Introduction To The Explicit Finite Element Method For Nonlinear Transient Dynamics

This is the first book to specifically address the explicit finite element method for nonlinear transient dynamics. This book aids readers in mastering the explicit finite element method as well as programing a code without extensively reading the more general finite element books. It consists of 12 chapters within four sections including: the variational principles and formulation of the explicit finite element method for nonlinear transient dynamics; the finite element technology with 4-node and 3-node Reissner-Mindlin plate bending elements, the 8-node solid elements, etc.; plasticity and nonlinear material models; and contact algorithms and other kinematic constraint conditions.


Each chapter contains a list of carefully chosen references intended to help readers to further explore the related subjects.


The authors—who have extensive experience in theoretical research, software development and industrial engineering applications—have successfully provided a book for engineers and researchers who need information about the explicit finite element method in a straightforward and streamlined manner.


Additional reading and referencing of the fundamentals on finite element concepts or solution methods for static analysis will not be needed or required. Fundamental theories and methods are presented with rich information about recent developments not yet published in other finite element books.

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