SUPERPOSITION OF THE MAIN EQUATIONS OF QUASISTATIC THERMOELASTICITY OF ANISOTROPIC THERMOSENSITIVE BODIES
Journal Title: Вісник Кременчуцького національного університету імені Михайла Остроградського - Year 2017, Vol 1, Issue 102
Abstract
Purpose. To develop and test a new approach to solving the problems of quasi-static thermal elasticity of aniso- tropic thermo-sensitive bodies, which are exposed to high-temperature heat exchange with the environment. Methodol- ogy. A new approach to solving the problem of anisotropic thermo-sensitive bodies nonlinear transient heat conduction problems has been applied to the thermal elasticity corresponding quasi-static problem superposition. For this purpose, physical and mechanical characteristics depending on the temperature, and the unit are expanded in the 1st type Fourier- Bessel on the relative temperature variations interval, enter them in each system equation and applying a generalized superposition, it has been obtained a set of boundary value problems of the linear thermal elasticity with constant given thermal elastic characteristics of the material. Determining the k-th solution components of the system and then sum- ming them according to k , the approximate analytical solution of the problem has been gained. Results. The 1st type nonlinearity and the double nonlinearity on the temperature distribution, stresses and displacements for cases of convec-tion change at a constant temperature environment and the temperature changes of the medium, up to high-speed heat- ing, with constant convection change on a large number of numerical calculations applied to infinite isotropic solid cylinder, the qualitative effect has been demonstrated. Originality. The proposed approach allows to obtain analytical solutions to thermal elasticity complex problems and analyze the processes that have been studied in a wide range of material physics-mechanical characteristics and heat exchange conditions with the environment. Practical value. The developed approach to the solution of quasi-static thermal elasticity problems allows take into account most fully and adequately the anisotropy, the sensitivity of the material and high temperature heat exchange with the environment in the temperature, stresses and structural elements displacements determination, working in a wide range of temperatures. In addition, this method allows use it as a receipt of test solutions in the complex structural elements calculations.
Authors and Affiliations
Y. Zaytsev
Keywords
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