Deflection of thin circular elastic plates under symmetrically distributed loading

Abstract

A spec ial application of Bassali's so lution for tran s ve rs e fl e xure of thin elastic plates supported at se ve ra l point s is prese nted for the case of co nce ntric sy mm e trica lly di s tributed load. Equations for d efl ectio n are prese nted for the ca se where the point supports lie within the load ed area. Unde r special co ndition s the num e rica l res ults fro m these equation s co inc id e with tho se of Nadai's. Key Word s: Ba ssa li' s theo ry, d e fl ec tio n, ela stic ity , fl exure , point s upports, symm e tri ca lly di s· tribute d load, thin plates. 1. Introduction Previous work [l] I dealt with the de Aection of centrally loaded thin circ ular elasti c plates on equally spaced point s upports in whi c h th e s upports we re lo cated along a co nce ntri c circl e out-side of the central loaded area. A sequ el to this pre vious work is presented in thi s paper whe re th e case in which the point supports lie within the loaded area is considered. Theoretical work give n by Bassali [2] is specialized to develop expressions for deAection which consider the sym metrically distributed load in general and the uniformly distributed load in particular. Previou s experimental res ults [l, 3] have bee n shown to be in good agree me nt with the results of other specialized treatm e nts of Bass ali's th eory for plates having thicknesses to span radii ratios up to 0.08 with s pa n radii to plate radii ratio s as s mall as 0.63. Even thou~h no experim e ntal res ults are presented in thi s pape r, no lesser agreement between experimental and th eore tical results s hould be expected for th e case considered he rein. x, y rectangular Cartesian coordinates