微分幾何学的考察に基づく一般外板展開法の精度解析について

抄録

It is not always possible that a curved surface in the Euclid space of three dimensions is developed on the Euclid plane of two dimensions. Therefore, we use many approximate methods for the development of undevelopable curved surfaces which are shell plates, because the amount of expansion and contraction of parts of shell plates are not much in practice.
Then the author analysed these methods by differential geometry for the purpose of investigating the accuracy. Namely two geodesic lines being at right angles on the shell surface and being competent for making the correct developed plane, are found out by the calculus of variations, and the position of base points or base line of each method being relaitive to the geodesic line on the curved shell surface, are compared with the correct position of them on the developed plane, then the accuracy of each method is known.
And the author analysed the question of back-sets and the roll line of the shell plate by differential geometry.
After all, it was verified that the geodesic line method had the best accuracy in practice.