ANALYSIS OF BENDING OF A SECTOR PLATE OF VARIABLE THICKNESS, CLAMPED ALONG A PORTION OF ITS ARCUATE EDGE, UTILIZING A HIGH-SPEED COMPUTER,

摘要

Making the usual assumptions for a thin plate, a plate of variable thickness is assumed to be subjected to a distributed load,to be clamped along a portion of its arcuate edge,and to be free over the remainder of the arcuate edge. The potential energy of the bent plate is expressed in polar coordinates,and a set of equations is derived in terms of the local thickness and pressure. Three sets of functions have to be solved,and the methods employed were specifically adapted for use with the computer 'Strela'. The subprogramme of differentiation was framed in terms of powers of polynomials,which led to exact solutions. Since it is convenient to express the thickness of the plate and its loading in the form of a Table,the programme included approximate integration over the area of the plate utilizing R. Cotes'formula. To obtain an adequate accuracy of integration, a sufficiently fine grid was drawn by dividing each of the three sections of the plate radially into ten equal parts. By proving that certain terms are equal to zero the computer time was significantly reduced. (Author)