Large Displacement Finite Element Analysis

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This first chapter Introduction introduces the notations which will be used throughout the document. An introduction to kinematics is also given.

Chapter 2 recalls the Basic Equations in nonlinear dynamics. Different aspects are covered:

•	Material and spatial coordinates

•	Mesh description

•	Kinematic and kinetic descriptions

•	Stress rates and stresses in solids

•	Updated and total Lagrangian formulations

•	Equations of equilibrium

•	Principle of virtual power and the physical names of power terms

•	The small strain formulation is also introduced

The Finite Element Formulation of the virtual power principle is introduced in Chapter 3, leading to the discretized equations of equilibrium.

Chapter 4, Dynamic Analysis deals with time discretization and the integration schemes. Stability and time step concepts are also discussed.

Different finite element models are presented in Chapter 5, Element Library. Tetrahedral solid elements, hexahedral solid and solid-shell elements, 3-node and 4-node shell elements, 2-node truss and beam elements and spring elements are successively presented.

Chapter 6 deals with Kinematic Constraints, i.e. constraints placed on nodal velocities.

Linear Stability is introduced in Chapter 7.

The very important concept of Interfaces is considered in Chapter 8. Interfaces allow the solution of contact and impact conditions between two parts of a model. The different interface types available in RADIOSS are presented.

Material Laws and failure models are discussed in Chapter 9.

In Chapter 10 the formulations of different kinds of Monitored Volumes are presented in detail. Airbag theory is also developed.

Chapter 11, Static deals with the use of explicit algorithms to model quasi-static or static problems. Different approaches are discussed: slow dynamic computation, dynamic relaxation, viscous relaxation and energy discrete relaxation. The dynamic relaxation approach is developed. The DYREL and DAMP options are introduced in this chapter.

Chapter 12 concerns the presentation of the fundamentals in RADIOSS Parallelization.