Topics in the mathematical modelling of composite materials / Andrej V. Cherkaev, Robert Kohn, editors.
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Full Text (via Springer) |
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| Other Authors: | , |
| Format: | eBook |
| Language: | English |
| Published: |
Cham, Switzerland :
Birkhäuser,
2018.
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| Series: | Modern Birkhäuser classics.
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| Subjects: |
Table of Contents:
- Intro; Contents; Introduction; References; On the Control of Coefficients in Partial Differential Equations; 1. Introduction; 2. The limit problem; 3. Physical interpretation; 4. Necessary conditions of optimality; References; Estimations of Homogenized Coefficients; 1. Introduction; 2. The model problem; 3. Bounds; 4. Comments; 5. References; H-Convergence; Foreword to the English Translation; 1 Notation; 2 Introductory Remarks; 3 The One-Dimensional Case; 4 Layering; 5 Definition of the H-Convergence; 6 Locality; 7 Two Fundamental Lemmata.
- Example 2.6. Nonspherical holes periodically distributed in volume in RNExample 2.9. Spherical holes periodically distributed on a hyperplane of RN; Generalizations; Example 2.14. Bilaplacian; Example 2.15. The operator -div(A grad) with constant coefficients; Example 2.16. The operator -div(A grad) with continuous coefficients; 3. Weak lower semicontinuity of the energy. Correctors; Generalizations; 4. Variational inequalities with highly oscillating obstacles; Generalizations; References; Afterword; Additional references; Design of Composite Plates of Extremal Rigidity.
- Part I. Optimal structures of composites1. Statement of the problem; 2. Derivation of the bounds for the stiffness; 3. The bounds for the stiffness of a composite; 4. Structures that saturate the bounds; 5. The analysis of obtained results; 6. Optimal design of a microstructure of composite plates with fixed volume fractions of phases; 7. Optimal distribution of materials throughout the plate; 8. Effect of optimization; 9. Sufficient conditions of absence of intermediate values of the thickness; References; Calculus of Variations and Homogenization; Introduction.
- PART I. PRELIMINARIESI.a. An Abstract Formulation of Relaxation; I.b. L. C. Young's Generalized Functions; I.c. Pontryagin's Principle; PART II. HOMOGENIZATION; PART III. GENERALIZED DOMAINS AND NECESSARY CONDITIONS OF OPTIMALITY; PART IV. EXAMPLE ONE; PART V. EXAMPLE TWO; REFERENCES; REFERENCES ADDED AT THE Tl1\IE OF THE TRANSLATION; Effective Characteristics of Composite Materials and the Optimal Design of Structural Elements; 1. Introduction; 2. On the specific features of optimal design problems for inhomogeneous bodies; 2.1. On the formulation of basic optimal design problems.
- 8 Irrelevance of the Boundary Conditions. Convergence of the Energy9 Sequential Compactness of M (α, β, Ω) for theTopology Induced by H -convergence; 10 Definition of the Corrector Matrix Pe; 11 Strong Approximation of grad ue. Correctors; References; References Added at the Time of the Translation; A Strange Term Coming from Nowhere; Introduction; 1. Dirichlet problems in perforated domains. Abstract framework; Comments on hypotheses (H.1) to (H.5); Generalizations; 2. Examples; Model example 2.1. Spherical holes periodically distributed in volume.