The Method to Determine Airy's Stress Function by Bending of Plate

Abstract

When the moments are given to a thin plate along its boundaries, the deflection function is biharmonic. And, if the boundary conditions of the plate are mathematically similar to those to be satisfied by Airy's stress function, we can find the Airy's stress function as the deflection of the plate. We make use of this mathematical similarity as a mean for experimental stress analysis. For this purpose we have to prepare an elastic plate satisfying the several necessary conditions and to device a method by which the deflection can be measured precisely. We made an experiment with several kinds of plates and concluded that the glass plate is the most suitable. We tried to measure the deflection, the first and the second derivative of the plate surface by various methods, and we found that the roughness meter may by used for measuring the deflection with high accuracy. Using the glass plate and the roughness meter, we analysed the stress distribution in plates having notches or fillets.