Temperature Stresses in a Functionally Graded Cylindrical Shell
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TEMPERATURE STRESSES IN A FUNCTIONALLY GRADED CYLINDRICAL SHELL R. М. Кushnir1 and U. V. Zhydyk2, 3
UDC 539.3
For functionally gradient isotropic circular cylindrical shells, we propose the nonstationary heatconduction and thermoelasticity equations with appropriate boundary conditions. The thermoelasticity equations take into account both transverse shear and transverse normal strains. The temperature distribution over the thickness of the shell is assumed to be linear. As the shell material, we take a metal– ceramics composite. The volume fractions of these components vary across the thickness of the shell according to a power law. The solution of the quasistatic problem of thermoelasticity for a finite simply supported shell subjected to local heating is obtained by the methods of Fourier and Laplace transformations. Keywords: thermoelasticity, cylindrical shell, functionally graded material, temperature load.
Shells and plates are important elements of contemporary structures. Composite materials with layered structures are extensively used for their manufacturing [1, 2]. However, abrupt changes in the properties observed in passing from one layer to another leads to the formation of interlayer strains and stresses, which may lead to exfoliations and fractures in the contact zone. Among the methods aimed at the prevention of this undesirable effect, we can mention the application of functionally graded (FG) materials in which the volume fractions of the components undergo gradual changes, as a rule, only across the thickness [3]. These materials are specially designed to have the required properties under given specific conditions, especially at elevated temperatures. Hence, the development of appropriate mathematical models and methods for the numerical analysis of structures made of these materials represents an important engineering problem. In recent years, the researchers give much attention to the investigation of plates and shells made of functionally graded materials [3, 4]. The ability of FG materials to withstand extreme temperature loads and the choice of the optimal composition of these materials with an aim to decrease temperature stresses and increase their thermal resistance were analyzed in [3]. Furthermore, the exact solutions of thermoelastic problems for the FG shells were found on the basis of three-dimensional equations in [5–8]. The analytic solutions of equations of the classical and refined theories of shells made of FG materials and subjected to the action of temperature and mechanical loads were obtained in [9, 10]. The finite-element method was applied in [11, 12] for the analysis of nonstationary processes in thermoelastic FG shells. The thermal resistance of inhomogeneous shells was also studied in [13]. A more detailed survey of different theories of simulation and investigation of FG shells and plates can be found in [14]. The aim of the present work is to analyze the thermoelastic state of a circular cylindrical shell made of functionally graded material under the conditions of
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