NEW INTEGRAL EQUATION FOR THE THERMALLY INSULATED CURVE CRACK PROBLEM IN AN INFINITE PLATE

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Abstract
In this paper the thermally insulated curve crack problem in an infinite plate is discussed. The proposed problem can be separated into two problems, one being the heat conduction problem and the other being the thermal stress problem. In the heat conduction problem, the temperature dislocation function is taken to be the unknown function in the resulting integral equation. Unlike usual choice, the heat stream function is taken as the right-hand term of the integral equation; therefore, a new integral equation for the heat conduction problem with weakly singular kernel (logarithmic) is obtained and suggested. Meantime, in the stress problem the dislocation is taken to be the unknown function and the resultant force function to be the right-hand term in the resulting integral equation. Similarly, a weakly singular integral equation for the thermal stress problem is also obtained. The obtained integral equations is compact inform and is easy to deal with for numerical analysis. Numerical examination is used to demonstrate the efficiency of the present approach, and a number of numerical examples are given.

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