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Asynchronous Variational Integration of Structural Collision Dynamics

Sebastian Wolff

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ISBN 10: 3838130464 / ISBN 13: 9783838130460
Published by Sudwestdeutscher Verlag Fur Hochschulschriften AG
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300 pages. Dimensions: 8.7in. x 5.9in. x 0.7in.The growing power of modern workstations enables engineers to simulate more and more complex mechanical models by computers. In particular, nonlinear problems from structural dynamics are computationally intensive. Hence, there is ongoing demand for improvement of existing algorithms. This PhD thesis deals with the simulation of the dynamics of flexible bodies subject to constitutive and geometrical nonlinearities, as well as discontinuous phenomena arising from collisions. Procedures covered by this book are: Hamiltons principle, properties of variational mechanics, explicit variational integrators, treatment of holonomic and unilateral constraints, finite elements with continuous assumed gradients, asynchronous integration, variable time steps, collision detection and asynchronous contact with friction. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Bookseller Inventory # 9783838130460

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Bibliographic Details

Title: Asynchronous Variational Integration of ...

Publisher: Sudwestdeutscher Verlag Fur Hochschulschriften AG

Binding: Paperback

Book Condition:New

Book Type: Paperback

About this title

Synopsis:

The growing power of modern workstations enables engineers to simulate more and more complex mechanical models by computers. In particular, nonlinear problems from structural dynamics are computationally intensive. Hence, there is ongoing demand for improvement of existing algorithms. This PhD thesis deals with the simulation of the dynamics of flexible bodies subject to constitutive and geometrical nonlinearities, as well as discontinuous phenomena arising from collisions. Procedures covered by this book are: Hamilton's principle, properties of variational mechanics, explicit variational integrators, treatment of holonomic and unilateral constraints, finite elements with continuous assumed gradients, asynchronous integration, variable time steps, collision detection and asynchronous contact with friction.

From the Inside Flap:

The growing power of modern workstations enables engineers to simulate more and more complex mechanical models by computers. In particular, nonlinear problems from structural dynamics are computationally intensive. Hence, there is ongoing demand in the development of new and improvement of existing algorithms. The present thesis deals with the simulation of the dynamics of flexible bodies subject to material and geometrical nonlinearities, as well as discontinuous phenomena arising from collisions.

The equation of motion is discretized following the principle of variational integration, by what conservation laws of the continuous problem are valid in the discrete model. Existing approaches are presented. By combination of different procedures a mollified implicit-explicit algorithm is developed. It allows larger critical time steps and is particular suited for problems with non-dominant nonlinearities. The presentation of variational integrators includes the temporal discretization of holonomic and unilateral constraints.
The spatial discretization is performed by a modified finite element method. The accuracy of isoparametric elements is increased by enforcing stress continuity locally. This happens by the assumption of a continuously interpolated deformation gradient. The stability of the formulation is discussed in detail.
For the temporal discretization an asynchronous strategy is employed. The equation of motion is integrated explicitly, whereby some critical time step length must not be exceeded. Asynchronous methods apply individual time steps to each spatial domain. Substructures with softer material behaviour or larger finite elements can, therefore, be integrated by a larger time step. The thesis develops strategies to estimate the local time step size for the new element formulation and to efficiently treat nodal restraint conditions. It studies, how temporally-adaptive step sizes influence stability and accuracy.
Furthermore, this work presents procedures for spatial discretization and detection of collision problems. In particular, the concept of distance fields is enhanced in this respect. The contact conditions from impenetrability and friction are enforced by discontinuous velocity changes in a spatially asynchronous and temporally adaptive manner.
Contents

1 Introduction

2 Variational mechanics

2.1 Introduction
2.2 Preliminaries
2.3 Principle of Hamilton
2.4 Preserved quantities
2.5 Example

3 Variational integrators

3.1 Introduction
3.2 Geometric integrators
3.3 Discrete Euler-Lagrange equation
3.4 Preserved discrete quantities
3.5 Error analysis
3.6 Linear stability analysis
3.7 Example integrators
3.8 Constraints
3.9 Examples

4 Continuous assumed gradient method

4.1 Introduction
4.2 Fundamentals of continuum mechanics
4.3 Finite element interpolation of the continuum
4.4 Assumed gradient field
4.5 Regular mesh generation
4.6 Nodal integration
4.7 Smoothed Finite Element Method
4.8 Stable interpolation schemes
4.9 Implementation
4.10 Error analysis
4.11 Examples

5 Asynchronous variational integration

5.1 Introduction
5.2 Asynchronous Euler scheme
5.3 Discretization of the space-time integral
5.4 Nodal restraints
5.5 Estimating the time step length
5.6 Example

6 Variable step size integration

6.1 Introduction
6.2 Explicit symplectic energy momentum integration
6.3 Time transformations
6.4 Variational kick and drift operators
6.5 Asynchronous variable time steps
6.6 Example time step functions
6.7 Time step selection and solution
6.8 Examples

7 Collision dynamics

7.1 Introduction
7.2 Contact mechanics
7.3 Distance field
7.4 Asynchronous collisions
7.5 Examples

8 Summary

Appendix

A Verification of CAG elements
B Gradient interpolating functions of CAG elements
C Variations on the contact interface
D Spatial discretization of the contact boundary
E Collision detection

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