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Viser: Mathematical Problems in Plasticity
Mathematical Problems in Plasticity
Roger Temam og L. S. Orde
(2019)
Sprog: Engelsk
Dover Publications, Incorporated
246,00 kr.
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Detaljer om varen
- Paperback: 368 sider
- Udgiver: Dover Publications, Incorporated (Januar 2019)
- Forfattere: Roger Temam og L. S. Orde
- ISBN: 9780486828275
This study of the problem of the equilibrium of a perfectly plastic body under specific conditions employs tools and methods that can be applied to other areas, including the mechanics of fracture and certain optimal control problems.
The three-part approach begins with an exploration of variational problems in plasticity theory, covering function spaces, concepts and results of convex analysis, formulation and duality of variational problems, limit analysis, and relaxation of the boundary condition. The second part examines the solution of variational problems in the finite-energy spaces; its topics include relaxation of the strain problem, duality between the generalized stresses and strains, and the existence of solutions to the generalized strain problem. The third and final part addresses asymptotic problems and problems in the theory of plates. The text includes a substantial bibliography and a new Preface and appendix by the author.
The three-part approach begins with an exploration of variational problems in plasticity theory, covering function spaces, concepts and results of convex analysis, formulation and duality of variational problems, limit analysis, and relaxation of the boundary condition. The second part examines the solution of variational problems in the finite-energy spaces; its topics include relaxation of the strain problem, duality between the generalized stresses and strains, and the existence of solutions to the generalized strain problem. The third and final part addresses asymptotic problems and problems in the theory of plates. The text includes a substantial bibliography and a new Preface and appendix by the author.
Table of Contents Preface 2018 Foreword
Chapter I Variational problems in plasticity theory Introduction
1. Function spaces
2. Convex analysis--a review of some basic concepts and results
3. Formulation of the variational problems of plasticity theory
4. Duality of the variational problems
5. Limit Analysis
6. Relaxation of the boundary condition
Chapter II Solution of the variational problems in the finite-energy spaces Introduction
1. Further results on the space LD (<>)
2. The space BD(<>) (I)
3. The space BD(<>) (II)
4. Convex functions of a measure
5. Convex functionals of a measure
6. Example of a convex function of a measure: relaxation of the strain problem
7. Duality between the generalised stresses and strains
8. Existence of solutions to the generalised strain problem
Chapter III Asymptotic problems and problems in the theory of plates Introduction
1. Some asymptotic problems: problems of imperfectly plastic bodies
2. Some problems in the theory of plates Principal Notations Index Bibliography Appendix
Chapter I Variational problems in plasticity theory Introduction
1. Function spaces
2. Convex analysis--a review of some basic concepts and results
3. Formulation of the variational problems of plasticity theory
4. Duality of the variational problems
5. Limit Analysis
6. Relaxation of the boundary condition
Chapter II Solution of the variational problems in the finite-energy spaces Introduction
1. Further results on the space LD (<>)
2. The space BD(<>) (I)
3. The space BD(<>) (II)
4. Convex functions of a measure
5. Convex functionals of a measure
6. Example of a convex function of a measure: relaxation of the strain problem
7. Duality between the generalised stresses and strains
8. Existence of solutions to the generalised strain problem
Chapter III Asymptotic problems and problems in the theory of plates Introduction
1. Some asymptotic problems: problems of imperfectly plastic bodies
2. Some problems in the theory of plates Principal Notations Index Bibliography Appendix
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