Computational flexible multibody dynamics a differential-algebraic approach Bernd Simeon

Format:

Book

Author/Creator:

Simeon, Bernd

Series:

Differential-algebraic equations forum

Language:

English

Subjects (All):

Multibody systems.

Dynamics--Mathematical models.

Dynamics.

Mathematical physics.

Mathematics.

Numerical Analysis.

Mechanics.

Ordinary Differential Equations.

Partial Differential Equations.

Medical Subjects:

Mathematics.

Local Subjects:

Mathematics.

Numerical Analysis.

Mechanics.

Ordinary Differential Equations.

Partial Differential Equations.

Physical Description:

1 online resource

Place of Publication:

Berlin New York Springer ©2013

System Details:

PDF

text file

Summary:

This monograph, written from a numerical analysis perspective, aims to provide a comprehensive treatment of both the mathematical framework and the numerical methods for flexible multibody dynamics. Not only is this field permanently and rapidly growing, with various applications in aerospace engineering, biomechanics, robotics, and vehicle analysis, its foundations can also be built on reasonably established mathematical models. Regarding actual computations, great strides have been made over the last two decades, as sophisticated software packages are now capable of simulating highly complex structures with rigid and deformable components. The approach used in this book should benefit graduate students and scientists working in computational mechanics and related disciplines as well as those interested in time-dependent partial differential equations and heterogeneous problems with multiple time scales. Additionally, a number of open issues at the frontiers of research are addressed by taking a differential-algebraic approach and extending it to the notion of transient saddle point problems

Contents:

Mathematical Models. A Point of Departure Rigid Multibody Dynamics Elastic Motion Flexible Multibody Dynamics Numerical Methods. Spatial Discretization Stiff Mechanical System Time Integration Methods Numerical Case Studies

Machine generated contents note: 1. Point of Departure

1.1. Elastic Pendulum

1.1.1. Small Elastic Displacement

1.1.2. Floating Reference Frame

1.1.3. Galerkin Projection

1.1.4. Time Integration

1.2. Objectives

1.2.1. Treatment of Constraints

1.2.2. Discretization in Space and Time

1.3. Overview

2. Rigid Multibody Dynamics

2.1. Equations of Motion

2.1.1. Kinematics

2.1.2. Dynamics

2.1.3. Relation to Hamiltonian Systems

2.1.4. Remarks

2.2. Examples

2.2.1. Slider Crank

2.2.2. Newton-Euler Equations

2.2.3. Wheel Suspension

2.3. Differential-Algebraic Equations

2.3.1. Basic Types of DAEs

2.3.2. Index

2.3.3. Constraint Manifold and Local State Space Form

2.3.4. Solution Invariants versus Constraints

2.3.5. Differential-Algebraic Equations in Saddle Point Form

2.3.6. Remarks and Further References

2.4. Analysis of the Equations of Constrained Mechanical Motion

2.4.1. Index and Existence of Solutions

2.4.2. Minimax Characterization of Constraints

2.4.3. Influence of Perturbations

2.4.4. Alternative Formulations

2.4.5. Remarks

3. Elastic Motion

3.1. Basic Equations of an Elastic Body

3.1.1. Variational Formulation

3.1.2. Equations of Motion

3.1.3. Smoothness and Appropriate Function Spaces

3.1.4. Trace Space

3.2. Constraints in Linear Elasticity

3.2.1. Variational Formulation

3.2.2. Appropriate Function Spaces

3.3. Mathematical Analysis

3.3.1. Existence of Solutions

3.3.2. Influence of Perturbations

3.3.3. Remarks

3.4. Related Mathematical Models

3.4.1. Domain Decomposition

3.4.2. Dynamic Contact

3.4.3. Incompressible Elastic Body

4. Flexible Multibody Dynamics

4.1. Floating Reference Frame

4.1.1. Variational Formulation

4.1.2. Equations of Unconstrained Motion

4.1.3. Extensions and Special Cases

4.2. Constraints

4.2.1. Weak Form of Equations of Constrained Motion

4.2.2. Modeling Joints

4.2.3. Remarks

4.3. Flexible Multibody System

4.3.1. Variational Formulation

4.3.2. Equations of Motion

4.4. Special Bodies

4.4.1. Plane Strain and Plane Stress

4.4.2. Beam Model

4.5. Examples

4.5.1. Slider Crank

4.5.2. Truck Model

4.5.3. Pantograph and Catenary

4.6. Summary of Key Formulas in Part I

5. Spatial Discretization

5.1. Finite Element Approximation of Elastic Body

5.1.1. Unconstrained Equations

5.1.2. Constrained Equations of Motion

5.1.3. Remarks

5.2. Spatial Discretization of Flexible Multibody System

5.2.1. Galerkin Projection for Floating Reference Frame

5.2.2. Flexible Multibody System

5.2.3. Model Reduction

5.3. Examples

5.3.1. Slider Crank with Elastic Connecting Rod

5.3.2. Loading Area of Planar Truck Model

5.3.3. Pantograph and Catenary

6. Stiff Mechanical System

6.1. Elastic Pendulum Revisited

6.2. General Framework

6.3. State Space Form

6.3.1. Asymptotic Expansion

6.3.2. Elastic Pendulum

6.3.3. Remarks

6.4. Differential-Algebraic Case

6.4.1. Structure-Preserving Local Parametrization

6.4.2. Computational Method

7. Time Integration Methods

7.1. Overview on Time Integration Methods

7.1.1. Alternative Formulations of the Equations of Motion

7.1.2. Basic Discretization Schemes

7.2. BDF and Implicit Runge-Kutta Methods

7.2.1. Backward Differentiation Formulas

7.2.2. Error Analysis

7.2.3. Implicit Runge-Kutta Methods of Collocation Type

7.2.4. Application to Differential-Algebraic Equations

7.2.5. Solving Constrained Mechanical Systems in Practice

7.3. Order Reduction for Stiff Mechanical Systems

7.3.1. Beam under Point Load

7.3.2. Model Problem

7.3.3. Runge-Kutta Methods

7.3.4. Rosenbrock-Wanner Methods

7.3.5. BDF Methods

7.3.6. Nonlinear Test Equation

7.3.7. Remarks

7.4. Special Integration Methods

7.4.1. Generalized-α Method

7.4.2. Variant of the Implicit Midpoint Rule

8. Numerical Case Studies

8.1. Slider Crank I

8.2. Slider Crank II

8.3. Pantograph and Catenary

8.4. Planar Truck Model

8.5. 3D Trailer Frame

Notes:

Includes bibliographical references and index

Online resource; title from digital title page (viewed July 14, 2014)

Other Format:

Printed edition:

ISBN:

9783642351587

3642351581

3642351573

9783642351570

OCLC:

850922686

Access Restriction:

Restricted for use by site license