Thermoelastic interaction between a hole and an elastic circular inclusion

The plane interaction problem for a circular elastic inclusion with an arbi trarily oriented hole, located either in the matrix or in the inclusion und er a remote uniform heat how, is solved. The proposed method is based on th e complex variable theory and the existing solutions for dislocation functi ons, which permit us to formulate boundary integral equations with a weak s ingular kernel. The unknown coefficients left in the singular integral equa tions thus can be solved numerically by applying the appropriate interpolat ion formulas. The hoop stresses, which are directly related to the coeffici ents of dislocation functions, are then determined accordingly. Several num erical examples are given to demonstrate the use of the present approach. C omparisons between the calculated numerical results and the corresponding e xisting solutions show that the method proposed is effective, simple, and g eneral.