Thermoelastic analysis based on hypersingular boundary integral representation

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Although the boundary element method can give us boundary displacements and tractions very accurately as the direct boundary solutions, boundary stress components are less accurate since they are calculated indirectly from the traction components and tangential derivatives of the displacement components. In the present research, we used a hypersingular boundary integral representation for the boundary displacement gradients in order to improve the accuracy of the boundary stress components in thermoelastic problems. A direct numerical evaluation scheme of the hypersingular boundary integral representation has been derived by considering the thermal strains. A boundary integral treatment of the domain integral term for the thermal strains based on the dual reciprocity method is also discussed. The numerical results have shown that the present approach could give very accurate boundary stress results.Singular treatment of the boundary integral equation is also useful in fracture mechanics application. Stress intensity factors of bimaterial interface cracks are evaluated based on the interaction energy release rates. The interaction energy release rate is defined based on the energy release rates of a cracked body, corresponding to two independent loading conditions, and is related to a boundary integral of the sensitivity coefficients of the displacement and the traction, with respect to the crack length: The boundary element sensitivity analyzes are used to calculate these quantities accurately. Some numerical demonstrations show that the present method can give accurate results for the stress intensity factors of various bimaterial interface cracks under coarse mesh discretizations