2014/03/31 by David Kapanadze, Kapanadze, David, Gennady Mishuris +3 · 1 citation
Computer Science · Engineering · Mathematics · #33E05 #34B15 #35B27 #74Q05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #Composite Structure Analysis and Optimization #FOS: Mathematics #Numerical methods in engineering #math.AP #msc:33E05 #msc:34B15 #msc:35B27 #msc:74Q05
paper · pdf · doi:10.48550/arxiv.1403.7914
25 pages
arxiv created 2014/03/31 · openalex publication_date 2014/03/31 · arxiv updated 2014/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An analytic solution to a stationary heat conduction problem in 2D unbounded doubly periodic composite materials with temperature dependent conductivities of their components is given. Corresponding nonlinear boundary value problem is reduced a Laplace equation with nonlinear transmission conditions. For special relationships between the conductivity coefficients of the matrix and inclusions, the problem is transformed to fully linear boundary value problem for doubly periodic analytic functions. This allows to reconstruct the solution of the originally nonlinear composite and to find its effective properties. The results are illustrated by numerical examples.