Mathematical modeling of the thermoelastic state in a circular disk with a crack due to the action of the heat source
Date
2019-03-20
Authors
Journal Title
Journal ISSN
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Publisher
Видавництво Львівської політехніки
Lviv Politechnic Publishing House
Lviv Politechnic Publishing House
Abstract
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.
Description
Keywords
crack, temperature stresses, heat source, stress intensity factor, singular integral equation
Citation
Zelenyak V. Mathematical modeling of the thermoelastic state in a circular disk with a crack due to the action of the heat source / Volodymyr Zelenyak, Liubov Kolyasa // Ukrainian Journal of Mechanical Engineering and Materials Science. — Lviv : Lviv Politechnic Publishing House, 2019. — Vol 5. — No 1. — P. 13–19.