Numerical Methods in Contact Mechanics

The book covers all 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 both for sequential and parallel computer architectures. The book is self-consistent and is intended for people working on implementation and improvement of contact algorithms in a finite element software. The book contains numerous examples and figures to make the material accessible for a broad audience. The book combines extended introductory parts with.

5.1.3. Application to non-differentiable functions.

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…