work Terms; 2.3.4 Principle of Virtual Work; 2.4 Finite Element Discretization in Total Lagrangian Formulation; 2.4.1 Finite Element Approximations; 2.4.2 Nodal Forces; 2.4.3 Semidiscrete Equations; 2.4.4 Initial Conditions. 2.4.5 Least-Square Fit to Initial Conditions2.4.6 Diagonal Mass Matrix; 2.5 Element and Global Matrices; 2.6 Governing Equations for Updated Lagrangian Formulation; 2.6.1 Boundary and Interior Continuity Conditions; 2.6.2 Initial Conditions; 2.7 Weak Form for Updated Lagrangian Formulation; 2.8 Element Equations for Updated Lagrangian Formulation; 2.8.1 Finite Element Approximation; 2.8.2 Element Coordinates; 2.8.3 Internal and External Nodal Forces; 2.8.4 Mass Matrix; 2.8.5 Equivalence of Updated and Total Lagrangian Formulations; 2.8.6 Assembly, Boundary Conditions and Initial Conditions. 2.8.7 Mesh Distortion2.9 Governing Equations for Eulerian Formulation; 2.10 Weak Forms for Eulerian Mesh Equations; 2.11 Finite Element Equations; 2.11.1 Momentum Equation; 2.12 Solution Methods; 2.13 Summary; 2.14 Exercises; 3 Continuum Mechanics; 3.1 Introduction; 3.2 Deformation and Motion; 3.2.1 Definitions; 3.2.2 Eulerian and Lagrangian Coordinates; 3.2.3 Motion; 3.2.4 Eulerian and Lagrangian Descriptions; 3.2.5 Displacement, Velocity and Acceleration; 3.2.6 Deformation Gradient; 3.2.7 Conditions on Motion; 3.2.8 Rigid Body Rotation and Coordinate Transformations; 3.3 Strain Measures. 3.3.1 Green Strain Tensor3.3.2 Rate-of-Deformation; 3.3.3 Rate-of-Deformation in Terms of Rate of Green Strain; 3.4 Stress Measures; 3.4.1 Definitions of Stresses; 3.4.2 Transformation between Stresses; 3.4.3 Corotational Stress and Rate-of-Deformation; 3.5 Conservation Equations; 3.5.1 Conservation Laws; 3.5.2 Gauss's Theorem; 3.5.3 Material Time Derivative of an Integral and Reynolds' Transport Theorem; 3.5.4 Mass Conservation; 3.5.5 Conservation of Linear Momentum; 3.5.6 Equilibrium Equation; 3.5.7 Reynolds' Theorem for a Density-Weighted Integrand; 3.5.8 Conservation of Angular Momentum.

Abstract:

This updated and expanded edition of the bestselling textbook provides a comprehensive introduction to the methods and theory of nonlinear finite element analysis. New material provides a concise introduction to some of the cutting-edge methods that have evolved in recent years in the field of nonlinear finite element modeling, and includes the eXtended finite element method (XFEM), multiresolution continuum theory for multiscale microstructures, and dislocation-density-based crystalline plasticity. Nonlinear Finite Elements for Continua and Structures, Second Edition focuses o.

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