Computational Analysis of Structured Media

ISBN-13: 9780128110461 / Angielski / Miękka / 2017 / 328 str.

Gluzman, Simon (Research Associate, PSU in Applied Mathematics. He held in the past held various research positions in I

Opis

Computational Analysis of Structured Media 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.

• Computational methodology for main classes of problems in structured media
• Theory of Representative Volume Element
• Combines exact results, Monte-Carlo simulations and Resummation techniques under one umbrella
• Contains new analytical formulae obtained in the last ten years and it combines different asymptotic methods with the corresponding computer implementations

Recenzje

"In conclusion, the treatise is very interesting and well written. The computational analysis of composites is given by using the classical analytic formulae in the complex domain. The analysis may be readily extended to special geometry, motion, material and alike of structured media. The treatise can be used even as a "basic reference” for teaching a graduate course, and it is highly recommended to researchers in applied mathematics and computational mechanics." --Zentralblatt MATH

Spis treści

1. Introduction2. Complex potentials and R-linear problem3. Constructive Homogenization4. From basic sums to effective conductivity and RVE5. Introduction to the method of Self-Similar Approximants6. Conductivity of Regular Composite. Square Lattice7. Conductivity of Regular Composite. Hexagonal Array8. Effective Conductivity of 3D Regular Composites9. Random 2D Composites10. Elastic problem11. Table of the main analytical formulae