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Mechanics and Physics of Structured Media
Asymptotic and Integral Equations Methods of Leonid Filshtinsky.
Builds on the monumental work of Leonid Filshtinsky, providing vital information on the macroscopic properties of various composite materials
Igor Andrianov (Edited by), Simon Gluzman (Edited by), Vladimir Mityushev (Edited by)
9780323905435, Elsevier Science
Paperback / softback, published 25 January 2022
524 pages, 330 illustrations (30 in full color)
22.9 x 15.2 x 3.3 cm, 0.45 kg
Mechanics and Physics of Structured Media: Asymptotic and Integral Methods of Leonid Filshtinsky provides unique information on the macroscopic properties of various composite materials and the mathematical techniques key to understanding their physical behaviors. The book is centered around the arguably monumental work of Leonid Filshtinsky. His last works provide insight on fracture in electromagnetic-elastic systems alongside approaches for solving problems in mechanics of solid materials. Asymptotic methods, the method of complex potentials, wave mechanics, viscosity of suspensions, conductivity, vibration and buckling of functionally graded plates, and critical phenomena in various random systems are all covered at length. Other sections cover boundary value problems in fracture mechanics, two-phase model methods for heterogeneous nanomaterials, and the propagation of acoustic, electromagnetic, and elastic waves in a one-dimensional periodic two-component material.
1. L.A. Filshtinsky’s contribution to Applied Mathematics and Mechanics of Solids Vladimir Mityushev, Igor Andrianov, and Simon Gluzman 2. Cracks in two-dimensional magneto-electro-elastic medium D. Nosov, L.A. Filshtinskii, and V. Mityushev 3. Two-dimensional equations of magneto-electro-elasticity V. Mityushev, D. Nosov, and R. Wojnar 4. Hashin-Shtrikman assemblage of inhomogeneous spheres A. Cherkaev and V. Mityushev 5. Inverse conductivity problem for spherical particles Vladimir Mityushev, Natalia Rylko, Zhanat Zhunussova, and Yeskendyr Ashimov 6. Compatibility conditions: number of independent equations and boundary conditions I.V. Andrianov and H. Topol 7. Critical index for conductivity, elasticity, superconductivity. Results and methods Simon Gluzman 8. Double periodic bianalytic functions Piotr Drygas 9. The slowdown of group velocity in periodic waveguides Yuri A. Godin and Boris Vainberg 10. Some aspects of wave propagation in a fluid-loaded membrane J. Kaplunov, L. Prikazchikova, and S. Shamsi 11. Parametric vibrations of axially compressed functionally graded sandwich plates with a complex planform Kurpa Lidiya and Shmatko Tetyana 12. Application of volume integral equations for numerical calculation of local fields and effective properties of elastic composites S. Kanaun and A. Markov 13. A slipping zone model for a conducting interface crack in a piezoelectric bimaterial V. Loboda, A. Sheveleva, and O. Mykhail 14. Dependence of effective properties upon regular perturbations Matteo Dalla Riva, Paolo Luzzini, Paolo Musolino, and Roman Pukhtaievych 15. Riemann-Hilbert problems with coefficients in compact Lie groups G. Giorgadze and G. Khimshiashvili 16. When risks and uncertainties collide: quantum mechanical formulation of mathematical finance for arbitrage markets Simone Farinelli and Hideyuki Takada 17. Thermodynamics and stability of metallic nano-ensembles Michael Vigdorowitsch 18. Comparative analysis of local stresses in unidirectional and cross-reinforced composites A.G. Kolpakov and S.I. Rakin 19. Statistical theory of structures with extended defects V.I. Yukalov and E.P. Yukalova 20. Effective conductivity of 2D composites and circle packing approximations Roman Czapla and Wojciech Nawalaniec 21. Asymptotic homogenization approach applied to Cosserat heterogeneous media Victor Yanes, Federico J. Sabina, Yoanh Espinosa-Almeyda, Jose A. Otero, and Reinaldo Rodríguez-Ramos
Subject Areas: Materials science [TGM], Mechanical engineering [TGB]
