The boundary integral approach to static and dynamic contact problems [electronic resource] : equality and inequality methods / H. Antes, P.D. Panagiotopoulos.
The fields of boundary integral equations and of inequality problems, or more gen erally, of nonsmooth mechanics, have seen, in a remarkably short time, a considerable development in mathematics and in theoretical and applied mechanics. The engineering sciences have also benefited from these develop...
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Full Text (via Springer) |
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
Basel ; Boston :
Birkhäuser,
1992.
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| Series: | International series of numerical mathematics ;
v. 108. |
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Table of Contents:
- Guidelines for the Reader
- Ch. 1. Introductory Material. 1.1. On the Evolution of the B.I.E.M./B.E.M. 1.2. Elements of Nonsmooth Analysis. 1.2.1. Elements of Nonsmooth-Convex Analysis. 1.2.2. Elements of Nonsmooth-Nonconvex Analysis. 1.3. Contact Problems. 1.3.1. Monotone Multivalued Boundary and Interface Conditions. Pointwise Formulations. 1.3.2. Extensions of the Monotone Multivalued Boundary Conditions to Function Spaces. 1.3.3. Nonmonotone Multivalued Boundary Conditions. 1.4. Bilateral and Unilateral Problems. 1.4.1. Variational Formulations. 1.5. Existence Results for Variational and Hemivariational Inequalities
- Ch. 2. The Direct and Indirect B.I.E.M. for Bilateral Problems. 2.1. The B.V.P. of Linear Elasticity. 2.2. The Method of Weighted Residuals. 2.3. Generalized Variational Principles. 2.4. The Use of Reciprocal Theorems. 2.5. The Singularity Method (Indirect Method)
- Ch. 3. Boundary Integral Formulations for Some Special Elastostatic B.V. Ps.
- 3.1. Bending of Beams and Stretching of Bars. 3.2. A Direct B.I.E.M. for Kirchhoff Plates. 3.3. A Direct B.I.E.M. for Reissner Plates
- Ch. 4. On the Numerical Implementation of Boundary Element Equations. 4.1. General Methods. 4.2. Kirchhoff Plate Boundary Element Equations by the Point Collocation Method. 4.3. The Galerkin B.E.M. in Reissner Plate Theory
- Ch. 5. Extension to Dynamic Problems. 5.1. Generalities. 5.2. Steady State and Harmonic Problems. 5.3. Numerical Applications. 5.3.1. Convergence Studies and Cut-off Errors. 5.3.2. Noise Distribution Around 2-D Barrier Models. 5.4. Time Domain Formulation for Transient Problems. 5.4.1. Wave Propagation in 2-D Elastic Media. 5.4.2. Sound Pressure Waves in 3-D Acoustics and Numerical Applications
- Ch. 6. Dynamic Interaction Problems. 6.1. Bilateral Coupling of Elastic Structures and Domains. 6.2. Fluid-Structure Interaction. 6.3. Unilateral Contact Problems. 6.3.1. Dynamical Problems. The Trial and Error Method.
- 6.3.2. Examples: Elastic Massive Foundations on Elastic
- Ch. 7. B.I. Formulations for the Signorini-Fichera Inequality Problem. 7.1. Primal, Dual and Mixed Formulations of the B.V.P. 7.2. Integral Formulation with Respect to the Tractions of the Contact Area. 7.3. Integral Formulation with Respect to the Displacements of the Contact Area. 7.4. The Numerical Treatment
- Ch. 8. Mathematical Study of the B.I. Formulations of the Signorini-Fichera B.V.P. 8.1. The Signorini-Fichera B.V.P.: The Multivalued B.I.E. with Respect to the Boundary Displacements. 8.2. The Signorini-Fichera B.V.P.: The Multivalued B.I.E. with Respect to the Boundary Tractions
- Ch. 9. Boundary Integral Formulation of the Frictional Unilateral Contact B.V.P. 9.1. The Signorini Problem with Given Friction. Primal Problem, Mixed Problem and Approximation Results. 9.2. The Derivation of a Multivalued B.I.E. for the Signorini Problem with Given Friction. 9.3. On the Coulomb's Friction Problem. Numerical Results.
- Ch. 10. Boundary Integral Formulations for the Monotone Multivalued Boundary Conditions. 10.1. Convex Problems. Primal, Dual and Mixed Problems. 10.2. The Multivalued B.I.E. with Respect to the Boundary Tractions on [Gamma][subscript 3]. 10.3. The Multivalued B.I.E. with Respect to the Displacements u on [Gamma][subscript 3]. 10.4. Certain Semicoercive Multivalued B.I. Es. Existence Results
- Ch. 11. Elastodynamic Unilateral Problems. A B.I.E. Approach. 11.1. The Time Discretization Scheme. Time-Difference Multivalued B.I. Es. 11.2. Numerical Applications
- Ch. 12. Nonconvex Unilateral Contact Problems. 12.1. A Boundary Integral Equation with Respect to the Boundary Tractions. 12.2. A Multivalued Boundary Integral Formulation with Respect to the Displacements on [Gamma][subscript 3]. 12.3. On the Numerical Treatment of Nonmonotone (Zigzag) Multivalued Contact Laws. A New Efficient Algorithm.
- 12.4. A Numerical Application: The Nonmonotone Friction and the Adhesive Contact Problem with Debonding. A Fixed Point Type Algorithm. 12.5. A Short Note on Certain Coercive and Semicoercive Nonconvex Unilateral Contact Problems
- Ch. 13. Miscellanea. 13.1. Unilateral Contact and Friction in Cracks. A General Indirect B.I.E.M. for Inequality Problems. 13.2. Debonding and Delamination in Adhesively Bonded Cracks. 13.3. Fractal Interfaces and Boundaries. 13.4. A Neurocomputing Approach to the Multivalued B.I. Es of the Inequality Contact Problems. 13.5. A Supervised Learning Approach to the Parameter Identification in Contact Problems.