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Mechanics and Physics of Structured Media: Symptotic and Integral Methods of Leonid Filshtinsky provides critical information on the macroscopic properties of various composite materials and the mathematical functions and equations key to understanding their mechanical behaviors. Centered around, and building upon, the monumental work of Leonid Filshtinsky, the book provides insights 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, sedimentation velocity, 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, short-time and non-local diffusion, and the propagation of acoustic, electromagnetic, and elastic waves in a one-dimensional periodic two-component material.
- Covers key issues around the mechanics of structured media, including modeling techniques, fracture mechanics in various composite materials, the fundamentals of integral equations, wave mechanics, and more
- Discusses boundary value problems of materials, techniques for predicting elasticity of composites, and heterogeneous nanomaterials and their statistical description
- Includes insights on asymptotic methods, wave mechanics, the mechanics of piezo-materials, and more
- Applies homogenization concepts to various physical systems
Researchers, graduate students, and professional engineers/R&D professionals in mechanical engineering, material science, physics
- L.A. Filshtinsky's contribution to Applied Mathematics and Mechanics of Solids
2. Cracks in two-dimensional magneto-electro-elastic medium
3. Two-dimensional equations of magneto-electro-elasticity
4. Hashin-Shtrikman assemblage of inhomogeneous spheres
5. Inverse problem for highly conducting spherical particles
6. Compatibility conditions: number of independent equations and boundary conditions
7. Critical Index for Conductivity, Elasticity, Superconductivity. Results and Methods
8. Double periodic bianalytic functions
9. Slowdown of group velocity in periodic waveguides
10. Some aspects of wave propagation in a fluid-loaded membrane
11. Parametric vibrations of axially compressed functionally graded sandwich plates with a complex planform
12. Homogenization method based on integral equations for heterogeneous media. Choice of representative volume element
13. A Slipping Zone Model for Conducting an Interface Crack in a Piezoelectric Bimaterial
14. Dependence of effective properties upon regular perturbations
15. Riemann-Hilbert problems with coefficients in compact Lie groups
16. Finance as Mechanics. Quantum Mechanical Formulation of Mathematical Finance for Arbitrage Markets
17. Thermodynamics and stability of metallic Nano-ensembles
18. Comparative analysis of local stresses in unidirectional and cross-reinforced composites
19. Statistical theory of structures with extended defects
20. Effective conductivity of 2D composites and circle packing approximations
- No. of pages:
- © Academic Press 2022
- 1st January 2022
- Academic Press
- Paperback ISBN:
Igor V. Andrianov is Professor Emeritus, RWTH Aachen University. He is the author or co-author of 14 books and more than 300 papers in peer-reviewed journals. He has presented papers at more than 150 international conferences and seminars and also supervised 21 PhD. Students. His research interests include mechanics of solids, mechanics of composite materials, nonlinear dynamics, and asymptotic methods.
Professor Emeritus, RWTH Aachen University, Germany
Simon Gluzman is presently an Independent Researcher (Toronto, Canada) and formerly a Research Associate at PSU in Applied Mathematics. He is interested in Re-summation methods in theory of random and regular composites and the method of self-similar and rational approximants.
Independent Researcher, Toronto, Canada
Vladimir Mityushev is the Professor of Cracow University of Technology, a leader of the research group www.materialica.plus. He is interested in mathematical modeling and computer simulations, Industrial mathematics and boundary value problems and their applications. .
Institute of Mathematics, Faculty of Computer Science and Telecommunications, Cracow University of Technology, Kraków, Poland
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