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  • 1
    Electronic Resource
    Electronic Resource
    Book reviews (1996)
    Springer
    Pure and applied geophysics 146 (1996), S. 393-404 
    Details
    ISSN: 1420-9136
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00876499
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  • 2
    Electronic Resource
    Electronic Resource
    Effective Conductivity of Nonlinear Two-Phase Media: Homogenization and Two-Point Padé Approximants (2000)
    Springer
    Acta applicandae mathematicae 61 (2000), S. 295-315 
    Details
    ISSN: 1572-9036
    Keywords: effective properties ; homogenization ; composites ; conductivities ; bounds, Padé approximants ; continued fractions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The aim of this paper is a study of the quasilinear transport equation, for instance the stationary heat equation. For periodically microheterogeneous media asymptotic homogenization has been performed with the local problem formulated as a minimization problem. The Golden–Papanicolaou integral representation theorem and some bounds developed for the linear equation have been extended. Two-point Padé approximants have been used to calculate bounds. Examples are also provided.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006487103815
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  • 3
    Electronic Resource
    Electronic Resource
    S-Continued Fraction Method for the Investigation of a Complex Dielectric Constant of Two-Components Composite (1997)
    Springer
    Acta applicandae mathematicae 49 (1997), S. 55-83 
    Details
    ISSN: 1572-9036
    Keywords: composite medium ; bounds ; dielectric constants ; Stieltjes function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The aim of this contribution is to examine the S-continued fraction method of obtaining bounds on the effective dielectric constant εe of a two-phase composite for the case where the dielectric coefficients ε1and ε2 of both components are either complex or real. The starting point for our study is a power expansion of εe (z) at(z)=0 (z)=ε2/ε1-1. The obtained S-continued fraction bounds have an interesting mathematical structure convenient for theoretical and numerical investigations of εe. They also agree with the earlier estimations reported by Bergman and Milton. Specific examples of calculation of bounds on εe by theS-continued fraction method are also provided.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1005861519473
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  • 4
    Electronic Resource
    Electronic Resource
    On a Saddle-Point Theorem in Minimum Compliance Design (2000)
    Springer
    Journal of optimization theory and applications 106 (2000), S. 441-450 
    Details
    ISSN: 1573-2878
    Keywords: saddle points ; minimization of compliance ; duality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This note deals with the displacement-based relaxed formulation of the minimum compliance layout problem of the optimal distribution of two isotropic materials within a given three-dimensional domain. In 1994, Lipton (Ref. 1) proved that minimization over elasticity tensors can be interchanged with maximization over displacements. This proof was based on the theory of Young measures. The aim of this contribution is to provide a new and straightforward proof of the Lipton saddle-point theorem by using a duality technique, thus bypassing the Young measure theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004667901231
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  • 5
    Electronic Resource
    Electronic Resource
    Stiffness reduction and stress analysis in cracked [0m 0/90n 0]s laminates (1998)
    Springer
    Acta mechanica 131 (1998), S. 177-201 
    Details
    ISSN: 1619-6937
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary A new method of modelling effective properties and stress distribution in cracked laminates [12]–[17] is applied to assess the loss of the effective Young, Kirchhoff and Poisson moduli of the [0 m 0/90 n 0] s laminates with transverse aligned cracks in the 90° layer and to find the stress distribution between interacting cracks and in the vicinity of isolated cracks. The decaying curve describing the loss of the effective Young's modulus in the tensile direction lies slightly over the curve found by Hashin [7] with the help of similar stress assumptions. The reduction of Kirchhoff's modulus is predicted in the same way as in Hashin [7] and Tsai and Daniel [28]. All components of the state of stress are given by closed-form relations. The stresses within periodicity cells are expressed in terms of macrodeformations. The explicit formulae for stresses derived in the present paper make it possible to interrelate the crack spacing with a magnitude of the applied stress. To this end a local stress-type criterion of the onset of cracks nucleation is used and reasonable good fit with experimental data of Highsmith and Reifsnider [9] is observed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01177224
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  • 6
    Electronic Resource
    Electronic Resource
    Bounds on effective moduli by analytical continuation of the Stieltjes function expanded at zero and infinity (1998)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 49 (1998), S. 137-155 
    Details
    ISSN: 0044-2275
    Keywords: Key words. Padé approximants, Stieltjes function, composites, bounds, effective conductivities.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract. By employing special continued fractions to two Stieltjes series with nonzero radii of convergence the inequalities for two- and three-point Padé approximants have been derived. These inequalities constitute an extension of the relevant relations valid for one-point Padé approximants [1,Cor.17.1] and two-point Padé ones [23, Th.1]. The Padé approximants inequalities achieved have been applied to the theory of inhomogeneous media for establishing of the new bounds on the effective transport coefficient of two-phase composite materials. As an example the low order estimations of the effective conductivity of a square array of cylinders have been computed and compared with the corresponding ones evaluated in [24].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s000330050085
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