Physics
Scientific paper
Nov 1965
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1965rspsa.288..371q&link_type=abstract
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Volume 288, Issue 1414, pp. 371-395
Physics
Scientific paper
A comprehensive method is presented for the numerical solution of the rectangular plate problem under a wide range of loadings and boundary conditions. A particular integral is obtained as a double Fourier sine series, which is the complete solution when the plate is simply supported with all edges in the same horizontal plane. This is summed to a highly convergent single series of negative exponentials in the plate variables U_2. The necessary calculus for differentiation and integration is established, from which the particular slopes, moments and shears follow whether for concentrated or line loads or loads distributed uniformly over polygonal regions. By treating a concentrated moment as a force-pair, this case is deduced from that for a concentrated load. The necessary complementary functions and the ensuing simultaneous equations are formulated in a manner suited to programming for an electronic computer. A master program for rectangular plates has been developed in Mercury Autocode at the University of Sheffield. An illustrative example is included of a concentrated moment acting on a fully fixed rectangular plate.
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