Rassias T. (Ed.) Computational Analysis of Structured Media

Academic Press, 2018. — 315 p. — (Mathematical Analysis and its Applications). — ISBN: 978-0-12-811046-1.This book presents a systematical approach to analytical formulae for the effective properties of deterministic and random composites. Schwarz’s method and functional equations yield for use in symbolic-numeric computations relevant to the effective properties. The work is primarily concerned with constructive topics of boundary value problems, complex analysis, and their applications to composites. Symbolic-numerical computations are widely used to deduce new formulae interesting for applied mathematicians and engineers. The main line of presentation is the investigation of two-phase 2D composites with non-overlapping inclusions randomly embedded in matrices.Complex potentials and R-linear problem
Constructive Homogenization
From basic sums to effective conductivity and RVE
Introduction to the method of Self-Similar Approximants
Conductivity of Regular Composite. Square Lattice
Conductivity of Regular Composite. Hexagonal Array
Effective Conductivity of 3D Regular Composites
Random 2D Composites
Elastic problem
Table of the main analytical formulaeTrue PDF