Thermoelastic analysis based on hypersingular boundary integral representation

虽然边界元方法可以非常准确地给出边界位移和牵引力作为直接边界解，但边界应力分量的精度较低，因为它们是由位移分量的牵引力分量和切向导数间接计算出来的。在本研究中，我们使用超奇异边界积分表示边界位移梯度，以提高热弹性问题中边界应力分量的精度。在考虑热应变的情况下，导出了超奇异边界积分表示的直接数值计算格式。文中还讨论了基于双互易方法的热应变区域积分项的边界积分处理。数值结果表明，该方法可以得到非常精确的边界应力结果，边界积分方程的奇异处理在断裂力学应用中也是有用的。基于相互作用能释放率，计算了双材料界面裂纹的应力强度因子。相互作用能量释放率是基于裂纹体的能量释放率定义的，对应于两个独立的加载条件，并与位移和牵引力对裂纹长度的灵敏度系数的边界积分有关：边界元灵敏度分析用于精确计算这些量。数值算例表明，该方法能较好地计算各种双材料界面裂纹在粗网格离散条件下的应力强度因子。

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