A Singularity Approach to Circular Plates

Abstract

Axisymmetric circular plate solutions can be found in several references. A designer, in using the classical technique must, for the most part, consider loading functions not continuous over the plate, as would occur in ring supported structures, thus requiring a great deal of continuity matching. Attempts have been made to reduce the amount of tedious algebra required to match deflections, etc., by developing influence coefficients. Paul and associates recently presented a computer oriented approach, referred to as the integral method that further reduces the solution effort for discontinuous loadings. The authors observed that in all cases some form of indirect superposition must be incorporated. The present paper reviews a method for integrating the fourth-order plate equation in which each load function is represented by a singularity expression. In addition, discussion and comparisons are made with the previously mentioned techniques. Finally, application of the singularity function approach is directed toward complex loading conditions.