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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 s...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
London :
Wiley,
2013.
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| Colección: | ISTE.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.