Sokolov

In this paper, the authors presented a mathematical model for calculating effective dielectric characteristics of complex structured composite materials influenced by an external alternating electric field. An asymptotic investigation of electro-dynamic differential equations with fast oscillating coefficients was carried out. A local electro-dynamic problem on the composite’s “periodicity cell” was formulated. An effective complex permittivity of composite materials with various volume fractions of the fine-dispersed ferroelectric ceramic inclusions was calculated by the finite element method and the biconjugate gradient stabilized method. The authors analyzed frequency dependence of dielectric characteristics and dielectric loss tangent of composite ceramics. The obtained results are good congruous to experimental data.

In this paper the authors formulated a problem of optimising the composite micro-structure, which is a problem of minimisation of the composite density under given restrictions on the components of effective elasticity and heat-conduction tensors, and effective limits of the composite strength. The authors proposed a method for solving an optimal design problem of a composite material reinforced with micro-spheres and designed for thermal shielding. The method of asymptotical averaging (homogenisation method) was used for calculating effective composite characteristics such as elastic and heat-conduction modulus tensors and strength limits; the finite element method was used for solving local 3D heat conduction and elasticity theory problems on the composite’s periodicity cells. The finite element method was implemented with the use of GCD software developed at “FN-11” department of Bauman MSTU. The Hooke Jeeves algorithm was used for solving optimisation problems. Numerical implementation of the proposed method of micro-structure optimisation was developed by the example of a composite based on glass micro-spheres.

In this paper, the authors consider calculation of effective dielectric parameters of composite materials with complex three-dimensional armoring. The method of asymptotic averaging of periodic structures is used for averaging of long-term quasi-static electric fields in composites with dielectric components. Series of local electrostatic tasks were formulated with the use of periodicity cells; electrostatic variational problems were also formulated. To solve spatial local problems for composite materials with three-dimensional complex armoring, the finite element numerical method was used. In this article, the authors proposed an algorithm for computation of effective tensor of dielectric permeability of three-dimensional armored composite materials. Test computations were carried out in order to obtain distribution of the local electric field, effective dielectric characteristics of three-dimensional orthogonal armored composite materials with different inclusion volume fractions.

In this work a method of microstructural finite element analysis for calculation of strength surface of composite materials with periodic fabric structure of reinforcement on the basis of a developed software was proposed. This method is a method of asymptotic averaging adapted for multi-scale periodic structures developed by Prof. Y. Dimitrienko at the "Computational Mathematics and Mathematical Physics" department. The method is based on solving a special class of elasticity problems on 1/8th of the periodicity cell of the composite in order to determine effective elastic properties of the material. The results of calculation of ultimate strength for disperse reinforced and textile composites are presented.