Optimal location of ring support for heavy Mindlin plates under axisymmetric loading

Abstract

Bending of an annular thick plate resting on a ring support is analyzed under the action of power-law axisymmetric loading. A single governing differential equation for the Mindlin plate theory is derived. By solving associated boundary value problem, the optimal support location is determined to achieve minimizing the maximum deflection of a moderately thick circular or annular plate. The minimum sag of a heavy solid circular plate with or without the center support under self-weight is also analyzed. In addition to applied loading and the restraint of plate's rims, the optimal location of the ring support is also related to Poisson's ratio and the ratio of inner-to-outer radius. Auxetic plates with negative Poisson's ratio require larger ring support's radius, and conventional plates require smaller ring support's radius. Usually, the optimal support location is closer to the outer rim and far to the inner rim for a plate of self-weight. The obtained results are useful in safety design of circular or annular plates under complicated loading.