点加熱による矩形板の収縮の簡易計算方法(第1報)

抄録

In the previous report, a method was proposed to exactly analyse shrinkage distortion due to spot heating on a rectangular plate. However, it was necessary to solve a set of infinite simultaneous equations for every aspect ratio of the plate and for every location of heated point. As this is rather inconvenient to perform, the authors sought for some methods for approximate analyses.
Analytical expression for the displacement due to a shrinkage source in an infinitely long straight zone should give good approximation when the aspect ratio of a rectangular plate exceeds a certain value. It was shown that the effect of the length diminishes quite rapidly. This leads to the conclusion that the shrinkages chiefly depend on the breadth of the plate, while the length has little effect on them.
It may be reasoned that the effect of the edges further away from heated point can be neglected if the heat is applied on a point in the vicinity of an edge or a corner of the plate. Then the principle of reflection may be taken to simplify the problem. In fact, the formulae have been substantially simplified.
The results obtained through the above analyses would contribute to the derivation of simple approximate formulae.