Optimization of the Modes of Heat Treatment of Structural Elements Made of Functionally Graded Materials
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OPTIMIZATION OF THE MODES OF HEAT TREATMENT OF STRUCTURAL ELEMENTS MADE OF FUNCTIONALLY GRADED MATERIALS M. H. Stashchuk1,2 and E. M. Irza3
UDC 359.3
We propose a procedure of control over the speed of response of thermal conditions in the case of thermal loading of the bodies of revolution made of functionally graded materials. The construction of solutions of the analyzed problems is based on numerical methods. To solve direct problems, we use the method of weighed residuals and the finite-element method. The solution of the posed extreme problem is based on the principle of step-by-step parametric optimization. Keywords: thermal stressed state, body of revolution, functionally graded material, finite-element method, hollow cylinder, optimization of modes.
Introduction The structures made of functionally graded materials often participate in the thermal processes connected with their heating and subsequent cooling. As a result of action of temperature fields upon these structures, we observe the appearance of temperature stresses that may exceed admissible values and can lead to the destruction of structures or to the deterioration of their operating characteristics. However, the modes of heat treatment are energy consuming. Therefore, it is necessary to use efficient mathematical tools with an aim to optimize the procedures of control over the modes of heat treatment according to certain criteria in the course of heating and cooling of these bodies. For this purpose, it is necessary to guarantee the optimality of the choice of a certain criterion under the restrictions imposed on the stress-state state of the analyzed structure and the technological conditions of heating and cooling. The general approaches to the development of the efficient mathematical methods in this field are fairly completely described in the available literature [1–6] devoted mainly to the analysis of the thermomechanical processes running in the bodies under various thermal loads. In the cited works, the properties of the material used to produce these structures are regarded as homogeneous. In what follows, we propose a procedure of control over the speed of response of thermal conditions in the processes of heating and cooling of the bodies of revolution made of functionally graded materials (whose shapes are different from canonical). It is assumed that the thermal characteristics and restrictions imposed on the stressed state are functions of the space coordinates and temperature. Statement of the Problem The statement of the problems of control over the speed of response of thermal conditions under thermal loading includes the following stages: the choice of a criterion and the corresponding optimization functional, 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, Ukraine.
Translated from Fizyko-Khimichna Mekhan
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