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ASYMPTOTIC MODELS OF FIELDS IN DILUTE AND DENSELY PACKED COMPOSITES
by A B Movchan, N V Movchan & C G Poulton (University of Liverpool, UK)
This monograph provides a systematic study of asymptotic models of continuum mechanics for composite structures, which are either dilute (for example, two-phase composite structures with small inclusions) or densely packed (in this case inclusions may be close to touching). It is based on the results of recent research and includes a comprehensive analysis of dipole and multipole fields associated with defects in solids. The text covers static problems of elasticity in dilute composites as well as spectral problems. Applications of the mathematical models included in the book are in damage mechanics and in problems of design of composite structures that can be used as filters or polarisers of elastic waves.
Dipole tensors are defined in Chapter 1 both for scalar boundary value problems for the Laplacian and for vector problems of elasticity. In Chapter 2 the dipole tensors are used in spectral problems involving domains with small defects. Chapter 3 introduces a multipole method for static problems (both electrostatics and elasticity) in composite structures containing doubly periodic arrays of circular inclusions. Chapter 4 presents a multipole method for eigenvalue problems of electromagnetism and elasticity.
Contents:
- Long and Close Range Interaction within Elastic Structures
- Dipole
Tensors in Spectral Problems of Elasticity
- Multipole Methods and Homogenisation in Two-Dimensions
Readership: Graduate students and researchers in applied mathematics and
mechanics who are interested in asymptotic theory of partial differential equations, spectral theory, and mathematical models of composite structures.
"The material is interesting and based on results of recent research."
| 204pp |
Pub. date: Nov 2002 |
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