BENDING OF AN ELASTIC RECTANGULAR CLAMPED PLATE - EXACT VERSUS ENGINEERING SOLUTIONS

This paper addresses the fascinating long history of the classical pro blem of bending of a thin rectangular elastic plate with clamped edges by uniform pressure. Among various mathematical and engineering appro aches, a method of superposition proposed by Lame (1852, 1859) and Mat hieu (1881, 1890) and developed by the mathematician Koialovich (1902) and engineers Boobnoff (1902, 1914), Hencky (1913) and Inglis (1925) appears to be very useful for the analysis of distribution of stresses and deflection inside a plate. The object of this paper is both to cl arify some purely mathematical questions connected with the solution o f the infinite systems of linear algebraic equations and to provide a considerable simplification of the numerical algorithm.