Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics (eBook)

SHEN R. WU, PHD, has teaching and research interest in shell theory, the finite element method, the variational principle, and contact problems. In addition, he has extensive experience in the explicit finite element method, including the convergence theory, the diagonal mass matrix, the Reisner-Mindlin element, contact algorithms, material models, software development, and its applications. 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.

PART 1 Fundamentals1 Introduction

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