Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics
1. Edition October 2012
352 Pages, Hardcover
Wiley & Sons Ltd
A systematic introduction to the theories and formulations of
the explicit finite element method
As numerical technology continues to grow and evolve with
industrial applications, understanding the explicit finite element
method has become increasingly important, particularly in the areas
of crashworthiness, metal forming, and impact engineering.
Introduction to the Explicit Finite Element Method for
Nonlinear Transient Dynamics is the first book to address
specifically what is now accepted as the most successful numerical
tool for nonlinear transient dynamics. The book aids readers in
mastering the explicit finite element method and programming code
without requiring extensive background knowledge of the general
finite element.
The authors present topics relating to the variational
principle, numerical procedure, mechanical formulation, and
fundamental achievements of the convergence theory. In addition,
key topics and techniques are provided in four clearly organized
sections:
* Fundamentals explores a framework of the explicit
finite element method for nonlinear transient dynamics and
highlights achievements related to the convergence theory
* Element Technology discusses four-node,
three-node, eight-node, and two-node element theories
* Material Models outlines models of plasticity and
other nonlinear materials as well as the mechanics model of ductile
damage
* Contact and Constraint Conditions covers subjects
related to three-dimensional surface contact, with examples solved
analytically, as well as discussions on kinematic constraint
conditions
Throughout the book, vivid figures illustrate the ideas and key
features of the explicit finite element method. Examples clearly
present results, featuring both theoretical assessments and
industrial applications.
Introduction to the Explicit Finite Element Method for
Nonlinear Transient Dynamics is an ideal book for both
engineers who require more theoretical discussions and for
theoreticians searching for interesting and challenging research
topics. The book also serves as an excellent resource for courses
on applied mathematics, applied mechanics, and numerical methods at
the graduate level.
1.1 Era of Simulation and Computer Aided Engineering
1.2 Preliminaries
2 Framework of Explicit Finite Element Method for Nonlinear Transient Dynamics
2.1 Transient Structural Dynamics
2.2 Variational Principles for Transient Dynamics
2.3 Finite Element Equations and the Explicit Procedures
2.4 Main Features of the Explicit Finite Element Method
2.5 Assessment of Explicit Finite Element Method
PART 2 Element Technology
3 Four-Node Shell Element (Reissner-Mindlin Plate Theory)
3.1 Fundamentals of Plates and Shells
3.2 Linear Theory of R-M Plate
3.3 Interpolation for Four-Node R-M Plate Element
3.4 Reduced Integration and Selective Reduced Integration
3.5 Perturbation Hourglass Control - Belytschko-Tsay (B-T) Element
3.6 Physical Hourglass Control - Belytschko-Leviathan (B-L) (QPH) Element
3.7 Shear Projection Method - Bathe-Dvorkin (B-D) Element
3.8 Assessment of Four-Node R-M Plate Element
4 Three-Node Shell Element (Reissner-Mindlin Plate Theory)
4.1 Fundamentals of a Three-Node C0 Element
4.2 Decomposition Method for C0 Triangular Element with One Point Integration
4.3 Discrete Kirchhoff Triangular (DKT) Element
4.4 Assessment of Three-Node R-M Plate Element
5 Eight-Node Solid Element
5.1 Trilinear Interpolation for the Eight-Node Hexahedron Element
5.2 Locking Issues of the Eight-Node Solid Element
5.3 One- Point Reduced Integration and the Perturbed Hourglass Control
5.4 Assumed Strain Method and Selective / Reduced Integration
5.5 Assumed Deviatoric Strain
5.6 An Enhanced Assumed Strain Method
5.7 Taylor Expansion of Assumed Strain about the Element Center
5.8 Evaluation of Eight-Node Solid Element
6 Two-Node Element
6.1 Truss and Rod Element
6.2 Timoshenko Beam Element
6.3 Spring Element
6.4 Spot Weld Element
PART 3 Material Models
7 Material Model of Plasticity
7.1 Fundamentals of Plasticity
7.2 Constitutive Equations
7.3 Software Implementation
7.4 Evaluation of Shell Elements with Plastic Deformation
8 Continuum Mechanics Model of Ductile Damage
8.1 Concept of Damage Mechanics
8.2 Gurson's Model
8.3 Chow's Isotropic Model of Continuum Damage Mechanics
8.4 Chow's Anisotropic Model of Continuum Damage Mechanics
9 Models of Nonlinear Materials
9.1 Vicoelasticity
9.2 Polymer and Engineering Plastics
9.3 Rubber
9.4 Foam
9.5 Honeycomb
9.6 Laminated Glazing
PART 4 Contact and Constraint Conditions
10 Three-Dimensional Surface Contact
10.1 Examples of Contact Problems
10.2 Description of Contact Conditions
10.3 Variational Principle for the Dynamic Contact Problem
10.4 Penalty Method and the Regularization of Variational Inequality
11 Numerical Procedures for Three-Dimensional Surface Contact
11.1 A Contact Algorithm with Slave Node Searching Master Segment
11.2 A Contact Algorithm with Master Segment Searching Slave Node
11.3 Method of Contact Territory and Defense Node
11.4 Pin- Ball Contact Algorithm
11.5 Edge (Line Segment) Contact
11.6 Evaluation of Contact Algorithm with Penalty Method
12 Kinematic Constraint Conditions
12.1 Rigid Wall
12.2 Rigid Body
12.3 Explicit Finite Element Procedure with Constraint Conditions
12.4 Application Examples with Constraint Conditions
LEI GU, PHD, has teaching and research interest in fracture mechanics, the finite element method, the mesh-free method, the optimization method, with extensive experience in the explicit finite element method such as software development, the diagonal mass matrix, robustness analysis, and its practical applications.
