The conjugate problem of aerodynamics and heat and mass transfer in heat-shielding structures made of ablating polymer composite materials is considered. To determine the heat fluxes in the shock layer, the chemical composition of the atmosphere is taken into account. A mathematical formulation of the joint problem is formulated and an algorithm for numerical solution is proposed. An example of a numerical solution of the problem for the reentry spacecraft Stardust is presented. It is shown that due to the high temperatures of aerodynamic heating of a structure made of a polymer composite material, an intense internal generation of gas appears in the structure of the material, which can lead to the destruction of the material.

Abstracts The problem of detailed calculation of micro-stresses in textile composite materials under arbitrary types of loading is considered. A model for calculating the effective characteristics of textile composites considering the real complex curvilinear anisotropy of fibers in tissues is proposed. The model is based on the asymptotic homogenization method, whereby local problems of elasticity theory for a curvilinear anisotropic body are formulated. For the numerical solution of these problems, the finite element method is used. The implementation of the proposed method was carried out within the framework of the SMCM software package, developed at the Department of Computational Mathematics and Mathematical Physics of the Bauman Moscow State Technical University. The SMCM software package allows you to perform a full cycle of finite element modeling, including the stages of pre-processing and post-processing. An example of numerical modeling of a textile carbon-carbon composite of twill weaving is carried out. It is shown that the developed software package provides (a very high accuracy of calculations of the effective elastic properties of composites. The comparison was carried out with the calculations obtained using the ANSYS software, which was modified to provide the possibility of solving local problems, the relative deviation in the calculations of the effective elastic constants did not exceed (-7) degrees.

The problem of modeling the effective integral viscoelastic properties of unidirectional composite materials is considered. To calculate the integral properties of viscoelasticity, the Fourier transform and the inverse Fourier transform are used, as well as the method of asymptotic averaging for composites with steady polyharmonic vibrations, and a finite element algorithm for solving local problems of the viscoelasticity theory on the periodicity cell of the composite. To obtain the material constants, a method of approximation of the Fourier images of the relaxation and creep kernels is proposed, which makes it possible to avoid the numerical error of the inverse Fourier transform.

The paper deals with three-scale modelling of the filtration of a weakly compressible liquid binder in the tissue material of the filler in the production of composite materials based on the RTM method. The technique is based on the application of the asymptotic homogenization method for the Navier-Stokes system of equations. Local filtration problems for the threads level and for the monofilaments level are obtained.

A method for multiscale supercomputer calculations of the composite structures strength has been developed. A feature of the proposed methodology is of division of the solution algorithm into 2 parts: solving problems at the micro level (in turn, these problems can consist of several sub-levels of calculation) and solving the problem at the macro level. Such a division, in which the solution of some problems is the input to problems at a higher level, helps to significantly reduce the consumption of computing resources. When solving problems, curvilinear anisotropy is taken into account at the macro level (structures), as well as at the micro level (composite material). The 3D finite element method was used for the numerical solution. To take into account curvilinear anisotropy, a special assembly algorithm is used, which requires the construction of anisotropy blocks (cells). A method is proposed for taking into account integral boundary conditions when solving problems of the linear theory of elasticity. A finite element modeling of the stress-strain state and damageability of a cylindrical structure with power ring elements has been carried out. As an example, textile composite materials (CM) with carbon and glass fibers are considered.