Efficient large deflection analysis of rectangular plates with general transverse form of displacement

Thin, elastic, rectangular plates are analysed. Each plate has symmetry abo ut the transverse centre line, but the transverse form of displacement can take any form, depending on the degree of support (if any) along each longi tudinal edge, and on the manner of loading. Classical plate theory is used (Love-Kirchhoff hypothesis), and large deflections compared to the thicknes s are accommodated. The lateral displacement is expressed as a series, each term of which involves the product of a sinusoidal term in the longitudina l direction, and a polynomial term in the transverse direction. The von Kar man/Marguerre compatibility equation is satisfied, and equilibrium found at each load stage by directly minimising the total potential energy. The met hod is presented, and is then used to analyse a wide variety of different p late types. The method is shown to be very efficient, and accurate, by comp arison with previous work. The results clearly show the subtle variations i n transverse form of displacement for the various examples considered. (C) 1999 Elsevier Science Ltd. All rights reserved.