A DISC SUBJECTED TO AN ODD NUMBER OF COMPRESSIVE LOADS ON ITS PERIPHERY

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  • 周邊に奇数個の壓縮力を受くる圓板

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The stress components are found by means of stress functions that must satisfy the differential equation ▽_1^4x=0 and the boundary conditions, when a disk is subjected to many equal radial compressive loads at equal pitches on its periphery. The contents of the paper are divided into the following four cases accordlog to the number of applied loads : -(I) Two loads ; (II) Any even number of loads ; (III) Three loads ; (IV) Any odd number of loads. Let x_0. be the stress function that cancels the surface stress components calculated from stress functions x_1,x_2,x_3,......etc due to applied loads, P, the applied load, d the diameter of the disk, and h, the thickness of the disk. Then we have the required stress function x for the four cases mentioned above as follows. (I)x_0 is [numerical formula]・r^2,and x=x_1+x_2+x_3. (II)In this case the problem is solved by the princple of superpositon using the solution obtained in (In). (III)x_0 is [numerical formula], and x=x_1+x_2+x_3+x_0. (IV)The number of loads is q+1,if q is even.x_0 is [numerical formula]・r^2,and x=x_1+x_2+x_3+......+x_q+x_<q+1>+x_0.

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