Asymptotic models of fields in dilute and densely packed composites /
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| Author / Creator: | Movchan, A. B. (Alexander B.) |
|---|---|
| Imprint: | London : Imperial College Press ; River Edge, NJ : World Scientific Pub. [distributor], ©2002. |
| Description: | 1 online resource (xi, 190 pages) : illustrations |
| Language: | English |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11185977 |
Table of Contents:
- Preface; Contents; Chapter 1 Long and close range interaction within elastic structures; 1.1 Dilute composite structures. Scalar problems; 1.1.1 An elementary example. Motivation; 1.1.2 Asymptotic algorithm involving a boundary layer; 1.1.2.1 Formulation of the problem; 1.1.2.2 The leading-order approximation; 1.1.2.3 Asymptotic formula for the energy; 1.1.3 The dipole matrix; 1.1.3.1 Definition of the dipole matrix; 1.1.3.2 Symmetry of the dipole matrix; 1.1.3.3 The energy asymptotics for a body with a small void; 1.1.4 Dipole matrix for a 2D void in an infinite plane.
- 1.1.5 Dipole matrices for inclusions1.1.6 A note on homogenization of dilute periodic structures; 1.2 Dipole fields in vector problems of linear elasticity; 1.2.1 Definitions and governing equations; 1.2.2 Physical interpretation; 1.2.3 Evaluation of the elements of the dipole matrix; 1.2.4 Examples; 1.2.5 The energy equivalent voids; 1.3 Circular elastic inclusions; 1.3.1 Inclusions with perfect bonding at the interface; 1.3.2 Dipole tensors for imperfectly bonded inclusions; 1.3.2.1 Derivation of transmission conditions at the zero-thickness interface; 1.3.2.2 Neutral coated inclusions.
- 1.4 Close-range contact between elastic inclusions1.4.1 Governing equations; 1.4.2 Complex potentials; 1.4.3 Analysis for two circular elastic inclusions; 1.4.4 Square array of circular inclusions; 1.4.5 Integral approximation for the multipole coefficients. Inclusions close to touching; 1.4.5.1 Scalar problem; 1.4.5.2 Vector problem; 1.5 Discrete lattice approximations; 1.5.1 Illustrative one-dimensional example; 1.5.2 Two-dimensional array of obstacles; Chapter 2 Dipole tensors in spectral problems of elasticity; 2.1 Asymptotic behaviour of fields near the vertex of a thin conical inclusion.
- 2.1.1 Spectral problem on a unit sphere2.1.2 Boundary layer solution; 2.1.2.1 The leading term; 2.1.2.2 Problem for w(2); 2.1.3 Stress singularity exponent A2; 2.2 Imperfect interface. ""Coated"" conical inclusion; 2.2.1 Formulation of the problem; 2.2.2 Boundary layer solution; 2.2.2.1 Change of coordinates for the ""coating"" layer; 2.2.2.2 Problem for w(1); 2.2.2.3 Problem for w(2); 2.2.2.4 Asymptotic behaviour of w(2) at infinity; 2.2.3 Stress singularity exponent A2; 2.2.4 Some examples. Discussion and conclusions; Chapter 3 Multipole methods and homogenisation in two-dimensions.
- 3.1 The method of Rayleigh for static problems3.1.1 The multipole expansion and effective properties; 3.1.2 Solution to the static problem; 3.2 The spectral problem; 3.2.1 Formulation and Bloch waves; 3.2.2 The dynamic multipole method; 3.2.3 The dynamic lattice sums; 3.2.4 The integral equation and the Rayleigh identity; 3.2.5 The dipole approximation; 3.3 The singularly perturbed problem and non-commuting limits; 3.3.1 The Neumann problem and non-commuting limits; 3.3.2 The Dirichlet problem and source neutrality; 3.4 Non-commuting limits for the effective properties.