This article describes solutions to the direct and inverse problems of the three-dimensional non-stationary heat conduction problem in a three-layer structure, using the finite element method for the direct problem and the gradient descent method for the inverse problem. A comparison of the FEM-solution and the analytical solution for a solid with a simple geometry is presented. Here are presented solutions of the direct and inverse three-dimensional non-stationary heat conductivity problem for a free three-stage turbine. The accuracy of the found and exact solutions is compared.

A model is proposed for the deformation of elastic-plastic particle reinforced composite materials of a periodic structure with allowance for the damage. The model is based on a variant of the deformation theory of plasticity under active loading, in which the damage parameter is introduced, taking into account the difference in the accumulation of damage in phases during shear, tension and compression. The method of asymptotic homogenization of periodic structures was used to model the effective characteristics of elastic-plastic composites. Examples of numerical calculation are carried out for particle-reinforced metal composite - aluminum matrix filled with SiC particles.

Abstracts The article describes the development of a new design technology for power engine structures (PES) hulls of increased reliability, based on the methods of system analysis using computer modeling of damage accumulation in structural elements, as well as the development of technical solutions for creating the PES hull design using new heat-resistant composite carbon-carbon and carbon-ceramic materials. To calculate the accumulation of damage, the chemical criteria of durable strength is used, for numerical calculation of the stress-strain state of structures taking into account creep, an iterative method for solving a three-dimensional problem of thermomechanics using the finite element method is applied. An example of the calculation of a high-pressure structural element, performed in the work, showed the possibility of practical implementation of the proposed technique and its effectiveness, in terms of reducing or replacing experimental studies to substantiate the reliability of structures.

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.

Abstracts A method for calculating stresses in the structure of a pressure cylinder made by winding a composite fibrous material has been developed. A special feature of the proposed method is that the problem is solved within the framework of the 3D formulation of the problem of the theory of elasticity, considering the curvilinear anisotropy of the structure, which changes from point to point. This technique allows one to consider the detailed microstructure of a composite material wound with overlapping tapes. To solve the problem, the 3D finite element method is used, as well as a special algorithm for constructing an additional mesh of elements, which makes it possible to relate the curvilinear anisotropy with the geometry of the thin-walled shell under study.