直角平面区域内固定圆形刚性夹杂问题的Green函数解

利用复变函数法、多极坐标移动技术研究了直角平面区域内含有固定圆形夹杂时的反平面问题Green函数解.首先构造出不含夹杂的完整直角平面区域内满足边界应力条件的入射位移场;其次,建立直角平面区域内固定圆形夹杂对该入射场产生的满足直角边界应力自由条件的散射波解,并由叠加原理得到介质内的总波场.最后利用夹杂边界处的位移条件确定出散射波解中的未知系数,最终得到问题的Green函数解,还通过算例讨论了夹杂边界处的径向应力和环向应力随不同波数、角度和不同夹杂位置及不同点源位置的变化情况.算例结果表明了该文方法的有效实用性.

THE ANTI PLANE GREEN FUNCTION SOLUTION OF THE PROBLEM OF A FIXED RIGID CIRCULAR INCLUSION IN RIGHT-ANGLE PLANE

Complex function method and multi-polar coordinate transformation are used to study the Green function of a fixed rigid circular inclusion in right-angle planar space under an anti-plane point loading on the horizontal straight boundary.First,the incident displacement function of complete right-angle planar space which satisfies the stress boundary conditions is constructed Accerding to the wave equation,the scattering wave solution of the fixed rigid circular inclusion existing in the right-angle space subjected to the anti-plane point loading is then constructed which can satisfy the free stress conditions of the two right-angle boundaries,The total displacement field can be formulated using the overlapping principle.The unknown coefficients in the scattering solution can be solved by using the displacement boundary conditions of the inclusion,An example is given to show the variations of the radial and the tangential stresses vs the different wave numbers,different angles and different locations of the fixed inclusion and the point loading.The results of the given example show the validity and effectiveness of the method proposed.