Numerical Solution of the Thermally Isolated Crack Problem Using Singular Integral Equations

The paper discusses the numerical solution of the thermally isolated crack problem using singular integral equations. A circular crack is given in an infinite body, on which the temperature distribution function is known. Determination of the intensity coefficients for stress distribution in a small region near the crack tips is based on a first-kind singular integral equation, which is solved using Markov-type quadrature formulas. The values of stresses in the vicinity of the crack are determined by Cauchy-type integrals; for their computation Professor M. Kublashvili’s quadratic formula is used. A specific test problem is discussed. The program “Mathematika” has been compiled in a symbolic language.