著者

許 金泉 付 列東 武藤 睦治

出版者

一般社団法人 日本機械学会

雑誌

日本機械学会論文集 A編 (ISSN:03875008)

巻号頁・発行日

vol.68, no.672, pp.1266-1272, 2002-08-25 (Released:2008-02-21)

参考文献数

7

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The three dimensional theoretical solution of a normal concentrated forces on the free surface of a coating material is deduced by introducing the infinite mirror points of the load point and applying the Dirichlet's uniqueness theorem. The deduction is based on the basic equations of the spatial axisymmetric problems. It is found that all the stress functions corresponding to the mirror points, which satisfy the continuous conditions at the interface and the free boundary conditions at the free surface, can be deduced from the fundamental solution of a concentrated normal force on the free surface of a semi-infinite homogeneous solid. It is also found that only the stress functions corresponding to the first few mirror points have an influence on the accuracy of the theoretical solution. It is also found that the effect of material combination cannot be expressed by Dunders' parameters only. The stress field can be described by using Dunders' parameters together with the additional parameter.

著者

許 金泉 武藤 睦治 付 列東

出版者

一般社団法人日本機械学会

雑誌

日本機械学會論文集. A編 (ISSN:03875008)

巻号頁・発行日

vol.68, no.672, pp.1259-1265, 2002-08-25

被引用文献数

1 7

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The theoretical solution of a concentrated force on the free surface of a coating material is deduced by introducing the infinite series mirror points of the load point and applying the Dirichlet's uniqueness theorem. In this study, the two dimensional solution is deduced in details by using the infinite series of the Goursat's stress function corresponding to every mirror point. It is found that the stress function corresponding to a higher order mirror point can be determined from that corresponding to a lower one, therefore, all the stress functions can be determined from that corresponding to the first order mirror point which is in fact the stress function for concentrated forces on the free surface of a semi-infinite body. It is also found that the contribution of the stress function to stress distribution decreases as the increasing of the corresponding order of the mirror point. It is confirmed that only the stress functions corresponding to the first several mirror points have an influence on the accuracy of theoretical solution. This theoretical solution can be expected to be very useful in evaluating the strength of coating materials or other surface modificated materials.