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Öğe Exact Transient Heat Conduction of Functionally Graded Thick Structures(Pleiades Publishing Inc, 2024) Eker, M.; Temo, E.; Yarimpabuc, D.Closed form solution of the transient thermal analysis in functionally graded cylindrical and spherical bodies under different thermal loads are presented. It is assumed that the material properties change according to the different inhomogeneity parameters according to the power-law in the radial direction. In the partial differential equation obtained under these conditions, the time dependence is eluted with the Laplace transform and transformed into Bessel differential equation in Laplacian space. This equation, which is solved with Bessel functions in Laplacian space, is transformed into physical space with the modified inverse Durbin method. Behaviors of cylindrical and spherical bodies under constant, convective and time-dependent boundary conditions are investigated. Besides, it is aimed to obtain benchmark solutions for these structures to the literature.Öğe Nonlinear thermal stress analysis of functionally graded spherical pressure vessels(Elsevier Sci Ltd, 2022) Yildirim, A.; Yarimpabuc, D.; Arikan, V.; Eker, M.; Celebi, K.In this study, nonlinear analysis of functionally graded spherical pressure vessels composed of metal/ceramic mixture for both high strength and high thermal resistance is discussed. The originality of this study is to think that all material properties change with temperature as well as thickness by using a realistic and physically meaningful graded material model with the Halpin-Tsai homogenization scheme. These conditions results in nonlinear differential equation that may not be solved with conventional methods. The nonlinear temperature and stress distributions of the functionally graded sphere under the thermo-mechanical loads are determined by using the pseudospectral Chebyshev method. Some stress results based on the assumptions of temperature -dependencies and temperature-independencies of the material properties are derived and effects of various parameters on the thermoelasticity are studied. Besides, elastic limits based on the von Mises' yield criterion are also discussed according to whether the material properties are dependent on temperature or not. Benchmark linear examples are used to check the accuracy of the method. The nonlinear solutions are verified with the finite element method using the ANSYS package program.Öğe Thermal wave propagation in a functionally graded annular fin with fixed base(Taylor & Francis Ltd, 2021) Yildirim, A.; Eker, M.; Yarimpabuc, D.; Celebi, K.Thermal wave propagation and efficiency analysis of thin axially symmetric functionally graded annular fins with a fixed base boundary condition are examined. All material properties are graded along the radial direction using the Mori-Tanaka homogenization scheme to design a realistic and physically meaningful graded material model and create a smooth distribution of elastic and thermal material properties. The novelty of this research is handling a more realistic annular fin, which has sufficient strength in practice and significantly reduces weight, using two different metal materials with the elasticity-based Mori-Tanaka model. These conditions result in two-point linear boundary value problems that are numerically solved by the pseudospectral Chebyshev method. The temperature distributions, thermal stresses and the efficiency in the functionally graded annular fin are compared with fins made of steel only and aluminium only.