Розглядається стаціонарна нелінійна задача теплопровідності для ізотропного шару з чужорідним тепловиділяючим паралелепіпедним включенням малих розмірів із тепловіддачею. Запропонована методика розв’язування цієї задачі та її застосування для конкретної залежності коефіцієнта теплопровідності матеріалу шару від температури.
Purpose. A two-dimensional mathematical model of the problem of thermo-elasticity for piecewise-homogeneous component plate containing a crack has been built. The stress intensity coefficients in the vertices of the crack increase affecting strength of the body significantly. This leads to the growth of a crack and, as a result, to further local destruction of a material. Therefore, such a model reflects, to some extent, the destruction mechanism of the elements of engineering structures with cracks.
Based on analysis of the Tech Summer for Teachers Bootcamp webinars for the educational community organized by the IT Company SoftServe, attention is focused on their interdisciplinary approach, in particular in the teaching of philosophical disciplines. Special attention was paid to the anthropological component in the field of information technologies, artificial intelligence, cybersecurity and virtual communication.
Purpose. A two-dimensional mathematical model of the problem of thermoelasticity for three-component plate containing a crack has been built. The stress intensity coefficients in the vertices of the crack increase affecting strength of the body significantly. This leads to the growth of a crack and, as a result, to further local destruction of a material. Therefore, such a model reflects, to some extent, the destruction mechanism of the elements of engineering structures with cracks.
The two-dimensional stationary problems of heat conduction and thermoelasticity for a semi-infinite elastic body containing an inclusion and a crack are considered. For this purpose, mathematical models of these two-dimensional problems in the form of a system of singular integral equations (SIEs) of the first and the second kinds are constructed. The numerical solution of the system of integral equations in the case of a half plane containing an inclusion and thermally insulated crack due to local heating by a heat flux is obtained using the method of mechanical quadratures. We pre
The Fourier integral transform has been used to reduce the diffraction problem of the normal SH-wave on a semi- infinite rigid inclusion in the elastic layer to the Wiener-Hopf equation. Its solution is obtained by the factorization method. The analytical expressions of the diffracted displacement fields have been represented in any region of interest. The dependences of the scattered field on the parameters of the structure have