轴对称界面端的扭转问题

基于弹性力学轴对称扭转问题的通解，研究了具有任意几何形状的双材料轴对称界面端，给出了界面端的应力奇异性及其附近的位移场和奇应力场，定义了扭转问题的Ｄｕｎｄｕｒｓ双材料参数。研究结果表明，应力奇异性只与界面端的结合角和扭转问题的Ｄｕｎｄｕｒｓ双材料参数有关，而与界面的角度以及界面端与对称轴之间的距离无关，在任何情况下，特征值均为实数，不会产生振荡应力奇异性。

TORSION OF AN AXISYMMETRIC INTERFACE EDGE

Many researches on the torsion problem of axisymmetric interface edges of bonded dissimilar materials have been made because of its wide range of applications. Then, up to now, Only some interface edges and cracks with particular geometrical shapes have been studied. In this paper, an axisymmetric interface edge of bonded dissimilar materials with the abitrary geomatrical shape is analyzed based on the general solution of the elastic axisymmetric torsion problem. The stress singularity, displacement and singular stress fields near the axisymmetric interface edge under torsion are obtained. A Dundurs' bimaterial parameter under torsion is defined. The results in this paper show that the stress singularity of the axisymmetric interface edge under torsion is only related to the two joining angles and the Dundurs' bimaterial parameter under torsion and it is independent of the interface angle and the distance between the interface edge and the axisymmetric axis. The stress singularity of the axsymmetric interface edge under torsion is somewhat different from that under the axisymmetric deformation. In any case the eigenvalue under torsion is always real, so that there is no oscillatory stress singularity. The results in this paper may have a wide range of applications in engineering if the joining angles of the interface edge and the interface angle as well as the distance between the interface edge and the axisymmetric axis are selected appropriately. For some interface edges and cracks with particular geometrical shapes, the present results can be easily degenerated to those which have been got by other researchers.