抄録
The problem may be solved easily by using the bipolar coordinates. The solutions which satisfy ▽^4ω=0 in our coordinates are [numerical formula]. The boundary conditions are (1) When we sum up the vertical shearing force N along any vertical cylindrical surface which include the single load P within it, we have ∫Nds=P (2) For a fixed plate, we have at the edge η=η_o, ω=0 and [numerical formula] (3) For a supported plate, we have at the edge η=η_o, ω=0 and G=0,G being a flexural couple. (4) At the pole η=∞, coshη and sinhη will be also infinitely large, the condition that ω shall be finite at the pole is satisfied by B'=-Λ' For the case of fixed boundary, we may take ω_2 only as the form of the deflection, but for supported edge, we must use ω_2 together with ω_1 and therefore the solution will extend to infinite series, but according to the properties of rapid convergency, a few of the lowest terms will be sufficient for practical purpose. For both cases, the deflection at the pole and the normal stress ηη on the centre line for various values of eccentricity e will be illustrated and tabulated.
