Thermal Stressed States of the Bodies of Revolution made of Functionally Graded Materials
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THERMAL STRESSED STATES OF THE BODIES OF REVOLUTION MADE OF FUNCTIONALLY GRADED MATERIALS M. H. Stashchuk1,2 and E. M. Irza3
UDC 359.3
We propose a method for the determination of the thermal stressed state of elastic bodies of revolution made of functionally graded materials. The formulation of the mathematical problem contains a thermal loading. A numerical algorithm for the solution of the corresponding problem is developed and realized for the problems of heat conduction and thermoelasticity. The thermoelastic state of a hollow cylinder is computed for a given mode of heating and different heat-conduction coefficients, elasticity moduli, specific heat capacities, and linear coefficients of thermal expansion. These results enable us to plot the graphic dependences of the thermal stressed state of a hollow cylinder. Keywords: thermal stressed state, body of revolution, functionally graded materials, finite-element method, hollow cylinder.
Introduction In recent years, we observe rapid progress in the development of nanotechnologies. Thus, it becomes possible to produce materials with given physicomechanical characteristics, which are continuous functions of the space coordinate and temperature. These materials are called functionally graded. The structures made of elastic functionally graded materials are frequently heated and cooled. Under the action of temperature fields, we observe the formation of temperature stresses in these materials. These stresses may exceed admissible values and lead to the failures of structures. The main part of available investigations deals with bodies of revolution. The analysis of thermal stressed state formed in the bodies of revolution made of functionally graded materials subjected to thermal loading was carried out in numerous works and, in particular, in [1–4]. These works also mainly deal with the bodies with canonical shapes of revolution. As compared with the results of investigations in this field available in the literature, we propose a new mathematical procedure aimed at determination of the thermal stressed state of bodies of revolution made of elastic functionally graded materials whose shapes are different from canonical ones. The thermophysical characteristics of the body depend on the space coordinate and temperature. The proposed method includes the mathematical formulation of the problem, the development of a numerical algorithm for finding its solution, and the software realization of the numerical algorithm. Statement of the Problem We assume that, under the analyzed thermal loads, the stressed state of the body does not affect its temperature. In other words, the problem of determination of the stress-strain state of the body is formulated in the quasistatic statement (in displacements). 1 2 3
Karpenko Physicomechanical Institute, Ukrainian National Academy of Sciences, Lviv, Ukraine. Corresponding author; e-mail: [email protected].
Pidstryhach Institute for Applied Problems in Mechanics and Mathematics, Ukrainian National Academy of Sciences, Lviv, Uk
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