MIRROR POINT METHOD FOR STRESS ANALYSIS OF BONDED DISSIMILAR MATERIALS
双材料应力分析中的镜像点方法

To analyze the fundamental solution of bonded dissimilar material structures, this paper has proposed an effective theoretical analysis method, based on the Dirichlet's uniqueness theorem and the mirror point technology. This method can be used to solve the problems of concentrated forces acting at the inside or at the free surface of infinite bonded dissimilar materials, by regarding the interface and the free surface as the reflection planes to the loading point. By introducing the mirror points, it is found that the whole stress function can be given as the summation of that defined under the local coordinate system fixed to each mirror point. From the interfacial condition of continuity and the free boundary condition, by adopting the Dirichlet's uniqueness theorem, then all the stress functions can be determined from that for concentrated forces acting at the inside of a infinite homogeneous media or at the free surface of a semi-infinite space. Therefore, the corresponding theoretical solution can be deduced in the closed series form of stress functions corresponding to each mirror point. If there are infinite mirror points, it is found that only the stress functions corresponding to the first several mirror points have effects on the accuracy of the solution, by the comparison of numerical and theoretical results. Such a theoretical solution can be used as the Green function to deal with the problem of distributed force, and also as the fundamental solution for boundary element method, so that it has extensive applications in engineering. Though the proposed method has been illustrated by only two examples of plane problem in this paper, it can also be used to deal with three dimensional problems. Moreover, this method can be applied not only for the case of single reflection plane, but also for the case of multiple reflection planes, which generally leads to infinite mirror points, due to the reflection after reflection.