# Mathematical modeling of the thermoelastic state in a circular disk with a crack due to the action of the heat source

2019;
: 13-19

Надіслано: Квітень 13, 2019
Переглянуто: Червень 06, 2019
Прийнято: Червень 26, 2019

V. Zelenyak, L. Kolyasa, "Mathematical modeling of the thermoelastic state in a circular disk with a crack due to the action of the heat source", Ukrainian Journal of Mechanical Engineering and Materials Science, vol. 5, no. 1, pp. 13-19, 2019.

Автори:
1
Lviv Polytechnic National University
2
Національний університет «Львівська політехніка», кафедра вищої математики

Purpose. To determine the two-dimensional thermoelastic state in a circular plate, weakened by an edge or internal crack induced by a stationary heat sourse. This paper proposes using singular integral equation (SIE) to investigate thermostressed intensity in the vicinity of the crack tip, depending on the local heat source placement and identify typical mechanical effects. Numerical results for the stress intensity factors (SIFs) can be potentially used to identify (with the limit equilibrium equations) critical values of the intensity of the local heat source at which crack begin to grow and the local destruction of the body. Methodology. The methods of studying two-dimensional thermoelastic state body with crack as stress concentrators based on the function of complex variable method by which the problem of stationary thermoelasticity are reduced to a SIE of the first kind, a numerical solution which was obtained by the method of mechanical quadratures. Findings. In this paper graphic dependences of stress intensity factors at the crack tip on the relative position of crack and local heat source placement and on the length of crack are obtained. Originality. Scientific novelty lies in the fact that the solutions of the new two-dimensional problems of thermoelasticity for a circular plate containing a crack under the influence of local heating of heat source. Practical value. The practical value is the ability to more fully take into account the real situation in the thermoelastic elements of engineering structures with cracks that operate under conditions of heat stress in various industries, particularly in mechanical engineering. The results of specific values in the crack tip SIF in graphs may be useful in the development of sustainable modes of structural elements in terms of preventing the growth of cracks.

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