Minimal Design of Sandwich Axisymmetric Plates II

Using the statical method, minimum volume designs are determined of annular axisymmetric sandwich plates obeying the Tresca criterion which carry one-directional loads and are either supported or clamped at the edges; the full plate supported at the center is obtained as a limiting case. Circular plates supported on more than one circle, described as indefinite, pose more difficulties than the definite (which are supported on one circle only) and have not been treated before in the technical literature. The particular class of indefinite plates considered has the characteristic of monotonically varying shear force. For this class the location of the inflection circles, at which the moments vanish, and of the regime circles, at which the relation of the moments changes from M_r = M_θ to Mθ = 0; M_r = arbitrary, or vice versa, is independent of the specific load applied. Their radii are given for the whole range of the ratio a/b of the inner to the outer radius of the plate so that applications to any particular geometry and load are reduced to routine calculations. Such applications are illustrated in concrete examples.