The Bending Stress in a Cracked Plate on an Elastic Foundation

is much more complicated and leads to slowly convergent or even divergent expressions for the stress resultants. 2 The circular support's action on the plate is equivalent to a line load, and so the discontinuity in the elastic constants certainly make the deflection function singular at r = a. This is reflected in the fact that two different expressions are needed to describe the deflection function in the region 0 < r < 03 , and that the functions wi and w2 are not analytic continuations of each other across r = a, even for the uniform plate. 3 The second equation following (S) is only intended to indicate one convenient way for obtaining Vhv*. If x,y; X\,yi; and x-i,y-2 are coordinate systems in the plane with different origins, and V2 , V r , and V22 denote Laplace's operators in these coordinate systems, it is clear that