Abstract:
To analyze the fundamental solution of bonded dissimilar material structures, this paperhas proposed an effective theoretical analysis method, based on the Dirichlet's uniquenesstheorem and the mirror point technology. This method can be used to solve the problems ofconcentrated 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. Byintroducing the mirror points, it is found that the whole stress function can be given as thesummation of that defined under the local coordinate system fixed to each mirror point. From theinterfacial condition of continuity and the free boundary condition, by adopting the Dirichlet'suniqueness theorem, then all the stress functions can be determined from that for concentratedforces acting at the inside of a infinite homogeneous media or at the free surface of a semi-infinitespace. Therefore, the corresponding theoretical solution can be deduced in the closed series formof stress functions corresponding to each mirror point. If there are infinite mirror points, it is foundthat only the stress functions corresponding to the first several mirror points have effects on theaccuracy of the solution, by the comparison of numerical and theoretical results. Such a theoreticalsolution can be used as the Green function to deal with the problem of distributed force, and alsoas the fundamental solution for boundary element method, so that it has extensive applications inengineering. Though the proposed method has been illustrated by only two examples of planeproblem in this paper, it can also be used to deal with three dimensional problems. Moreover, thismethod can be applied not only for the case of single reflection plane, but also for the case ofmultiple reflection planes, which generally leads to infinite mirror points, due to the reflectionafter reflection.
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