Numerical methods in contact mechanics
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...
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| Hlavní autor: | |
|---|---|
| Médium: | E-kniha Kniha |
| Jazyk: | angličtina |
| Vydáno: |
Newark
WILEY
2013
John Wiley & Sons, Incorporated Wiley-Blackwell ISTE/Wiley |
| Vydání: | 1 |
| Edice: | Numerical methods in engineering series |
| Témata: | |
| ISBN: | 1118648048, 9781848215191, 9781118648049, 1848215193 |
| On-line přístup: | Získat plný text |
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Obsah:
- Numerical methods in contact mechanics -- Contents -- Foreword -- Preface -- Notations -- Chapter 1: Introduction to Computational Contact -- Chapter 2: Geometry in ContactMechanics -- Chapter 3: Contact Detection -- Chapter 4: Formulation of Contact Problems -- Chapter 5: Numerical Procedures -- Chapter 6: Numerical Examples -- Appendix 1: Vectors, Tensors and s-Structures -- Appendix 2: Variations of Geometrical Quantities -- Bibliography -- Index
- 5.5. Method of partial Dirichlet-Neumann boundary conditions -- 5.5.1. Description of the numerical technique -- 5.5.2. Frictionless case -- 5.5.3. Frictional case -- 5.5.4. Remarks -- 5.6. Technical details -- 5.6.1. Rigid master surface -- 5.6.2. Multi-face contact elements and smoothing techniques -- 5.6.3. Heterogeneous friction -- 5.6.4. Short remarks -- Chapter 6. Numerical Examples -- 6.1. Two dimensional problems -- 6.1.1. Indentation by a rigid flat punch -- 6.1.2. Elastic disk embedded in an elastic bored plane -- 6.1.3. Indentation of an elastic rectangle by a circular indenter -- 6.1.4. Axisymmetric deep cup drawing -- 6.1.5. Shallow ironing -- 6.1.6. Axisymmetric post-buckling of a thin-walled cylinder -- 6.2. Three-dimensional problems -- 6.2.1. Accordion post-buckling folding of a thin-walled tube -- 6.2.2. Hydrostatic extrusion of a square plate through a circular hole -- 6.2.3. Frictional sliding of a cube on a rigid plane -- Appendix 1. Vectors, Tensors and s-Structures -- A1.1. Fundamentals -- A1.2. Vector space basis -- A1.2.1. Transformation matrices, covariant and contravariant objects -- A1.2.2. Gradient operator or Hamilton's operator -- A1.3. Sub-basis, vector function of v-scalar argument -- A1.4. Tensors -- A1.5. Tensor as a linear operator on vector space -- A1.6. S-structures -- A1.6.1. Formal definition, notations and types -- A1.6.2. Simple operations -- A1.6.3. Invariant s-structures -- A1.6.4. Scalar products of v-vectors -- A1.6.5. Inverse v-vector -- A1.6.6. Isomorphism of s-space and tensor space -- A1.6.7. Tensor product of v-vectors -- A1.7. Reduced form of s-structures -- Appendix 2. Variations of Geometrical Quantities -- A2.1. First-order variations -- A2.1.1. Normal projection case -- A2.1.2. Shadow-projection case: infinitely remote emitter -- A2.1.3. Shadow-projection case: close emitter
- A2.2. Second-order variations -- A2.2.1. Normal projection case -- A2.2.2. Shadow-projection case: infinitely remote emitter -- A2.2.3. Shadow-projection case: close emitter -- Bibliography -- Index
- 4.1.5. Interpretation of frictional conditions Idea 4.2. Replacement of frictional contact conditions by Dirichlet- Neumann boun -- 4.2. 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 law -- 4.4. 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 -- 5.1.4. Subdifferentials and subgradients -- 5.1.5. Generalized Newton method -- 5.2. Return mapping algorithm -- 5.3. Finite element method -- 5.3.1. Introduction -- 5.3.2. Contact elements -- 5.3.3. Discretization of the contact interface -- 5.3.4. Virtual work for discretized contact interface -- 5.3.5. Linearization of equations -- 5.3.6. Example -- 5.4. Residual vectors and tangent matrices for contact elements -- 5.4.1. Penalty method: frictionless case -- 5.4.2. Penalty method: frictional case -- 5.4.3. Augmented Lagrangian method: frictionless case -- 5.4.4. Augmented Lagrangian method: frictional case
- Intro -- 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 geometry -- 2.5.1. 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-slave -- 3.5. 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