Özet:

Based on the semi-analytical finite element method it is developed solution for solving of spatial problem of non-stationary heat conduction for prismatic bodies of complex shape cross-section. The basis of the initial equation is correlations of spatial unsteady heat conduction problem in curvilinear coordinates in differential and variational formulations. The formula for determining the matrix elements of thermal conductivity and heat capacity based on semi-analytical finite element method are obtained based on the presentation of temperature distribution along the coordinate by x3 Mikhlin polynomials allowing to use effective algorithm of the iterations block of upper relaxation systems for linear algebraic equations and implement efficient algorithm solution for solution system of differential equations in time. The value of semi-analytical finite element method and algorithms implemented in the form of problem-oriented subsystems for computer modeling of unsteady thermal processes are obtained. The reliability of results is substantiated by the interpretation of test cases with analytical and numerical results. Author Biographies Олександр Іванович Гуляр, Kyiv National University of Construction and Architecture, Str. Povitroflotsky 31, Kyiv, 03680 Doctor of Technical Sciences, Professor, Pensioner Department of structural mechanics

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