Plate Bending Problems

Abstract

One of the earliest and most productive applications of linear elasticity theory has been the analysis of small bending deformations of thin plates by transverse load. The problem is traditionally posed as a boundary value problem over the plane region occupied by the plate’s middle surface:--to find the deflection function whose bilaplacian is proportional * to the transverse load intensity, and for which, along the boundary of the plate, the function and certain particular combinations of derivatives satisfy conditions imposed by the plate’s supports. This problem can also be reformulated in terms of Boundary Integral Equations in a number of different ways- each with its own set of advantages and liabilities. We will single out one such method, the so called direct method, and explore in detail some considerations which arise here because of the essential fourth order nature of the underlying boundary value problem. The treatment follows Stern, 1979 and 1983. Similar treatments via the direct method are given by Bezine, 1978 and Hartmann, 1982. A brief review of other methods can be found in Tottenham, 1979.