コーティング材自由表面集中力の理論解 : 第1報,2次元問題の解

抄録

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.