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|Additional Physical Format:||Print version:
Movchan, A.B. (Alexander B.).
Asymptotic models of fields in dilute and densely packed composites.
London : Imperial College Press ; River Edge, NJ : World Scientific Pub. [distributor], ©2002
|Material Type:||Document, Internet resource|
|Document Type:||Internet Resource, Computer File|
|All Authors / Contributors:||
A B Movchan; N V Movchan; C G Poulton
|Description:||1 online resource (xi, 190 pages) : illustrations|
|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; 18.104.22.168 Formulation of the problem; 22.214.171.124 The leading-order approximation; 126.96.36.199 Asymptotic formula for the energy; 1.1.3 The dipole matrix; 188.8.131.52 Definition of the dipole matrix; 184.108.40.206 Symmetry of the dipole matrix; 220.127.116.11 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; 18.104.22.168 Derivation of transmission conditions at the zero-thickness interface; 22.214.171.124 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; 126.96.36.199 Scalar problem; 188.8.131.52 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; 184.108.40.206 The leading term; 220.127.116.11 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; 18.104.22.168 Change of coordinates for the ""coating"" layer; 22.214.171.124 Problem for w(1); 126.96.36.199 Problem for w(2); 188.8.131.52 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.|
|Responsibility:||A.B. Movchan, N.V. Movchan, C.G. Poulton.|
"The material is interesting and based on results of recent research." Mathematical Reviews, 2003