Numerical methods in contact mechanics / Vladislav A. Yastrebov.

Format:

Book

Author/Creator:

Yastrebov, Vladislav A.

Series:

ISTE

Numerical methods in engineering series

Language:

English

Subjects (All):

Nonlinear mechanics.

Friction.

Physical Description:

1 online resource (412 p.)

Edition:

1st ed.

Place of Publication:

London : ISTE, 2013.

Language Note:

English

Summary:

Computational contact mechanics is a broad topic which brings together algorithmic, geometrical, optimization and numerical aspects for a robust, fast and accurate treatment of contact problems.This book covers all the basic ingredients of contact and computational contact mechanics: from efficient contact detection algorithms and classical optimization methods to new developments in contact kinematics and resolution schemes for both sequential and parallel computer architectures. The book is self-contained and intended for people working on the implementation and improvement of conta

Contents:

Title Page; Contents; Foreword; Preface; Notations; Chapter 1. Introduction to Computational Contact; 1.1. Historical remark; 1.1.1. The augmented Lagrangian method; 1.2. Basics of the numerical treatment of contact problems; 1.2.1. Contact detection; 1.2.2. Contact discretization; 1.2.3. Contact resolution; Chapter 2. Geometry in ContactMechanics; 2.1. Introduction; 2.2. Interaction between contacting surfaces; 2.2.1. Some notations; 2.2.2. Normal gap; 2.3. Variations of geometrical quantities; 2.3.1. First-order variations; 2.3.2. Second-order variations; 2.4. Numerical validation

2.5. Discretized geometry2.5.1. Shape functions and finite elements; 2.5.2. Geometry of contact elements; 2.6. Enrichment of contact geometry; 2.6.1. Derivation of enriched quantities; 2.6.2. Variations of geometrical quantities; 2.6.3. Example of enrichment; 2.6.4. Concluding remarks; Chapter 3. Contact Detection; 3.1. Introduction; 3.2. All-to-all detection; 3.2.1. Preliminary phase; 3.2.2. Detection phase; 3.3. Bucket sort detection; 3.3.1. Preliminary phase; 3.3.2. Numerical tests; 3.3.3. Detection phase; 3.3.4. Multi-face contact elements; 3.3.5. Improvements

3.4. Case of unknown master-slave3.5. Parallel contact detection; 3.5.1. General presentation; 3.5.2. Single detection, multiple resolution approach; 3.5.3. Multiple detection, multiple resolution approach; 3.5.4. Scalability test; 3.6. Conclusion; Chapter 4. Formulation of Contact Problems; 4.1. Contact of a deformable solid with a rigid plane; 4.1.1. Unilateral contact with a rigid plane; 4.1.2. Interpretation of contact conditions; 4.1.3. Friction; 4.1.4. An analogy with plastic flow

4.1.5. Interpretation of frictional conditions Idea 4.2. Replacement of frictional contact conditions by Dirichlet- Neumann boun4.2. Contact of a deformable solid with an arbitrary rigid surface; 4.2.1. Non-penetration condition; 4.2.2. Hertz-Signorini-Moreau's contact conditions; 4.2.3. Interpretation of contact conditions; 4.2.4. Frictional conditions and their interpretation; 4.2.5. Example: rheology of a one-dimensional frictional system on a sinusoidal rigid substrate; 4.3. Contact between deformable solids; 4.3.1. General formulation and variational inequality

4.3.2. Remarks on Coulomb's frictional law4.4. Variational equality and resolution methods; 4.5. Penalty method; 4.5.1. Frictionless case; 4.5.2. Example; 4.5.3. Nonlinear penalty functions; 4.5.4. Frictional case; 4.6. Method of Lagrange multipliers; 4.6.1. Frictionless case; 4.6.2. Frictional case; 4.6.3. Example; 4.7. Augmented LagrangianMethod; 4.7.1. Introduction; 4.7.2. Application to contact problems; 4.7.3. Example; Chapter 5. Numerical Procedures; 5.1. Newton's method; 5.1.1. One-dimensional Newton's method; 5.1.2. Multidimensional Newton's method

5.1.3. Application to non-differentiable functions

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

1-118-64797-1

1-299-24250-2

1-118-64804-8

OCLC:

829460538