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 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.
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The material is interesting and based on results of recent research. -- Mathematical Reviews, 2003
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Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
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In this chapter we discuss an asymptotic scheme developed for perturbation problems modelling small defects in solids, as well as "thin bridge" problems associated with inclusions close to touching. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
stress singularity exponent, conical inclusion, perfectly bonded inclusion, dipole matrices, phononic band structure, bonded inclusions, dilute composites, asymptotic algorithm, circular inclusions, dipole tensors, doubly periodic array, multipole coefficients, equivalent voids, multipole method, lattice sums, ideal contact, elastic inclusions, imperfect interface, filling fraction, dipole matrix, asymptotic models, perfect bonding, boundary layer solution, elastic matrix, circular cavities Key Phrases - Capitalized Phrases (CAPs): (learn more)
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Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
In this chapter we discuss an asymptotic scheme developed for perturbation problems modelling small defects in solids, as well as "thin bridge" problems associated with inclusions close to touching. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
stress singularity exponent, conical inclusion, perfectly bonded inclusion, dipole matrices, phononic band structure, bonded inclusions, dilute composites, asymptotic algorithm, circular inclusions, dipole tensors, doubly periodic array, multipole coefficients, equivalent voids, multipole method, lattice sums, ideal contact, elastic inclusions, imperfect interface, filling fraction, dipole matrix, asymptotic models, perfect bonding, boundary layer solution, elastic matrix, circular cavities Key Phrases - Capitalized Phrases (CAPs): (learn more)
Lord Rayleigh, Keller's Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
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