Compressive Buckling of a Long Simply Supported Plate on an Elastic Foundation

TLDR: In this article, the authors define a deflection function for a given width of a plate and a fraction of half-buckle wavelength representing the length of the region of the plate in which the foundation is compressed.

Abstract: A, B = constants appearing in deflection functions b = width of plate c = fraction of half-buckle wavelength representing length of region of plate in which the foundation is compressed D = flexural stiffness of plate [D = Et*/12(1 v)} E = Young's modulus of plate material F(x) = function representing variation in ^-direction of the plate deflection k = buckling load coefficient (k = bN/wD) k = foundation modulus N = critical compressive load per inch of plate width t = plate thickness w = plate deflection x = distance along plate longitudinal axis [see Fig. 1(b)] y = distance along width of plate 7 = foundation modulus parameter (7 = bk/irD) V^ = (d/dx) + 2(d/dxdy) + ( d 4 / ^ 4 ) X = ' half-wavelength of buckle v = Poisson's ratio