By A. B. Movchan

ISBN-10: 1860943187

ISBN-13: 9781860943188

This monograph presents a scientific research of asymptotic versions of continuum mechanics for composite buildings, that are both diluted or densely packed. textual content covers static difficulties of elasticity in dilute composites in addition to spectral difficulties.

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**Extra resources for Asymptotic models of fields in dilute and densely packed composites**

**Example text**

128) is due to this symmetry condition. We also note that, if af2, a?? are principal components of the stress tensor at infinity, then h +^2 ); l+

Complex potentials. ) 1{x(j>(z) - z(j>'{z) - ip(z)}. Here z = xi + 1x2. Let z = w(£) be the conformal mapping function N -(o = ^ + E | ? 87) S which establishes a correspondence between points of the R 2 \ g and points in the exterior of the unit disk |£| > 1. 89) with given complex coefficients a, 7. 91) (<0 m=^+£r=i $ Dipole fields in vector problems of linear elasticity 23 Let 5+ = {|£| < 1} and S~ = {|£| > 1}. Using the Cauchy theorem we deduce 2m JLa 2m ™ -£ JL°-£ 2m JL a - £ i and similarly 2m 1

1 r / 2/ 2 f i 1 ea2)p/m. 5B). Let d be a period of the array. 175) with unknown amplitudes u,v. 174) we have { (w 2 m! - 2c)u + c(l + e-ikod)v = 0, ikod )u + (w 2 m 2 - 2c)v = 0. c ( l 4. e ^ ^' ' 50 Long and close range interaction within elastic structures Fig. 6 Acoustic and optical bands for a one-dimensional array of particles connected by linear springs a = 1, m i = 1, m,2 — 2 and c = 10. This system has a non-trivial solution if and only if the following equation holds mim 2 w 4 - 2c(mi + m 2 )w 2 + 2c 2 (l - cos(k0d)) = 0.

### Asymptotic models of fields in dilute and densely packed composites by A. B. Movchan

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